US 2015O1393 02A9 (19) (12) (54) United States (10) Pub. No.: US 2015/0139302 A9 (48) Pub. Date: May 21, 2015 Patent Application Publication JOSET et al. METHOD AND APPARATUS FOR SIGNAL ENCOOING REALIZING OPTIMIAL FIDELITY (71) Applicant: ECOLE DETECHNOLOGIE SUPERIEURE, MONTREAL (CA) (72) Inventors: Didier JOSET, Rannee (FR): Stéphane COULOMBE, Brossard (CA); Maged E. BESHAI, Maberly (CA) (73) Assignee: ECOLE DETECHNOLOGIE SUPERIEURE, MONTREAL (CA) (21) Appl. No.: 14/217,007 (22) Filed: (60) Provisional application No. 61/802,782, filed on Mar. 18, 2013. (30) Foreign Application Priority Data Mar. 18, 2013 (CA) ...................................... 2809731 Publication Classification (51) Int. Cl. H04N 9/34 H04N 9/24 Prior Publication Data (15) Correction of US 2014/0269907 A1 Sep. 18, 2014 See Claim 13. Sep. 18, 2014 Related U.S. Application Data (63) Continuation-in-part of application No. 14/188,537, filed on Feb. 24, 2014, now abandoned, Continuation in-part of application No. 14/192,682, filed on Feb. 27. 2014, now abandoned. 130 Network (2006.01) (2006.01) (52) U.S. Cl. CPC. H04N 19/001.33 (2013.01); H04N 19/0009 (2013.01) (57) Mar 17, 2014 (65) US 2014/O269907 A1 CORRECTED PUBLICATION ABSTRACT Methods of optimal encoding of signals to be compatible with characteristics of target receivers while meeting constraints pertinent to sizes of encoded signals or capacities of paths communicating signals to the target receivers are disclosed. The methods are based on analytical modeling of the encod ing process guided by experimental data relating measured performance indicators of encoded signals of diverse classi fications to respective encoding parameters. A computation ally-efficient technique is devised to determine optimal encoding parameters based on pre-processed data derived from the analytical models. The methods may be imple mented at an encoder of original signals or a transcoder of pre-encoded signals. 160-a Inform ation Receiving sink node 112 Information SOCC 120 Signal adaptation 114 Encoder node Information sink 160-b Receiving node 110 Originating node Receiver Patent Application Publication May 21, 2015 Sheet 1 of 31 Ieu?IS uo?eJ I 30IT OS uolgendp apou US 2015/O139302 A9 Patent Application Publication May 21, 2015 Sheet 2 of 31 US 2015/O139302 A9 ----- - JOS0I& 037 -- - - Patent Application Publication May 21, 2015 Sheet 3 of 31 JOS0I& US 2015/O139302 A9 Patent Application Publication May 21, 2015 Sheet 4 of 31 JOS01& US 2015/O139302 A9 Patent Application Publication US 2015/O139302 A9 Patent Application Publication OF9 May 21, 2015 Sheet 6 of 31 US 2015/O139302 A9 Patent Application Publication May 21, 2015 Sheet 7 of 31 US 2015/O139302 A9 OFL Z'{DICH Patent Application Publication 093 US 2015/O139302 A9 Patent Application Publication May 21, 2015 Sheet 9 of 31 US 2015/O139302 A9 OF6 056 076 OT6 H I. 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US 2015/O139302 A9 May 21, 2015 US 2015/O 1393O2 A9 METHOD AND APPARATUS FOR SIGNAL ENCOOING REALIZING OPTIMIAL FIDELITY CROSS-REFERENCE TO RELATED APPLICATIONS 0001. This application is a continuation in part of U.S. patent application Ser. No. 14/188,537 and U.S. patent appli cation Ser. No. 14/192,682, the entire contents of which are incorporated herein by reference. The application claims the benefit of provisional application 6 1/802.782, filed on Mar. 18, 2013, the content of which is incorporated herein by reference in its entirety. The application also claims priority to Canadian Application 2,809.731, filed on Mar. 18, 2013, the content of which is incorporated herein by reference in its entirety. FIELD OF THE INVENTION 0002 The present invention relates to signal encoding and transcoding in a multimedia system. In particular, the inven tion is directed to methods and apparatus for realizing opti mum encoding or transcoding. BACKGROUND 0003. Multimedia Messaging Services (MMS) allow users with heterogeneous terminals to exchange structured messages composed of text, audio, images, and video. The rapid development of the mobile-communications technol ogy contributes to the rapid proliferation of mobile terminals of different types, thus creating interoperability problems. Consequently, signals may need adaptations to be compatible with target terminal's characteristics while maximizing visual quality. Such problems also arise in video streaming where content needs to be adapted to Support various termi nals operating over numerous wired and wireless networks. 0004. There is a need to develop signal adaptation tech niques which optimize performance while taking into account constraints relevant to encoding as well as constraints relevant to storage and transfer of encoded signals. SUMMARY 0005. The application discloses methods and apparatus for determining encoding parameters of an encoder or a transcoder which yield an encoded signal of optimal measur able properties, with emphasis on video-signal components of multimedia data streams. For a video signal, the encoding parameters may include quantization granularity, a measure of display resolution, and a frame rate. The measurable prop erties of an encoded signal may include a fidelity index, a relative size, and a relative flow rate (bitrate). Several options of applying the teaching of the present application may be considered. 0006. In one implementation, it may be desirable to deter mine encoding parameters which result in an encoded signal of the highest attainable fidelity index while observing either a constraint pertinent to the size of the produced encoded signal, a constraint pertinent to the flow rate, or constraints pertinent to both the size and flow rate. 0007. In another implementation, it may be desirable to determine encoding parameters which result in an encoded signal of the least size while observing either a requisite lower bound of a fidelity index, a constraint pertinent to the flow rate, or both constraints pertinent to fidelity and flow rate. 0008. In a further implementation, it may be desirable to determine encoding parameters which result in an encoded signal of the least flow rate while observing either a requisite lower bound of a fidelity index, a constraint pertinent to size, or both constraints pertinent to fidelity and size of an encoded signal. 0009. The method of the invention relies on acquiring reference data records each quantifying properties of a sample signal encoded according to one of experimental sets of encoding parameters. For example, the fidelity index may be based on human perception, using a mean opinion score. The acquired reference data records are used to define param eters (constants) of conjectured analytical functions charac terizing the encoding or transcoding functions. Predictive regression-analysis techniques are used to determine param eters (constants) of the analytical functions resulting in a minimum value of a positive-definite function of deviation of predicted values from reference values. The analytical func tions are then used to generate Granular tables of estimated measures of encoded-signal properties. 0010 Three analytical functions are considered for quan tifying the properties of encoded signals. A first analytical function relates a fidelity index to the encoding parameters. A second analytical function relates a relative size of an encoded signal to the encoding parameters. The relative size is the ratio of a size determined for an arbitrary set of encod ing parameters to the size corresponding to the boundary set of encoding parameters which corresponds to the finest quan tization granularity, the finest display resolution, and the highest frame rate. A third analytical function relates a rela tive flow rate of an encoded signal to the encoding param eters. The relative flow rate is the ratio of a flow determined for an arbitrary set of encoding parameters to the flow rate corresponding to the boundary set of encoding parameters. 0011. The invention provides a fast search mechanism which uses the granular tables, together with sorted arrange ments of the granular tables, to determine preferred encoding parameters for multimedia data streams received at an encoder or a transcoder. Determining the preferred encoding parameters need be computationally efficient to be suitable for real-time implementation. 0012. In accordance with one aspect, the present invention provides a method, implemented in an encoder having a pro cessor assembly and memory devices for storing data and processor-executable instructions. The method starts with determining descriptors of a received signal, identifying a destination of the received signal, and acquiring characteris tics of the destination receiver. The characteristics may include limitations relevant to quantization, display resolu tion, and/or frame rate. A preferred set of encoding param eters compatible with the descriptors and the receiver char acteristics is selected for encoding the received signal to produce an encoded signal of a requisite fidelity index. The preferred set of encoding parameters is then submitted to the encoder. 0013 The received signal is generally a multimedia signal having components of different types such as a video signal, an audio signal, images, and texts. Considering the video signal, the set of encoding parameters considered herein includes a quantization step, a display resolution, and a frame rate. 0014. In order to facilitate accurate and fast computation and to gain an opportunity to produce an optimally encoded signal, a large number of reference data records would be US 2015/O 1393O2 A9 needed. The reference data records are, however, determined on the basis of actual experimentation and producing a suffi ciently large number of such records would be quite costly. A viable alternative, according to the present invention is to generate analytical expressions characterizing the encoding or transcoding process based on a relatively small number of experimentally determined reference data records. 0015 Thus, according to one embodiment, two analytical functions are formulated. The first quantifies dependence of a fidelity index of the encoded signal on encoding parameters including the quantization step, the display resolution, and the frame rate and the second quantifies dependence of a relative size of the second signal on the same encoding parameters. 0016. A number of reference data records is acquired, with each reference data record indicating a fidelity index and a relative signal size corresponding to a respective set of experi mental encoding parameters. Regression analysis is then applied to define parameters of the two analytical functions. 0017. It is plausible that the effects of the encoding param eters of quantization, resolution, and frame rate be mutually uncorrelated. This valuable property may be exploited to simplify the synthesis of the analytical functions. A method of separation of variables, well known in the art of applied mathematics, may be applied to express each of the analytical functions as a multiplication of a respective one-dimensional function of quantization step, a respective one-dimensional function of display resolution, and a respective one-dimen sional function of frame rate. 0018. A first granular table is generated, based on the first analytical function, to indicate fidelity indices corresponding to a relatively large number of sets of encoding parameters. Likewise, second granular table is generated, based on the second analytical function, to indicate relative file sizes (nor malized file sizes) corresponding to a relatively large number of sets of encoding parameters. 0019. An exhaustive search approach may be adopted according to which each set of encoding parameters consid ered in generating the granular tables is examined to deter mine compatibility with characteristics setting boundaries of encoding parameters acceptable to a target receiver. For each set of compatible encoding parameters, corresponding entry of the first granular table and a corresponding entry of the second granular table are examined. 0020. In one implementation, a requisite fidelity index is a constraint and a least file size is an objective. In this case, the entry of the first granular table is examined to determine its compatibility with the objective value. If the entry indicates a fidelity indeX larger than, or equal to, the objective, the cor responding set of encoding parameter is a candidate and is retained together with the entry of the first granular table and the entry of the second granular table. The process is repeated for each encoding parameter and the set of encoding param eters corresponding to the least value of normalized encoded signal size is selected as a preferred set. 0021. In another implementation, a requisite upper bound of encoded-signal size is a constraint and a highest fidelity index is an objective. In this case, the entry of the second granular table is examined to determine its compatibility with the objective size. If the entry indicates a normalized size less than, or equal to, the objective, the corresponding set of encoding parameter is a candidate and is retained together with the entry of the first granular table and the entry of the second granular table. The process is repeated for each encod May 21, 2015 ing parameter and the set of encoding parameters correspond ing to the highest value of the fidelity index is selected as a preferred set. 0022 Exhaustive search is suitable for granular tables generated for a relatively small number, such as 100, of sets of encoding parameters. However, for encoders or transcoders devised for high performance, where a granular table may have a significantly larger number of entries, exhaustive search may not be suitable for real-time applications. 0023. In an alternative search method according to the present invention, the first granular table is sorted in an ascending order of fidelity indices to produce a sorted table. Conventional bisecting search is then applied to determine a first entry of the sorted table corresponding to a fidelity index nearest to and not less than a requisite fidelity index. Each entry of the sorted table succeeding the first entry has a fidelity index larger than, or equal to, the requisite fidelity index. Thus, sets of encoding parameters corresponding to the first entry and Succeeding entries, which are also compatible with the characteristics of the target receiver, are candidate sets. A number of Successive candidate sets may be selected and corresponding relative signal sizes of the second table may be examined to select a preferred set of encoding param eter as one of the candidate set of encoding parameters cor responding to a least relative signal size. 0024. The second granular table may be based on the third analytical function, to indicate relative flow rates (normalized flow rates) corresponding to a relatively large number of sets of encoding parameters. The processes described above for determining the least encoded-signal size may be applied mutatis mutandis with the normalized encoded-signal sizes replaced with normalized flow rates in order to determine a preferred set of encoding parameters which yield the least flow rate given an objective fidelity index. 0025. In accordance with another aspect, the present invention provides a method implemented in an encoderhav ing a processor for determining optimal encoding parameters under a constraint of a permissible flow rate over a path from the encoder to a target receiver. A received signal is analysed to determine descriptors such as classification with respect to temporal rate of variation. Characteristics of the target receiver are then acquired either through communication with the receiver or through consulting a database maintaining information relevant to receiver types. 0026. A preferred set of encoding parameters compatible with the descriptors of the received signal and the receiver characteristics is determined for encoding the received signal to produce an encoded signal of a requisite fidelity index while observing the permissible flow rate. 0027. In accordance with a further aspect, the present invention provides an apparatus for signal encoding compris ing at least one processor and multiple memory devices for storing reference data records, produced granular tables, and processor-executable instructions. 0028 Reference data records, each indicating a fidelity index and a relative signal size corresponding to one of a collection of experimental sets of encoding parameters are stored in a memory device coupled to a processor. 0029. The processor-executable instructions may be stored in multiple more memory devices. The instructions may be organized into modules. A first module may be devised to define a first analytical model for determining fidelity indices and a second analytical model for determining relative signal sizes based on the reference data records. A US 2015/O 1393O2 A9 second module may be devised to generate two tables of fidelity indices and relative signal sizes corresponding to a number of sets of encoding parameters exceeding a number of the reference data records. A third module may be devised to determine characteristics of a target receiver of a video recording. A fourth module may be devised to examine the granular tables and the corresponding data structures to iden tify a set of encoding parameters compatible with the char acteristics of the target receiver and corresponding to a least relative signal size at a fidelity index at least equal to a speci fied lower bound. 0030 The processor-executable instructions further include a module for rearranging and Sorting the contents of the tables into respective data structures and implementing bisecting search to identify entries of requisite values. 0031. The apparatus includes a network interface for receiving signals to be encoded or transcoded and for acquir ing the reference data records, where each reference data record indicates a fidelity index and a relative signal size corresponding to a respective set of encoding parameters. 0032. The processor-executable instructions further include a module for determining a permissible flow rate over a path from the apparatus to the target receiver. 0033. The processor-executable instructions further include a module implementing a predictive regression method for determining parameters defining the first analyti cal model and the second analytical model. 0034. In accordance with a further aspect, the present invention provides a method, implemented in an encoder having a processor. The method comprises determining descriptors of a first signal to be transcoded, and acquiring characteristics of a target receiver of the transcoded signal. A preferred set of encoding parameters compatible with the descriptors and the characteristics of the receiver is selected for encoding the first signal to produce a second signal of a file size not exceeding a specified upper bound. The first signal is encoded according to the preferred set of encoding param eters. 0035. Where the first signal is a video signal, the set of encoding parameters comprises a quantization step, a display resolution, and a frame rate. A first number of reference data records is acquired, each reference data record indicating file size corresponding to a respective set of encoding parameters and a table indicating file sizes corresponding to a relatively large number of sets of encoding parameters is generated. The table may be based on an analytical function relating file size to encoding parameters. The table may be examined to iden tify at least one set of encoding parameters compatible with the receiver characteristics and corresponding to a file size not exceeding the specified maximum file size. 0036. According to one embodiment, a first granular table relating fidelity indices to encoding parameters and a second granular table indicating file sizes corresponding to the encoding parameters may be generated based on synthesized analytical functions. The second table may be examined to identify candidate sets of encoding parameters each corre sponding to a file size not exceeding the specified maximum file size and compatible with the receiver characteristics. The first table is then examined to determine fidelity indices cor responding to the candidate encoding parameters. The candi date set of encoding parameters corresponding to a highest fidelity index is then selected for encoding the first signal. 0037. The second table may be sorted in an ascending order of file sizes to produce a sorted table and bisecting May 21, 2015 search may be applied to determine a first entry of the sorted table corresponding to a file size nearest to and not exceeding the specified maximum file size. Consecutive entries of the sorted table may be examined, starting with the first entry, to select an entry corresponding to the highest fidelity index. 0038. In accordance with a further aspect, the invention provides a method implemented in a transcoder having a processor for transcoding a first signal to produce a second signal of different encoding parameters. The method com prises determining descriptors of the first signal, acquiring characteristics of a receiver, and determining a permissible flow rate over a path from the encoder to the receiver. A preferred set of encoding parameters compatible with the first-signal descriptors and the receiver characteristics is selected for encoding the first signal to produce the second signal taking into account the permissible flow rate of the second signal. The first signal is encoded according to the selected encoding parameters. 0039. Where the first signal is a video signal, the set of encoding parameters comprises a quantization step, a display resolution, and a frame rate. Predetermined data records, each indicating a flow rate corresponding to one of a collection of sets of encoding parameters, are acquired and used to identify candidate data records each corresponding to a flow rate not exceeding the permissible flow rate. The candidate data records correspond to a set of encoding parameters compat ible with the signal descriptors and the characteristics of the receiver. The candidate data record corresponding to the high est fidelity index is selected. 0040. The method further comprises generating a first table, based on a first analytical function indicating fidelity indices corresponding to a preselected number of sets of encoding parameters, and a second table, based on a second analytical function, indicating relative flow rates correspond ing to the preselected number of sets of encoding parameters. 0041. The second table may be examined to identify can didate sets of encoding parameters compatible with the receiver characteristics and corresponding to a flow rate not exceeding the permissible flow rate. The first table is exam ined to determine fidelity indices corresponding to the can didate encoding parameters. A preferred set of encoding parameters is determined as one of the candidate sets of encoding parameters having a highest fidelity index. 0042 Preferably, the second table is sorted in either an ascending or a descending order of relative flow rates to produce a sorted table. Conventional bisecting search may then be used to determine a first entry of the sorted table corresponding to a relative flow rate nearest to and not exceeding the permissible flow rate. Entries of the sorted table adjacent to the first entry may be examined to select more candidate sets of encoding parameters. Where more than one candidate set is found, the first table is examined to determine fidelity indices corresponding to the candidate sets of encod ing parameters and determine a preferred set of encoding parameters as one of the candidate sets of encoding param eters corresponding to a highest fidelity index. 0043. In accordance with a further aspect, the present invention provides an apparatus for signal encoding compris ing a processor and at least one memory device. The memory devices store data records as well as processor-executable instructions. Reference data records, each indicating a fidelity index and a file size corresponding to one of a collection of sets of encoding parameters, are stored in a memory device. Other memory devices store processor-executable instruc May 21, 2015 US 2015/O 1393O2 A9 tions devised to define a first analytical model for determining fidelity indices and a second analytical model for determining file sizes based on the reference data records. Two tables of fidelity indices and file sizes corresponding to a relatively large number of sets of encoding parameters, exceeding a number of the reference data records, are generated and stored in one of the memory devices. A module of processor executable instructions is devised to cause the processor to examine the tables to identify a set of encoding parameters compatible with the desired characteristics and correspond ing to a highest fidelity index and a file size not exceeding a specified upper bound. BRIEF DESCRIPTION OF THE DRAWINGS 0044) Embodiments of the present invention will be fur ther described with reference to the accompanying exemplary drawings, in which: 0045 FIG. 1 illustrates a communications system imple menting the method of the invention; 0046 FIG. 2 illustrates an apparatus for encoding or transcoding signals to produce encoded signals of specified properties, in accordance with an embodiment of the present invention; 0047 FIG. 3 illustrates an apparatus for pre-processing data to expedite real-time execution of the methods of the invention; 0048 FIG. 4 illustrates an apparatus for determining video signal descriptors, receiving node characteristics, and capac ity of a path from the apparatus to a receiving node, in accor dance with an embodiment of the present invention; 0049 FIG. 5 illustrates an apparatus for encoding or transcoding signals to produce encoded signals of specified properties, employing outputs of the apparatus of FIG.3 and FIG. 4, in accordance with an embodiment of the present invention; 0050 FIG. 6 illustrates a method of generating param etrized functions for determining properties of encoded sig nals corresponding to arbitrary values of encoding param eters, in accordance with an embodiment of the present invention; 0051 FIG. 7 illustrates a first analytical description of a first encoded-signal property as a function of encoding parameters, in accordance with an embodiment of the present invention; 0052 FIG. 8 illustrates a second analytical description of a second encoded-signal property as a function of encoding parameters, in accordance with an embodiment of the present invention; 0053 FIG. 9 illustrates a third analytical description of a third encoded-signal property as a function of encoding parameters, in accordance with an embodiment of the present invention; 0054 FIG. 10 illustrates generating granular tables of fidelity indices, files sizes, and flow rates for a predefined set of encoding parameters, for use in an embodiment of the present invention; 0055 FIG. 11 illustrates a process of determining a set of encoding parameters yielding a maximum fidelity index con strained by an upper bound of encoded-signal size and/or an upper bound of flow rate of an encoded signal, in accordance with an embodiment of the present invention; 0056 FIG. 12 illustrates a process of determining a set of encoding parameters yielding a minimum file size con strained by a lower bound of encoded-signal fidelity index and/or an upper bound of flow rate of an encoded signal, in accordance with an embodiment of the present invention; 0057 FIG. 13 illustrates a process of determining a set of encoding parameters yielding a minimum flow rate con strained by a lower bound of encoded-signal fidelity index and/or an upper bound of size of an encoded signal, in accor dance with an embodiment of the present invention; 0.058 FIG. 14 illustrates schemes for determining encod ing parameters for different objectives under corresponding constraints, in accordance with an embodiment of the present invention; 0059 FIG. 15 illustrates a method of determining encod ing parameters yielding a minimal file size at a specified minimum fidelity index, in accordance with an embodiment of the present invention; 0060 FIG. 16 illustrates a method of determining encod ing parameters yielding a highest fidelity index at a specified maximum file size, in accordance with an embodiment of the present invention; 0061 FIG. 17 illustrates a bisection process for locating optimal encoding parameters within data structures generated by the pre-processing apparatus of FIG. 3; 0062 FIG. 18 illustrates a first objective of encoding a received signal to produce an encoded signal having a highest fidelity indexata specified maximum flow rate, in accordance with an embodiment of the present invention; 0063 FIG. 19 illustrates a second objective of encoding a received signal to produce an encoded signal having a highest fidelity index at a specified maximum file size, in accordance with an embodiment of the present invention; 0064 FIG. 20 illustrates a third objective of encoding a received signal to produce an encoded signal having a mini mal flow rate at a specified minimum fidelity index, in accor dance with an embodiment of the present invention; 0065 FIG. 21 illustrates a fourth objective of encoding a received signal to produce an encoded signal having a mini mal file size at a specified minimum fidelity index, in accor dance with an embodiment of the present invention; 0.066 FIG. 22 illustrates a method of determining a set of encoding parameters for encoding a specific signal to yield an encoded signal having a flow rate not exceeding a specified limit with a highest fidelity of the encoded signal while observing limitations of a receiving node, in accordance with an embodiment of the present invention; 0067 FIG. 23 illustrates a method of determining a set of encoding parameters for encoding a specific signal to yield an encoded signal having a file size not exceeding a specified limit with a highest fidelity of the encoded signal while observing limitations of a receiving node, in accordance with an embodiment of the present invention; 0068 FIG. 24 illustrates a method of determining a set of encoding parameters for encoding a specific signal to yield an encoded signal having a fidelity index of a specified lower bound with a minimum flow rate of the encoded signal while observing limitations of a receiving node, in accordance with an embodiment of the present invention; 0069 FIG. 25 illustrates a method of determining a set of encoding parameters for encoding a specific signal to yield an encoded signal having a fidelity index of a specified lower bound with a minimum size of the encoded signal while observing limitations of a receiving node, in accordance with an embodiment of the present invention; 0070 FIG. 26 illustrates exemplary parameter sets, for use in an embodiment of the present invention; May 21, 2015 US 2015/O 1393O2 A9 (0071 FIG. 27 illustrates a table indicating fidelity indices for each of the parameter sets of FIG. 26, for use in an embodiment of the present invention; 0072 FIG. 28 illustrates a table indicating file sizes for each of the parameter sets of FIG. 26, for use in an embodi ment of the present invention; 0073 FIG. 29 illustrates an implementation of the encod ing scheme of FIG. 19 and FIG. 23; 0074 FIG. 30 illustrates an implementation of the encod ing scheme of FIG. 21 and FIG. 25; and 0075 FIG.31 illustrates optimal encoding schemes based on the methods of the present invention. TERMINOLOGY 0076 Signal: A data stream occupying a time window is herein referenced as a “signal'. The duration of the time window may vary from a few microseconds to several hours. 0077. Encoding parameters: Encoding a signal produced by a signal Source into a digital encoded format entails select ing several parameters to represent the signal in the encoded format. The encoding process entails two Successive stages: signal representation modification and signal compression. In the first stage, the signals representation is modified if it is required or desired. In the second, the resulting signal is compressed to reduce its size orbitrate. The parameters used in the first stage are called signal representation parameters while the ones used in the second stage are called compres sion parameters. Together, they form the encoding param eters. The signal representation parameters affect the signals intrinsic characteristics before compression Such as sampling rate for audio or display resolution and frame rate for video. The compression parameters affect how the compression stage is performed and include the quantization step. A video signal is encoded in a format Suitable for display on a screen as a Succession of images (frames). 0078 Quantization: the term refers to a process of con Verting a signal, which can take N possible values, to a signal which can take N possible values with N-Ni. The set of possible values are called levels. This conversion, or map ping, can, for instance, be performed by rounding the input values to the nearest available output values or by truncating them. For instance the process of taking 16 bit samples and converting them to 8 bit samples represents a quantization operation. Quantization reduces the fidelity of a signal but also the size to represent it. 0079 Quantization step: the quantization step or quanti zation step size is defined as the difference between two adjacent quantization levels. The quantization step is only defined when the quantization is uniform, i.e. when the pos sible values or levels are equidistant. 0080 Fidelity: A source signal, i.e., a signal generated at a signal source, is encoded into an “encoded signal'. An encoded signal is decoded at a decoder to produce a “detected signal'. The degree of resemblance of the detected signal to the source signal, herein called “fidelity', is a measure of encoding quality. Fidelity may be determined based on human perception or by Some automated means. The highest realizable fidelity corresponds to the boundary values of encoding parameters. I0081 Fidelity index: The ratio of a measure of fidelity for a given set of encoding parameters to a measure of fidelity corresponding to the maximum realizable value is herein called a “fidelity index”. A fidelity index is less than or equal to 1.0 but greater than Zero. The terms “fidelity index”, rela tive fidelity index’, and “normalized fidelity index' may be used synonymously. I0082 File size: The size of an encoded signal depends heavily on the encoding method and, of course, the size of the Source signal. The largest size corresponds to reference val ues of encoding parameters. The ratio of the size of the encoded signal for a given set of encoded parameters to the maximum size is herein referenced as a “file size'. A file size is less than or equal to 1.0 but greater than Zero. The terms “file size”, “relative file size', and “normalised file size' may be used synonymously. I0083 Flow rate: A signal may be encoded (or transcoded) in segments and transmitted to a receiver for storage or dis play in real time. The highest bit rate of the produced encoded signal corresponds to reference values of the encoding param eters. The ratio of the bit rate for a given set of encoding parameters to the maximum bit rate is herein referenced as a “flow rate'. A flow rate is less than or equal to 1.0 but greater than Zero. The terms “flow rate”, “relative flow rate', and “normalised flow rate may be used synonymously. I0084 Properties of encoded signal: The fidelity index, the file size, and flow rate constitute properties of an encoded (or transcoded) signal. According to the present invention, the properties are modeled as parametric functions T(q, r, p), S(q, r, (p), and B(q, r, p), representing the fidelity index, the file size, and the flow rate respectively, where q is the ratio of the minimum quantization step to the quantization step used, ris the ratio of the used display resolution to the maximum dis play resolution, and p is the ratio of the frame rate used to the maximum frame rate, 0<qs 1, 0<rs 1, and 0<qs1. I0085 Parametric constraints: The values of q, r, and (p may be limited to decoder-specific values which may vary from one decoder to another. The decoder-specific values are para metric constraints. I0086) System constraints: As far as the encoder or transcoder is concerned, the parametric functions T(q, r, p), S(q, r, p), and B(q, r, (p) are independent of each other, each being uniquely determined according to the selected values of q, r, and (p. However, the encoder or transcoder belongs to a communications system which is subject to further con straints which are either dictated by technological limitations, or regulated for other considerations. Thus, it may be desir able to impose a constraint, unrelated to the encoder or transcoder, regarding the file size or flow rate. It may also be desirable to impose a constraint regarding a lower bound of an acceptable fidelity index. I0087 Constraint function: The parametric function corre sponding to a constrained property is herein called a “con straint function. Thus, if the file size is subject to constraints, the parametric function S(q, r, (p) becomes a constraint func tion. If the flow rate is subject to constraints, the parametric function B(q, r, (p) becomes a constraint function. If the fidel ity index is subject to constraints, the parametric function T(q. r, (p) becomes a constraint function. I0088 Objective function: The parametric function corre sponding to a property to be optimized is herein called an objective function. There may more than one constraint func tions, but there is one, and only one, objective function. Thus, if T(q, r, (p) is selected as an objective function with the objective of maximizing the fidelity index, then either or both of the parametric functions S(q, r, (p) and B(q, r, (p) may serve as constraint function(s) pertinent to limitations of file size and flow rate, respectively. If S(q, r, (p) is selected as an US 2015/O 1393O2 A9 objective function with the objective of minimizing the file size, then either or both of the parametric functions T(q, r, p) and B(q, r, (p) may serve as constraint function(s) pertinent to a requisite lower bound of the fidelity index and/or limitations imposed on the flow rate, respectively. If B(q, r, (p) is selected as an objective function with the objective of minimizing the flow rate, then either or both of the parametric functions T(q, r, (p) and S(q, r, (p) may serve as constraint function(s) perti nent to a requisite lower bound of the fidelity index and/or limitations imposed on the file size, respectively. DETAILED DESCRIPTION 0089 FIG. 1 illustrates a communications system where an originating node 110 distributes multimedia signals to a number of receiving nodes 160 through a network 130. The originating node has an encoder 114 for encoding signals acquired from an information source 112. Naturally, a receiver and other rudimentary elements of a communica tions node precede the encoder and are not illustrated in FIG. 1. The information source 112 may represent a plurality of information sources any of which may be collocated with the encoder or accessed through a dedicated communications path or a path through a network, including the illustrated network 130. A transmitter 116 transmits encoded signals produced by encoder 116 over a channel to network 130. The originating node may have multiple encoders 114 and mul tiple transmitters 116 and may connect to network 130 through multiple channels directed to multiple network ports. 0090. A receiving node 160 (individually 160-a, 160-b, etc.) has a receiver 164 for demodulating received signal and submitting the information content to a decoder 162 which delivers decoded information content to a respective informa tion sink 168 where the decoded information may be stored or presented (e.g., displayed) in real time. 0091. The originating node 110 may have access to data indicating characteristics of a target receiving node, in which case encoder 112 would select encoding parameters compat ible with the characteristics and deliver the encoded signals to the target receiving node 160 over apath 132 through network 130 and a channel 140-a from a network port to the receiving node 160-a. Alternatively, the communications system may provide a signal adaptation node 120 storing Sufficient infor mation pertinent to a multiplicity of receiving nodes, or con figured to communicate with receiving nodes to acquire req uisite characterizing data. Various methods of obtaining characterizing data are presented in a paper entitled "Multi media Adaptation for the Multimedia Messaging Service'. Coulombe, Stephane, and Guido, Grassel, 2004. IEEE Com munications Magazine 42 (7) (July): 120-126. 0092 An originating node 110 accesses the signal adap tation node 120 through a network path 135. The signal adap tation node 120 transcodes signals according to characteris tics of respective receiving nodes. A transcoded signal is transmitted to a target receiving node 160-b through a net work path 137 and a path 140-b from a network port to the receiving node 140-b. A signal adaptation node 120 may be shared by many originating nodes 110. While in this embodi ment they are performed by a same node, the functionalities of transcoding and obtaining characterizing data may also be performed by different nodes. Encoding Options 0093. In transforming an analogue signal into a digital signal, the analogue signal is sampled at an adequate Sam May 21, 2015 pling rate. The magnitude of each sample, or the value of a predefined function of each sample, is approximated by one of a number of discrete levels, often referenced as quantiza tion levels. The larger the number of quantization levels, or equivalently the Smaller a quantization step, the more accu rate the digital representation. A video signal transformed into digital format is further organized into a succession of sets of samples, where each set of samples, often called a frame, may be displayed as an image using a display device. Each image is defined by a number of "picture elements' (pixels), often called display resolution. 0094 Naturally the higher the pixels spatial density, the closer the image to the original picture it represents. A dis played image persists until replaced by a succeeding image. Thus, the higher the rate of changes of displayed images, the higher the image rate, also called frame rate. Each video frame is compressed by exploiting spatiotemporal redundan cies. In the encoding process, spatiotemporal predictions are performed to reduce redundancies and differences from these predictions (also called residual information) are transformed (often using a discrete cosine transform or a similar trans form), quantized, entropy coded, and transmitted. A good overview of the compression tools used in the context of H.264/AVC video coding standard is presented in: Wiegand, T., G.J. Sullivan, G. Bontegaard, anda. Luthra. 2003. “Over view of the H.264/AVC Video Coding Standard.” IEEE Transactions on Circuits and Systems for Video Technology 13 (7) (July): 560-576. As in the quantization of analogue signals, the quantization of transformed residual information affects the fidelity (visual quality) as well as the bit rate of the encoded signal. A Smaller quantization step leads to a better signal fidelity and to a higher bit rate. The three above param eters (display resolution, frame rate and quantization (or quantization step)) affect the flow rate (bitrate) or file size, as well as the fidelity, of a video sequence. The higher the display resolution, the higher the flow rate (or size) and fidel ity. The lower the quantization step, the higher the flow rate (or size) and fidelity. The higher the frame rate, the higher the flow rate (or size) and fidelity (for time-varying sequences). There are several methods of encoding video signals which aim at reducing the size of an encoded video recording and/or the flow rate of an encoded video signal. 0.095 An encoder of a video signal may encode the signal according to a specific quantization step, a specific display resolution, and a specific frame rate compatible with a target receiving node 160. Alternatively, an encoder of a video sig nal may encode the signal according to a nominal quantiza tion step, a nominal display resolution, and a nominal frame rate to be further transcoded into a different quantization step, a different display resolution, and/or a different frame rate. The transcoding may be necessitated by the capability of a receiving node 160, the capacity of a communication path to a receiving node, or both. Several originating nodes 110, each having a respective encoder, may direct initially encoded Video signals to a shared signal adaptation node to be indi vidually re-encoded (transcoded) and directed to respective receiving nodes 160. 0096 Encoding a video signal, or transcoding an already encoded video signal, for delivery to a target receiving node requires initial processes of acquiring characteristics of the receiving node to determine an upper bound of display reso lution, and an upper bound of frame rate. It is also desirable to determine descriptors of the video signals, such as a classifi cation according to rate of temporal image variation which May 21, 2015 US 2015/O 1393O2 A9 may influence the selection of the encoding parameters. Clas sification of a video signal may be based on a representative rate of temporal variation, a quantifier of spectral content in terms of bandwidth occupied by the signal, or some indicator of Scene variation rate. 0097. A degree of resemblance of a visual display of the encoded signal to a display of a respective original signal (i.e., the signal before it is encoded) is a measure of fidelity of the encoded signal. Likewise, resemblance of a visual display of a transcoded video signal to a display of a respective already encoded video signal is a measure offidelity of the transcoded video signal. The fidelity of an encoded or transcoded video signal may be quantified according to some means and rep resented as a normalized “fidelity index' which may vary between 0 and 1.0 (where a value near 0 indicates poor quality and a value near 1 indicates high quality). 0098 Naturally, encoding a video signal at the bounds of encoding parameters (i.e. Smallest allowable quantization step, highest allowable display resolution and highest allow able frame rate) yields the highest resemblance of a visual display of the encoded signal to a display of a respective original analogue signal. Likewise, transcoding an already encoded video signal at the bounds of encoding parameters yields the highest resemblance of a visual display of the transcoded signal to a display of already encoded video sig nal. However, encoding (or transcoding) at the bounds of encoding parameters would normally yield a video recording of a larger size in comparison with a size of a recording produced according to other encoding parameters. Likewise, encoding (or transcoding) at the bounds of encoding param eters would normally yield an encoded signal of a higher flow rate in comparison with a flow rate of an encoded signal produced according to other encoding parameters. Thus, the encoding or transcoding process may be based on satisfying a requisite fidelity index while minimizing a resulting record ing size or a flow rate of an encoded or transcoded signal delivered to a receiving node 160. Alternatively, the encoding or transcoding process may be based on satisfying a requisite upper bound of encoded-signal size or upper bound of flow rate while maximizing a corresponding fidelity index of an encoded or transcoded signal delivered to a receiving node 160. 0099 Selecting appropriate encoding parameters requires means for relating properties of the outcome of encoding or transcoding to the encoding parameters. Determining the fidelity index, file size, or flow rate corresponding to a set of encoding parameters depends heavily on the nature of the scenes captured by the video signal and the method of encod ing, which may vary significantly from one encoding stan dard to another. Thus, it may be difficult to express the fidelity index, file size, or flow rate as a function of encoding param eters and/or descriptors of the video signal. An alternate approach is to exploit known data records of evaluations of properties of outputs of encoders or transcoders correspond ing to selected experimental sets of encoding parameters. The known data records may be used as reference points to guide processes of evaluation of outputs of encoders and transcod ers for arbitrary values of encoding parameters. 0100 Considering the unavoidable random fluctuations in measuring or estimating properties of Such outputs, use of interpolation, linear or otherwise, may falsify the result or complicate the prediction models. A more reliable method, in accordance with the present invention, is to conjecture appro priate individual analytical functional relationships of the fidelity index, the file size, and the flow rate to the encoding parameters and adjust parameters (constants) of the functions to minimize a positive definite function of deviation of refer ence data from corresponding values computed according to the functional relationship. The analytical functions may then be used directly for selecting appropriate encoding param eters or, preferably, used to produce tables offine granularity indicating fidelity indices, file sizes, and flow rates for a large number of encoding parameters. For example, while the num ber of the reference data records may be of the order of 50, the computed granular tables may store fidelity indices, file sizes, and flow rates for 64 quantization steps, 64 display-resolution values, and 64 frame rates, to a total of 262144 records. 0101 The analytical functions used for modeling the dependence of encoding properties on encoding parameters may have different forms. Thus, a first analytical function is formulated for quantifying dependence of a fidelity index of the encoded (transcoded) signal on the quantization step, the display resolution, and the frame rate. A second analytical function is formulated to quantify dependence of a relative size of the encoded/transcoded signal on the quantization step, the display resolution, and the frame rate. A third ana lytical function is formulated to quantify dependence of a relative flow rate of the encoded/transcoded signal on the quantization step, the display resolution, and the frame rate. 0102 The analytical functions used for modeling the dependence of the fidelity index on encoding parameters are preferably selected based on separation of the variables rep resenting the quantization step, the display-resolution, and the frame rate. Thus, first analytical function may be expressed as a multiplication of a respective one-dimensional function of quantization step, a respective one-dimensional function of display resolution, and a respective one-dimen sional function of frame rate. Likewise each of the second function relating file size to encoding parameters and the third function relating flow rate to encoding parameters may be expressed as multiplications of respective one-dimensional functions. 0103) To select a set of encoding parameters yielding a fidelity index at least equal to a specified value, the granular table of fidelity indices is examined to identify a number of candidate records each corresponding to a fidelity index at least equal to the specified value and a set of encoding param eters compatible with descriptors of the video signal and characteristics of a target receiver. If the number of candidate records exceeds one, the granular table of file sizes may be indexed using the indices of the candidate records in order to determine corresponding file sizes. The set of encoding parameters of the candidate record corresponding to the mini mum file size is then selected as a preferred set of encoding parameters. Likewise, if the number of candidate records exceeds one, the granular table of flow rates may be indexed using the indices of the candidate records in order to deter mine corresponding flow rates. The set of encoding param eters of the candidate record corresponding to the minimum flow rate is then selected as a preferred set of encoding param eters. 0104. To select a set of encoding parameters yielding a file size not exceeding a specified value, the granular table of file sizes is examined to identify a number of candidate records each corresponding to a file size not exceeding the specified value and a set of encoding parameters compatible with descriptors of the video signal and characteristics of a target receiver. If the number of candidate records exceeds one, the May 21, 2015 US 2015/O 1393O2 A9 granular table of fidelity indices is indexed using the indices of the candidate records in order to determine corresponding fidelity indices. The set of encoding parameters of the candi date record corresponding to the highest fidelity index is then selected as a preferred set of encoding parameters. 0105 To select a set of encoding parameters yielding a flow rate not exceeding a specified upper bound, the granular table of flow rates is examined to identify a number of can didate records each corresponding to a flow rate not exceed ing the specified upper bound and a set of encoding param eters compatible with descriptors of the video signal and characteristics of a target receiver. If the number of candidate records exceeds one, the granular table of fidelity indices is indexed using the indices of the candidate records in order to determine corresponding fidelity indices. The set of encoding parameters of the candidate record corresponding to the high estfidelity index is then selected as a preferred set of encoding parameters. 0106. It may be required that the selection of a set of encoding parameters used for encoding or transcoding take into consideration specified upper bounds of both the file size and the flow rate of an encoded signal. In Such case, both granular tables of files sizes and flow rates may be examined to identify at least one candidate set of encoding parameters yielding a file size and a flow rate not exceeding their respec tive specified upper bounds while being compatible with descriptors of the video signal and characteristics of a target receiver. If the number of candidate records exceeds one, the granular table of fidelity indices is indexed using the indices of the candidate records in order to determine corresponding fidelity indices. The set of encoding parameters of the candi date record corresponding to the highest fidelity index is then selected as a preferred set of encoding parameters. 0107. It is well known in the art of analytical or numerical optimization that an objective function representing some desirable property can only be optimized with respect to one, and only one, property. Thus, with the three properties of fidelity, size, and flow rate, one may opt to maximize fidelity while observing upper bound constraints relevant to the file size, the flow rate, or both. Alternatively, one may opt to minimize the file size of an encoded signal while observing a lower bound constraint relevant to a predefined fidelity index and/oran upper size constraint relevant to flow rate. Likewise, one may opt to minimize the flow rate of an encoded signal while observing a lower bound constraint relevant to a pre defined fidelity index and/or an upper size constraint relevant to file size. 0108 FIG. 2 illustrates an apparatus 200 for determining signal encoding parameters. The apparatus comprises a pro cessor 270, a number of memory devices, and an interface 280 with a communications network. A memory device 210 stores reference data records indicating properties of encoded signals at selected encoding parameters. Each reference data record indicates a fidelity index, a relative signal size, and/or a relative flow rate corresponding to one of a collection of sets of encoding parameters. 0109. A memory device 220 stores processor-executable instructions representing analytical functions relating prop erties of encoded signals to values of encoding parameters. The properties include a fidelity index, an encoded-signal size, and a flow rate of an encoded signal. 0110. The processor-executable instructions are devised to define a first analytical model for determining fidelity indices and a second analytical model for determining rela tive signal sizes based on the reference data records. The instructions may also be devised to define a third analytical model for determining a flow rate of an encoded signal. The instructions also cause the processor 270 to generate a granu lar table offidelity indices, a granular table of relative sizes of encoded signals, and a granular table of flow rates of encoded signals corresponding to predefined sets of encoding param eters. The number of the predefined sets of encoding param eters is preferably significantly larger than the number of reference data records in order to facilitate selecting a pre ferred set of encoding parameters yielding a value of an objective property close to a sought optimum value. 0111. A memory 230 stores granular tables storing fidelity indices, file sizes, and flow rates corresponding to the pre defined set of encoding parameters. The contents of memory devices 210, 220, and 230 are relevant to processes executed before engaging the apparatus 200 in time-critical processes of determining appropriate encoding parameters and encod ing or transcoding signals accordingly. 0112 A buffer 240 stores video signals, or video record ings, directed to a target receiving node 160. A memory device 250 stores processor-executable instructions for deter mining characteristics of the target receiving node 160. The characteristics of the receiving node may be acquired through exchange of messages with the target receiving node 160, or through accessing a relevant database (not illustrated). 0113. A memory device 260 stores processor-executable instructions which cause processor 270 to examine the granu lar tables to identify a preferred set of encoding parameters compatible with the characteristics of the target receiving node and corresponding to a least relative signal size at a fidelity index at least equal to a specified lower bound. Alter natively, the preferred set of encoding parameters may be selected to correspond to a highest fidelity index under the constraint of a relative encoded-signal size not exceeding a specified upper bound. The processor-executable instructions may also be devised to cause processor 270 to examine the granular tables to identify a preferred set of encoding param eters compatible with the characteristics of the target receiv ing node and corresponding to a least relative flow rate at a fidelity index at least equal to a specified lower bound. Alter natively, the preferred set of encoding parameters may be selected to correspond to a highest fidelity index under the constraint of a relative encoded-signal flow rate not exceeding a specified upper bound. 0114 Thus, memory devices 240, 250, and 260 hold data used for real-time processes. It may be desirable to employ different processors to separately execute the pre-processing functions and the time-critical functions. 0115 FIG.3 illustrates a pre-processing apparatus 300 for generating granular tables relating encoded-signal properties to encoding parameters. The apparatus comprises a processor 370, a memory device 310, a memory device 320, a memory device 330, and a network interface 380. Memory device 320 stores processor-executable instructions similar to the instructions stored in memory device 220 of apparatus 200. Memory device 310 stores reference data records and memory device 330 stores granular tables as described above with reference to memory devices 210 and 230, respectively. The reference data records may be acquired from external databases through network interface 380. 0116 FIG. 4 illustrates an apparatus 400 for determining descriptors of a video signal, characteristics of a target receiv ing node, and capacity of a path from the apparatus to the target receiving node. A video signal may be received over a communication channel 410 and directed, through a network interface 420, to a video-signal buffer 430 which may store segments of a video stream, or an entire video recording, to be transcoded and directed to a target receiving node 160. The apparatus has a processor 470 coupled to a memory device US 2015/O 1393O2 A9 May 21, 2015 440 storing processor-executable instructions forming a module which causes the processor to extract descriptors of a video signal held in the video-signal buffer 430. A memory device 450 stores processor-executable instructions forming a module for determining characteristics of a target receiving node 160. The characteristics of the target receiving node may be acquired through exchange of messages with the target receiving node 160. The characteristics of receiving nodes may also be retrieved from a relevant database (not illus trated) which may be collocated with the apparatus or accessed through a communication path. A memory device 460 stores processor-executable instructions, forming a mod ule, for acquiring capacity (permissible bit rate) of a commu nication path from an originating node 110 or a signal adap tation node 120 Supporting the apparatus to a target receiving node. A buffer 480 holds descriptors (determined in module 440) of the video signal, characteristics (determined in mod ule 450) of the target receiving node, and the capacity (deter mined in module 460) of the communication path to the target receiving node. 0117 FIG. 5 illustrates an apparatus 500 for encoding or transcoding signals to produce encoded signals of specified properties, employing outputs of apparatus 300 of FIG.3 and apparatus 400 of FIG. 4. A processor 570 is coupled to buffer 480 which holds descriptors of a video signal, characteristics of a target receiving node, and capacity of a communication path to a target receiving node as determined by apparatus 400. Processor 570 is coupled to memory device 330 which stores granular tables determining fidelity indices, file sizes, and flow rates corresponding to a large number of sets of encoding parameters as determined by apparatus 300. A memory device 560, coupled to processor 570, stores proces process of encoding and transcoding. The independent vari ables of each function area normalized quantization step"q. a normalized display resolution “r”, and a normalized frame rate “p'. A universal predictive regression module 630 is used to determine the constants defining each function based on the reference property data and corresponding encoding parameters. The constants are stored in a memory 640. The software instructions 620 defining the analytical functions and the constants determined from the regression module are used in module 680 for generating granular tables of encoded signal properties corresponding to a relatively large number of preselected sets of encoding parameters 650. 0.120. The analytical function relating any of the proper ties to encoding parameters is based on the concept of sepa ration of variables and is formulated as a composite function combining a respective one-dimensional function of quanti Zation step, a respective one-dimensional function of display resolution, and a respective one-dimensional function of frame rate. A preferred composite function used herein is a multiplication of one-dimensional functions. I0121 With the normalized independent variables of the ratio of a minimum quantization step to a candidate quanti Zation step; the ratio of a candidate display resolution to a maximum display resolution; and the ratio of a candidate frame rate to a maximum frame rate; denoted q, r, and (p. respectively, a composite function relating fidelity to encod ing parameters may be expressed as: in memory device 260 of apparatus 200, which cause proces sor 570 to examine the granular tables to identify a set of preferred encoding parameters compatible with the charac teristics of the target receiving node and corresponding to an optimum value of a selected property of an encoded signal under a variety of constraints. A transcoder (or an encoder) 590 extracts segments of a video stream stored in video-signal buffer 430, transcodes (or encodes) the segments according to the optimal encoding parameters 580, and submits the encoded or transcoded video signal to a network interface to be directed to a target receiving node. 0118. The operations of processors 470 and 570 may be pipelined. Processors 470 and 570 may also be operated according to some other load-sharing discipline. 0119 FIG. 6 illustrates a method implemented at the pre processing apparatus 300 for generating parametrized func tions for determining properties of encoded signals corre sponding to arbitrary values of encoding parameters. Memory device 310 of apparatus 300 stores a number of I0123 a composite function relating the flow rate of an encoded video signal to encoding parameters may be expressed as: I0122) Likewise, a composite function relating the size of an encoded Video signal to encoding parameters may be expressed as: sor-executable instructions, similar to the instructions stored reference data records where each reference data record includes a fidelity index, a file size, and a flow rate corre sponding to a respective experimental set of encoding param eters. The analytical modeling instructions stored in memory device 320 of apparatus 300 include software instructions relevant to conjectured analytical functions 620 determining properties of an encoded signal corresponding to any set of encoding parameters. The properties include a fidelity index, a file size, and a flow rate. The encoding parameters include a quantization step, a display resolution, and frame rate. The conjectured functions are defined by parameters (constants) which may be selected according to information extracted from the reference data records. For clarity, the parameters defining a function are referenced hereinafter as “constants' since the term “parameters' has been associated with the I0124. Each of the one-dimensional functions T (q), T(r), T(cp), S(q), S(r), S(cp), B(q), B(r), and B(cp) is a function defined according to respective constants. 0.125. As mentioned above, the independent variables are normalized: q is a ratio of a minimum quantization step to a candidate quantization step, r is a ratio of a candidate display resolution to a maximum display resolution; and p is a ratio of a candidate frame rate to a maximum frame rate. 0.126 FIG. 7 illustrates forming a first analytical function 740 including: a marginal function relating the fidelity index to quantization only; a marginal function relating the fidelity index to display resolution only; and a marginal function relating the fidelity index to frame rate only. I0127 FIG. 8 illustrates forming a second analytical func tion 840 including: a marginal function relating the relative size of an encoded signal to quantization only; a marginal function relating the relative size to display resolution only; and a marginal function relating the relative size to frame rate only. I0128 FIG. 9 illustrates forming a third analytical function 940 including: a marginal function relating the relative flow rate of an encoded signal to quantization only; a marginal function relating the relative flow rate to display resolution only; and a marginal function relating the relative flow rate to frame rate only. I0129. Table I and Table II, below, are exemplary tables produced according to the method of FIG. 6 indicating fidel ity indices and files sizes corresponding to 48 preselected experimental sets of encoding parameters. May 21, 2015 US 2015/O 1393O2 A9 0130 Table I is based on the first analytical function 740 quantifying dependence of a fidelity index on encoding parameters q, r, and (p. The marginal functions 710, 720, and 730 are respectively formulated as: 0131 So that the first analytical function is expressed as: T(q, rcp)=(1+e P*2)x(1+e(Y)x(mxln(p)+1). 0132 Module 630 (FIG. 6) executes a first regression analysis process to determine constants C, B, Y, Ö, and m defining the first analytical function. 0.133 Table II is based on the second analytical function 840 quantifying dependence of a relative signal size on encoding parameters q, r, and (p. 0134) The marginal functions 810, 820, and 830 are respectively formulated as: determined by numerical experimentation to be very close to unity, so that 0<(1-2)<1.0. A preferred value of S2 is 0.999. 0144. Thus, the augmented second analytical function is expressed as: 0145 Table I and Table II may be used to select a preferred set of encoding parameters yielding fidelity index at least equal to a specified lower bound while minimizing the size of the encoded signal. A straightforward method is to examine each entry of Table I to identify each candidate set of encod ing parameters compatible with characteristics of a target receiving node and corresponding to an acceptable value of the fidelity index. If more than one candidate set is found, which is likely to be the case, then corresponding entries of Table II are examined to select a set of encoding parameters corresponding to a least relative size of an encoded signal. 0146 For example, if the fidelity index to be observed in encoding or transcoding a specific video signal is 0.52, and a target receiver operates at a relative quantization not exceed ing 0.6, then the number of candidate sets of encoding param eters is 10. The number of candidate sets is the number of 0135 So that the second analytical function may be expressed as: 0.136 Module 630 (FIG. 6) executes a second regression analysis process to determine constants W. 0, O, e, and () defining the second analytical function. 0.137 The second analytical function may be further aug mented to reduce deviation from reference data using a parameter S2, determined by numerical experimentation to be very close to unity, so that 0<(1-2)<1.0. A preferred value of SD is 0.999. 0.138. Thus, the augmented second analytical function is expressed as: 0.139. The marginal functions 910, 920, and 930 are respectively formulated as: B(r)=(1+e); and 0140. So that the third analytical function may be expressed as: 0141 Module 630 (FIG. 6) executes a third regression analysis process to determine constants W. 0, O, e, and () defining the second analytical function. 0142. It is of paramount importance to note that while the functions S(q, r, (p) and B'(q, r, (p) have the same form with the same parametric definitions, the numerical values of the parameters (constants) W. 0, O, e, and () of B'(q, r, (p) need not bear any specific relationship to corresponding values of S(q, r, (p). 0143. As in the case of the second analytical function, the third analytical function B'(q, r, (p) may be further augmented to reduce deviation from reference data using a parameter S2. entries in Table I corresponding to values of q not exceeding 0.6 and fidelity indices each at least equal to 0.52. The can didate sets and corresponding relative file sizes of encoded signals are listed in Table III below which indicates a fidelity index determined from the first analytical function and listed in Table I and a relative file size determined from the second analytical function and listed in Table II. The fidelity index corresponding to each of the sets of encoding parameters is larger than the requisite value of 0.52. The least relative file size is 0.04899 which corresponds to the set of encoding parameters q 0.25, r–0.25, and (p=1.0. It is seen that the set of encoding parameters q0.1575, r-1.0, and p=1.0 corre sponds to a lower fidelity index 0.52877 (yet meeting the requirement) yet a higher relative file size of 0.13151. Also, the set of encoding parameters q=0.3970, r=1.0, and (p=0.125 corresponds to a slightly lower fidelity index 0.53437 yet a higher relative file size of 0.10319 (compared to 0.04899). 0147 Table IV below, derived from Table I and Table II, lists 12 sets of encoding parameters corresponding to relative file sizes less than 0.1 with the encoding parameters selected so that qs0.6, rs().5, and ps0.4. The set {0.397, 0.25, 0.25} of encoding parameters yields the highest fidelity index of 0.50215. 0.148. The parameters (constants) defining each of the ana lytical functions are specific to a set of reference data records which may be acquired for video streams of a specific clas sification. Video streams may be classified according to cat egories Such as peak flow rates, mean flow rates, rate of variation of content of Successive images caused by spatial variation and/or temporal variation of captured scenes. 0149. As described above, analytical functions are devised to model an encoding or transcoding process for each video stream classification. Thus, while the forms of the first, sec ond, and third analytical functions T(q, r, p), S(q, r, p), and B(q, r, (p) may be applicable to several video-stream classifi cations, the respective parameters (constants) defining the functions may differ significantly from one video-stream classification to another. 0150. The analytical functions, discussed above, relating properties of encoded signals to encoding parameters, apply to encoding parameters relevant to three independent vari ables q, r, and (p representing a relative quantization step, a relative display resolution, and a relative frame rate. A pro cess of direct examinations of granular tables relating prop May 21, 2015 US 2015/O 1393O2 A9 11 erties of encoded signals to encoding parameters may be computationally intensive when the number of sets of encod ing parameters is large. TABLE I Fidelity index as a function of normalized quantization (q), display resolution (r), and frame rate (cp). The independent variables q, r, and p are normalized values, each being greater than 0 and less than or equal 1. -op r O.157SO 0.2SOOO O.3970 1.OOO O.125 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO O.13494. O.25464 O.32680 O.16273 O.30710 O.39412 O.19053 O.35955 0.46145 O.21833 O.412O1 O.S2877 O.17539 O.33098 0.42478 0.21152 O.39916 O.S1228 0.24765 0.4673S 0.59979 0.28378 O.S3553 O.68729 O.22064 0.41638 O.S3437 O.26609 0.50215 O.64445 0.31154 O.S8792 0.75453 O.35700 0.6737O O.86461 O.25458 0.48043 0.61657 O.30702 O.S7939 O.74359 0.35947 O.678.36 0.87O60 0.41.191 O.77733 O.99761 O.2SO OSOO 1.OOO 0151 Table I is generated using the function T(q, r, p), defined above. TABLE II Size of encoded video recording as a function of normalized quantization (q), display resolution (r), and frame rate (cp). The independent variables q, r, and p are normalized values, each being greater than 0 and less than or equal 1. -op r O.157SO 0.2SOOO O.3970 1.OOO O.125 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO 0.0625 O.2SOO 1.OOOO O.OO244 O.OO918. O.O3798 O.OO319 O.O1346 O.OS73O O.OO434 O.O1997 O.O8672 O.OO608 O.O2987 O.13151 O.OO339 O.O1460 0.06247 O.OO46S 0.02171 O.O9458 O.OO6SS O.O32S2 0.14348 O.OO945 O.O4899 0.21791 O.OO498 0.02361 O.10319 O.OO7O6 O.O3S42 0.15658 O.O1023 O.OS341. O.23787 OO150S 0.08079 O-36162 0.01.200 O.O6346 O.28328 O.O1774 0.09609 0.43076 O.O2649 O.14576 0.65528 0.03981 0.22140 0.99721 O.2SO OSOO 1.OOO TABLE III-continued Fidelity indices and relative file sizes corresponding to 12 candidate sets of encoding parameters - the constraints are: qs0.6, and a fidelity index 20.52 Encoding parameters Fidelity Relative {0.397, 1.0, 0.25} {0.397, 0.25, 0.50} {0.397, 1.0, 0.50} {0.397, 0.25, 1.0} {0.397, 1.0, 1.0} O64445 0.58792 0.75453 0.67370 O86461 O.15658 O.OS341 0.23787 O.08079 O.36.162 {q, r, p} index file size TABLE IV Relative file sizes and Fidelity indices corresponding to 12 candidate sets of encoding parameters - the constraints are: qs0.6, rsO.S. ps0.4, and a relative file size sO.10 Encoding parameters {q, r, p} Relative file size Fidelity index { 0.1575,0625, 125} { 0.1575, 0.25, 0.125} {.1575,.0625, 0.25} {.1575, 0.25, 0.25} { 0.25, 0.0625, 0.125} { 0.25, 0.25, 0.125} { 0.25, 0.0625, 0.25} { 0.25, 0.25, 0.25} {0.397, .0625, 0.125} {0.397, 0.25, 0.125} {0.397, .0625, 0.25} {0.397, 0.25, 0.25} O.OO244 O.OO918 O.OO319 O.O1346 O.OO339 O.O1460 O.OO46S O.02171 O.OO498 O.O2361 O.OO7O6 O.O3S42 O.13494 O.25464 O.16273 O.30710 0.17539 O.33098 O.21152 O.39916 O.22064 O41638 O.26609 OSO215 0153 FIG. 10 illustrates generating sorted granular tables of relative fidelity indices, relative files sizes, and relative flow rates for a predefined set of encoding parameters. 0154) To expedite the process of selecting encoding parameters to realize a specified property objective under constraints relevant to other properties, the content of the granular tables may be presented in data structures which facilitate fast search. Denoting the numbers of discrete values for the variables q, r, and p, as m, m, and m, respectively, the number of M of reference sets of encoding parameters would be M-mixmaxim. The M sets are preferably indexed as 0 to (M-1) and a reference data structure of M records, such as a 3xM matrix, may be used to indicate a fidelity index, a relative file size, and a relative flow rate for each of the M 0152 Table II is generated using the function S(q, r, p), defined above. TABLE III Fidelity indices and relative file sizes corresponding to 12 candidate sets of encoding parameters - the constraints are: qs 0.6, and a fidelity indeX eO.52 Encoding parameters Fidelity Relative { 0.1575, 1.0, 1.0} { 0.25, 1.0, 0.50} { 0.25, 0.25, 1.0} { 0.25, 1.0, 1.0} {0.397, 1.0, 0.125} 0.52877 0.59979 0.53553 O.68729 O.S3437 O.13151 O.14348 O.04899 O.21791 O.10319 {q, r, p} index file size reference sets of encoding parameters. 0.155 The entries of the reference data structure corre sponding to the fidelity indices may be sorted in an ascending order to produce a first data structure of M records, such as a 2xM matrix, with each record indicating an index of a set of encoding parameters and a corresponding fidelity index. 0156 The entries of the reference data structure corre sponding to the relative sizes of encoded signals may also be Sorted in an ascending order to produce a second data struc ture of M records, such as a 2xM matrix, with each record indicating an index of a set of encoding parameters and a corresponding relative file size. O157 Likewise, the entries of the reference data structure corresponding to the relative flow rates may also be sorted in an ascending order to produce a second data structure of M May 21, 2015 US 2015/O 1393O2 A9 records, such as a 2xM matrix, with each record indicating an index of a set of encoding parameters and a corresponding relative flow rate. 0158. The process of FIG. 10 starts with acquiring refer ence data records (step 1010) of fidelity indices, relative file sizes, and relative flow rates for a number of sets of encoding parameters. The reference data records may be acquired from a data base which may be collocated with an encoding or transcoding apparatus or accessible through a communica tions path. 0159. In step 1020, a first analytical function relating a fidelity index to a set of encoding parameters is devised. The parameters may be determined according to a predictive regression procedure as described above with reference to FIG. 6. In step 1030, a granular first table of fidelity indices corresponding to the M reference sets of encoding parameters is generated using the first analytical function. The number M is preferably much larger than the number of reference data records in order to realize fidelity indices of decoded signals close to envisaged optimum objectives. The M generated fidelity indices are sorted (step 1040) in either an ascending order or descending order to produce Sorted records each indicating a fidelity index and a corresponding index of a set of encoding parameters. 0160. In step 1022, a second analytical function relating a normalized file size to a set of encoding parameters is devised. The parameters may be determined according to a predictive regression procedure as described above with reference to FIG. 6. In step 1032, a granular second table of normalized file sizes corresponding to the M reference sets of encoding parameters is generated using the second analytical function. The number M is preferably much larger than the number of reference data records in order to realize file sizes of decoded signals close to envisaged optimum objectives. The Mgen erated fidelity indices are sorted (step 1042) in either an ascending order or descending order to produce Sorted records each indicating a normalized file size and a corre sponding index of a set of encoding parameters. 0161 In step 1024, a third analytical function relating a normalized flow rate to a set of encoding parameters is devised. The parameters may be determined according to a predictive regression procedure as described above with ref erence to FIG. 6. In step 1034, a granular third table of normalized file sizes corresponding to the M reference sets of encoding parameters is generated using the third analytical function. The number M is preferably much larger than the number of reference data records in order to realize flow rates of decoded signals close to envisaged optimum objectives. The M generated fidelity indices are sorted (step 1044) in either an ascending order or descending order to produce Sorted records each indicating a normalized flow rate and a corresponding index of a set of encoding parameters. 0162 FIG. 11 illustrates a process of determining a set of encoding parameters yielding a maximum fidelity index con strained by an upper bound of encoded-signal size and/or an upper bound of flow rate of an encoded signal. The process is implemented in apparatus 500 where the processor-execut able instructions stored in memory device 560 are structured in modules which include a primary-search module 1110 relying on a granular table 1180 of file sizes and/or a granular table 1190 of flow rates. Granular table 1180 represents the table produced in step 1032 or the sorted table produced in step 1042. Granular table 1190 represents the table produced in step 1034 or the sorted table produced in step 1044. The primary-search module causes processor 570 to perform either or both of two processes of: 0.163 (i) searching the granular table 1180 of file sizes to identify a first group of candidate sets of encoding parameters corresponding to a requisite upper bound of file sizes; and 0.164 (ii) searching the granular table 1190 to identify a second group of candidate sets of encoding parameters corresponding to a requisite upper bound of flow rates. 0.165 If both the upper bound offile sizes and upper bound offlow rates are to be observed, then group 1120 of candidate set of encoding parameters to be considered is the intersection of the first group and the second group. If only the upper bound of file sizes is to be observed, then group 1120 of candidate set of encoding parameters to be considered is the first group. If only the upper bound of flow rates is to be observed, then group 1120 of candidate set of encoding parameters to be considered is the second group. 0166 The processor-executable instructions stored in memory device 560 include an optimal encoding module 1130 which accesses a granular table 1140 offidelity indices to determine a fidelity index corresponding to each candidate set of encoding parameters. Granular table 1140 lists fidelity indices corresponding to indices of sets of encoding param eters and is produced in step 1030. The set of encoding param eters yielding the highest fidelity index is considered the preferred set and is submitted to an encoder or transcoder 1150. 0167 FIG. 12 illustrates a process of determining a set of encoding parameters yielding a minimum file size con strained by a lower bound of encoded-signal fidelity index and/or an upper bound of flow rate of an encoded signal. The process is implemented in apparatus 500 where the proces sor-executable instructions stored in memory device 560 are structured in modules which include a secondary-search module 1210 relying on a granular table 1280 of fidelity indices and/or a granular table 1190 of flow rates. Granular table 1280 represents the table produced in step 1030 or the sorted table produced in step 1040. Granular table 1190 rep resents the table produced in step 1034 or the sorted table produced in step 1044. The secondary-search module causes processor 570 to perform either or both of two processes of: 0168 (iii) searching the granular table 1280 of fidelity indices to identify a third group of candidate sets of encoding parameters corresponding to a requisite lower bound of fidelity indices; and 0.169 (iv) searching the granular table 1190 to identify a fourth group of candidate sets of encoding parameters corresponding to a requisite upper bound of flow rates. 0170 If both the lower bound of fidelity indices and upper bound of flow rates are to be observed, then group 1220 of candidate set of encoding parameters to be considered is the intersection of the third group and the fourth group. If only the lower bound of fidelity indices is to be observed, then group 1220 of candidate set of encoding parameters to be consid ered is the third group. If only the upper bound offlow rates is to be observed, then group 1120 of candidate set of encoding parameters to be considered is the fourth group. 0171 The processor-executable instructions stored in memory device 560 include an optimal encoding module 1230 which accesses a granular table 1240 of normalized file sizes to determine a file size corresponding to each candidate set of encoding parameters. Granular table 1240 lists normal ized file sizes corresponding to indices of sets of encoding US 2015/O 1393O2 A9 parameters and is produced in step 1032. The set of encoding parameters yielding the lowest file size is considered the preferred set and is submitted to an encoder or transcoder 1150. 0172 FIG. 13 illustrates a process of determining a set of encoding parameters yielding a minimum flow rate con strained by a lower bound of encoded-signal fidelity index and/or an upper bound of size of an encoded signal. The process is implemented in apparatus 500 where the proces sor-executable instructions stored in memory device 560 are structured in modules which include a ternary-search module 1310 relying on a granular table 1280 of file sizes and/or a granular table 1180 of file sizes. Granular table 1280 repre sents the table produced in step 1030 or the sorted table produced in step 1040. Granular table 1180 represents the table produced in step 1032 or the sorted table produced in step 1034. The ternary-search module causes processor 570 to perform either or both of two processes of: 0173 (v) searching the granular table 1280 of fidelity indices to identify a fifth group of candidate sets of encoding parameters corresponding to a requisite lower bound of fidelity indices; and 0.174 (vi) searching the granular table 1180 to identify a sixth group of candidate sets of encoding parameters corresponding to a requisite upper bound of file sizes. (0175. If both the lower bound offidelity and upper bound of file sizes are to be observed, then group 1320 of candidate set of encoding parameters to be considered is the intersection of the fifth group and the sixth group. If only the lower bound of fidelity indices is to be observed, then group 1320 of candidate set of encoding parameters to be considered is the fifth group. If only the upper bound of file sizes is to be observed, then group 1320 of candidate set of encoding parameters to be considered is the sixth group. 0176 The processor-executable instructions stored in memory device 560 include an optimal encoding module 1330 which accesses a granular table 1340 of flow rates to determine a flow corresponding to each candidate set of encoding parameters. Granular table 1340 lists normalized flow rates corresponding to indices of sets of encoding param eters and is produced in step 1034. The set of encoding param eters yielding the highest fidelity index is considered the preferred set and is submitted to an encoder or transcoder 1150. 0177 FIG. 14 illustrates processes for determining encod ing parameters for different objectives under corresponding constraints as described above with reference to FIG. 11, FIG. 12, and FIG. 13. The set of M sets of encoding parameters {q, r, p} is generated (step 1410) in the pre-processing apparatus 300 as described with reference to FIG. 10. Process 1030 of generating a granular table offidelity indices for the M sets of encoding parameters has been described above with refer ence to FIG. 10. Processes 1032 of generating a granular table of file sizes, and 1034 of generating a granular table of flow rates for the M sets of encoding parameters have been described above with reference to FIG. 10. Processes 1040, 1042, and 1044 of sorting respective granular tables have been described above. 0.178 Process 1450 uses the sorted granular table of indi ces of sets of encoding parameters corresponding to normal ized flow rates (determined in process 1044) to determine candidate sets of encoding parameters. Each candidate set need be compatible with characteristics of a target receiving node 160 and yielding an encoded signal of a flow rate not May 21, 2015 exceeding a specified upper bound. Process 1450 further uses the granular table of fidelity indices corresponding to indices of sets of encoding parameters (determined in process 1030) to identify a preferred set of encoding parameters yielding an encoded signal of highest fidelity index. 0179 Process 1460 uses the sorted granular table of indi ces of sets of encoding parameters corresponding to fidelity indices (determined in process 1040) to determine candidate sets of encoding parameters. Each candidate set need be compatible with characteristics of a target receiving node 160 and yielding an encoded signal of a fidelity index at least equal to a specified lower bound. Process 1460 further uses the granular table of normalized file sizes corresponding to indices of sets of encoding parameters (determined in process 1032) to identify a preferred set of encoding parameters yielding an encoded signal of least file size. Process 1460 may also use the granular table of normalized flow rates corre sponding to indices of sets of encoding parameters (deter mined in process 1034) to identify a preferred set of encoding parameters yielding an encoded signal of least flow rate. 0180 Process 1470 uses the sorted granular table of indi ces of sets of encoding parameters corresponding to normal ized file sizes (determined in process 1042) to determine candidate sets of encoding parameters. Each candidate set need be compatible with characteristics of a target receiving node 160 and yielding an encoded signal of a normalized file size not exceeding a specified upper bound. Process 1470 further uses the granular table of fidelity indices correspond ing to indices of sets of encoding parameters (determined in process 1030) to identify a preferred set of encoding param eters yielding an encoded signal of highest fidelity index. 0181 FIG. 15 presents the main processes described above of determining encoding parameters yielding a mini mal file size at a specified lower bound of the fidelity index. In process 1510, a video signal is acquired through a network interface of an encoder or a transcoder. The video signal is supplied to the encoder or transcoder and to the apparatus 400 of FIG. 4 which has memory devices storing processor-ex ecutable instructions organized into a module 440 for extract ing or acquiring descriptors of the video signal, a module 450 for acquiring characteristics of a target receiving node 160, and a module 460 for determining or acquiring an estimate of the capacity (in bits-per-second, for example) of a path from the encoder or transcoder to the target receiving node 160. The outputs of apparatus 400, held in a buffer 480, together with the outputs of apparatus 300, are supplied to apparatus 500 to be processed using processor-executable instructions, stored in memory device 560, identified as 560-A, which may be structured as a module 1550 for identifying candidate sets ofencoding parameters each corresponding to a fidelity index not less than a specified lower bound and a module 1560 for selecting a candidate set of encoding parameters compatible with characteristics of the target receiving node 160 and hav ing the minimum attainable relative file size. 0182 FIG. 16 presents the main processes described above of determining encoding parameters yielding highest fidelity indexata specified upper bound offile size. In process 1610, a video signal is acquired through a network interface of an encoder or a transcoder. The video signal is Supplied to the encoder or transcoder and to the apparatus 400 of FIG. 4 as described above with reference to FIG. 15. The outputs of apparatus 400, held in a buffer 480, together with the outputs of apparatus 300, are supplied to apparatus 500 to be pro cessed using processor-executable instructions, stored in US 2015/O 1393O2 A9 memory device 560, identified as 560-B, which may be struc tured as a module 1650 for identifying candidate sets of encoding parameters each corresponding to a relative file size not exceeding a specified upper bound and a module 1660 for selecting a candidate set of encoding parameters compatible with characteristics of the target receiving node 160 and hav ing the maximum attainable fidelity index. 0183 FIG. 17 illustrates a conventional bisection process for locating optimal encoding parameters using data struc tures generated by the pre-processing apparatus of FIG. 3. Consider an array P having N entries sorted in ascending order, N>1. To determine the index of P corresponding to the nearest value greater than or equal to a number W, the process illustrated in FIG. 17 is implemented to yield an index m of an entry P(m) which is less than or equal to W. If array P stores fidelity indices sorted in an ascending order, with an associ ated array indicating corresponding indices of the sets of encoding parameters (table 2050 of FIG. 30), then P(m)sW. and P(m+1)-W. A similar process may be used if the entries of array P is sorted in a descending order and it is desired to determine the index of P corresponding to the nearest value less than or equal to a number W. the number of steps is limited to log N. 0184 FIGS. 18 to 21 present exemplary schemes of encoding a received signal to produce an encoded signal having optimal quantified properties under a variety of con straints. 0185 FIG. 18 illustrates a first scheme of encoding a received signal to produce an encoded signal having a highest fidelity index constrained by an upper bound of flow rate of the encoded signal. A module 1820, devised as processor executable instructions stored—for example—in memory device 560 of FIG. 5, causes a processor to use content of a table 1850 of indices of encoding parameters corresponding to sorted flow rates and content of a table 1860 of fidelity indices corresponding to sets of encoding parameters to determine an optimal set of encoding parameters {q, r, p}. defined above, yielding the highest attainable fidelity index under constraints 1810 relevant to encoding parameters and constraint 1830 of an upper bound of flow rates. 0186 FIG. 19 illustrates a second scheme of encoding a received signal to produce an encoded signal having a highest fidelity index constrained by an upper bound offile size of the encoded signal. A module 1920, devised as processor-execut able instructions stored—for example—in memory device 560 of FIG. 5, causes a processor to use content of a table 1950 of indices of encoding parameters corresponding to sorted file sizes and content of table 1860 of fidelity indices corresponding to sets of encoding parameters to determine an optimal set of encoding parameters {q, r, p}, defined above, yielding the highest attainable fidelity index under constraints 1910 relevant to encoding parameters and constraint 1930 of an upper bound of file sizes. 0187 FIG. 20 illustrates a third scheme of encoding a received signal to produce an encoded signal having a mini mal flow rate constrained by a lower bound offidelity index of the encoded signal. A module 2020, devised as processor executable instructions stored—for example—in memory device 560 of FIG. 5, causes a processor to use content of a table 2050 of indices of encoding parameters corresponding to sorted fidelity indices and content of a table 2060 of flow rates corresponding to sets of encoding parameters to deter mine an optimal set of encoding parameters {q, r, p}, defined above, yielding the least realizable flow rate under constraints May 21, 2015 2010 relevant to encoding parameters and constraint 2030 of a lower bound of the fidelity index of the encoded signal. 0188 FIG. 21 illustrates a fourth scheme of encoding a received signal to produce an encoded signal having a mini mal file size constrained by a lower bound offidelity index of the encoded signal. A module 2120, devised as processor executable instructions stored—for example—in memory device 560 of FIG. 5, causes a processor to use content of table 2050 of indices of encoding parameters corresponding to sorted fidelity indices and content of a table 2160 of file sizes corresponding to sets of encoding parameters to deter mine an optimal set of encoding parameters {q, r, p}, defined above, yielding the least realizable file size under constraints 2110 relevant to encoding parameters and constraint 2030 of a lower bound of the fidelity index of the encoded signal. (0189 FIG. 22 illustrates details of a method of determin ing a set of encoding parameters for encoding a specific signal to yield an encoded signal of the highest attainable fidelity index and having a flow rate not exceeding a specified limit while observing limitations of a target receiving node 160. Using sorted table 1850 (FIG. 18), bisection search may be performed to determine the nearest set of encoding param eters yielding a flow rate not exceeding a maximum value (process 2210). Staring with the nearest set of encoding parameters, indices of candidate sets of encoding parameters corresponding to sequential values of flow rates satisfying the flow rate constraint are identified (process 2220). Table 1860 (FIG. 18) is then indexed to determine fidelity indices corre sponding to the candidate sets of encoding parameters (pro cess 2230). The candidate set of encoding parameters yield ing the highest attainable fidelity index is selected as a preferred set (process 2240). 0.190 FIG. 23 illustrates details of a method of determin ing a set of encoding parameters for encoding a specific signal to yield an encoded signal of the highest attainable fidelity index and having a file size not exceeding a specified limit while observing limitations of a target receiving node 160. Using sorted table 1950 (FIG. 19), bisection search may be performed to determine the nearest set of encoding param eters yielding a file size not exceeding a maximum value (process 2310). Staring with the nearest set of encoding parameters, indices of candidate sets of encoding parameters corresponding to sequential values of file sizes satisfying the file-size constraint are identified (process 2320). Table 1860 (FIG. 19) is then indexed to determine fidelity indices corre sponding to the candidate sets of encoding parameters (pro cess 2330). The candidate set of encoding parameters yield ing the highest attainable fidelity index is selected as a preferred set (process 2340). (0191 FIG. 24 illustrates details of a method of determin ing a set of encoding parameters for encoding a specific signal to yield an encoded signal of the least flow rate and having a fidelity index at least equal to a specified lower bound while observing limitations of a target receiving node 160. Using sorted table 2050 (FIG. 20), bisection search may be per formed to determine the nearest set of encoding parameters yielding a fidelity index at least equal to a specified lower bound (process 2410). Staring with the nearest set of encod ing parameters, indices of candidate sets of encoding param eters corresponding to sequential values of fidelity indices satisfying the fidelity-index constraint are identified (process 2420). Table 2060 (FIG. 20) is then indexed to determine flow rates corresponding to the candidate sets of encoding param May 21, 2015 US 2015/O 1393O2 A9 eters (process 2430). The candidate set of encoding param eters yielding the least flow rate is selected as a preferred set (process 2440). (0192 FIG. 25 illustrates details of a method of determin ing a set of encoding parameters for encoding a specific signal to yield an encoded signal of the least file size and having a fidelity index at least equal to a specified lower bound while observing limitations of a target receiving node 160. Using sorted table 2150 (FIG. 21), bisection search may be per formed to determine the nearest set of encoding parameters yielding a fidelity index at least equal to a specified lower bound (process 2510). Staring with the nearest set of encod ing parameters, indices of candidate sets of encoding param eters corresponding to sequential values of fidelity indices satisfying the fidelity-index constraint are identified (process 2520). Table 2160 (FIG. 21) is then indexed to determine file sizes corresponding to the candidate sets of encoding param eters (process 2530). The candidate set of encoding param eters yielding the least flow rate is selected as a preferred set (process 2540) to be supplied to an encoder or transcoder. 0193 FIG. 26 illustrates exemplary sets of encoding parameters {q, r, p} for which fidelity indices and normalized file sizes are determined using analytical functions derived from a number of reference data records acquired from a database. As defined earlier, the encoding parameters are normalized with q being a ratio of a minimum quantization step to a candidate quantization step, r being a ratio of a candidate display resolution to a maximum display resolu tion, and (p being a ratio of a candidate frame rate to a maxi mum frame rate. 0194 The sets of encoding parameters of FIG. 26 corre spond to only two values of q three values of r, and 3 values of p to a total number, M, of 18. It is an objective, however, that the granular tables cover a large number of encoding parameters in order to enable determining encoding param eters yielding near-optimal properties of encoded signals. For example, 64 discrete values of each of q, r, and (p may be used resulting in a number, M, of sets of encoding parameters of 262144. 0.195 The fidelity indices are determined from a first ana lytical function: The constants C, B, Y. Ö, and m are determined from the reference data records according to a regression-analysis pro CCSS, 0196. The fidelity indices are determined from a second analytical function: 0197) The constants S2, W, 0, o, e, and () are determined from the reference data records according to a regression analysis process. (0198 FIG. 27 illustrates a first table 2700 indicating fidel ity indices 2740 for each of the parameter sets of FIG. 26. The encoding parameter q (reference 2730) has two values of 0.25 and 1.0. The encoding parameterr (reference 2720) has three values 0.0625, 0.250, and 1.0. The encoding parameter (p has three values 0.25, 0.5, and 1.0. The fidelity indices 2740 are determined from the above expression of T(q, r, (p). (0199 FIG. 28 illustrates a second table 2800 indicating normalized file sizes 2840, determined from the above expression of S(q, r, p), for each of the parameter sets of FIG. 26. 0200 FIG. 29 illustrates an implementation of the scheme of encoding of FIG. 19 and FIG. 23 where sorted table 1950 is derived from table 2800 of FIG. 28 and table 1860 is formulated from table 2700 of FIG. 27. If, for example, the normalized file size is constrained to an upper bound of 0.043. sorted table 1950 indicates that parameter sets 0, 6, 12, 3, 1,9. 7, and 15 correspond to file sizes less than 0.043. The corre sponding fidelity indices determined from table 1860 are 0.212, 0.248, 0.284, 0.307, 0.399, 0.359, 0.467, and 0.412, respectively. The highest fidelity index of 0.467 corresponds to parameter set 7 which may be selected as the preferred set of encoding parameters. 0201 FIG. 30 illustrates an implementation of the scheme of encoding of FIG.21 and FIG. 25 where sorted table 2050 is derived from table 2700 of FIG. 27 and table 2160 is formulated from table 2800 of FIG. 28. If, for example, the fidelity index is required to be at least 0.5, sorted table 2050 indicates that parameter 2, 13, 4, 8, 10, 14, 5, 16, 11, and 17 correspond to fidelity indices greater than 0.5. The corre sponding file sizes determined from table 2160 are 0.095, 0.049, 0.096, 0.143, 0.146, 0.218, 0.431, 0.221, 0.655, and 0.997, respectively. The least file size of 0.049 corresponds to parameter set 13 which may be selected as the preferred set of encoding parameters. 0202 FIG.31 illustrates optimal encoding schemes based on the methods of the present invention. As described above, the properties of an encoded signal are modelled using the parametric functions T(q, r, p), S(q, r, p), and B(q, r, (p). The values of q, r, and (p may be constrained to decoder-specific values which may vary from one decoder to another. In addi tion to parametric constraints, other constraints relevant to the file size of or flow rate of an encoded signal may be imposed. It may also be desirable to impose a constraint regarding a lower bound of an acceptable fidelity index. 0203. In accordance with one embodiment, the objective is to select a set of encoding parameters (q, r, (p) which yields an encoded signal of least file size while satisfying at least one of two conditions: having a fidelity index higher than, or equal to, a specified lower bound; and having a flow rate not exceed ing a specified upper bound. The function S(q, r, (p) would then be an objective function (3130) while at least one of the two functions T(q, r, p), B(q, r, p), would be a constraint function (3120, 3110). 0204. In accordance with another embodiment, the objec tive is to select a set of encoding parameters (q, r, (p) which yields an encoded signal of least flow rate while satisfying at least one of two conditions: having a fidelity index higher than, or equal to, a specified lower bound; and having a file size not exceeding a specified upper bound. The function B(q. r, (p) would then be an objective function (3150) while at least one of the two functions T(q, r, p), S(q, r, p), would be a constraint function (3120,3140). 0205 Inaccordance with a further embodiment, the objec tive is to select a set of encoding parameters (q, r, (p) which yields an encoded signal of highest fidelity index while sat isfying at least one of two conditions: having a file size not exceeding a specified upper bound; and having a flow rate not exceeding a specified upper bound. The function T(q, r, p) would then be an objective function (3160) while at least one of the two functions S(q, r, (p) and B(q, r, p), would be a constraint function (3140, 3110). What is claimed is: 1. A method, implemented in an encoder having a proces Sor, comprising: acquiring a first signal; determining descriptors of said first signal; acquiring characteristics of a receiver; selecting a preferred set of encoding parameters compat ible with said descriptors and said characteristics for May 21, 2015 US 2015/O 1393O2 A9 encoding said first signal to produce a second signal of limited by a specified maximum file size; and encoding said first signal according to said set of encoding parameters. 2. The method of claim 1 wherein said first signal is a video signal and said descriptors include an indicator of scene varia tion rate. 3. The method of claim 1 wherein said characteristics include a lower bound of quantization step, an upper bound of a display resolution, and an upper bound of a frame rate. 4. The method of claim 1 wherein: said first signal is a video signal; and said set of encoding parameters comprises a quantization step, a display resolution, and a frame rate. 5. The method of claim 4 further comprising: acquiring a first number of reference data records, each reference data record indicating file size corresponding to a respective set of encoding parameters; and generating a table, based on an analytical function relating file size to encoding parameters, said table indicating file sizes corresponding to a second number of sets of encod ing parameters, said second number exceeding said first number. 6. The method of claim 5 further comprising examining said table to identify at least one set of encoding parameters compatible with said receiver characteristics and correspond ing to a file size not exceeding said specified maximum file size. 7. The method of claim 4 further comprising generating: first table, based on a first analytical function relating fidel ity indices to encoding parameters, said first table indi cating fidelity indices corresponding to a second number of sets of encoding parameters, said second number exceeding said first number; and a second table, based on a second analytical function relat ing file sizes to encoding parameters, said second table indicating file sizes corresponding to said second num ber of sets of encoding parameters. 8. The method of claim 7 further comprising: examining said second table to identify candidate sets of encoding parameters each corresponding to a file size not exceeding said specified maximum file size and compatible with said receiver characteristics; examining said first table to determine fidelity indices cor responding to said candidate encoding parameters; and determining said preferred set of encoding parameters as one of said candidate sets of encoding parameters cor responding to a highest fidelity index. 9. The method of claim 7 further comprising: Sorting said second table in an ascending order of file sizes to produce a sorted table: using bisecting search to determine a first entry of said Sorted table corresponding to a file size nearest to and not exceeding said specified maximum file size; examining at least two Successive entries of said sorted table, starting with said first entry, corresponding to candidate sets of encoding parameters compatible with said receiver characteristics; examining said first table to determine fidelity indices cor responding to said candidate set of encoding parameters; and determining said preferred encoding parameter set as one of said candidate set of encoding parameters corre sponding to a highest fidelity index. 10. The method of claim 4 wherein said selecting com prises: acquiring predetermined data records, each indicating a fidelity index and a file size corresponding to one of a collection of sets of encoding parameters; identifying a number of candidate data records each corre sponding to: a file size not exceeding said specified maximum file size; and a set of encoding parameters compatible with said descriptors and said characteristics; and identifying a data record of said candidate data records corresponding to a highest fidelity index. 11. The method of claim 4 wherein said selecting com prises: acquiring reference data records, each indicating a fidelity index and a file size corresponding to one of a collection of sets of encoding parameters; devising a first analytical function relating a fidelity index of said second signal to encoding parameters; devising a second analytical function relating a file size of said second signal on encoding parameters; and evaluating said first analytical function and said second analytical function to identify a set of encoding param eters corresponding to a file size not exceeding said specified maximum file size and a highest fidelity index as said preferred set of encoding parameters. 12. The method of claim 4 wherein said selecting com prises: acquiring a first number of reference data records, each reference data record indicating a fidelity index corre sponding to a respective set of encoding parameters; executing a regression-analysis process to determine con stants C, B, Y, Ö, and m defining a second analytical function quantifying dependence of a fidelity index on encoding parameters q, r, and (p, said first analytical function being of the form where q is a ratio of a minimum quantization step to a candidate quantization step, r is a ratio of a candidate display resolution to a maximum display resolution, and (p is a ratio of a candidate framerate to a maximum frame rate. 13. The method of claim 4 wherein said selecting com prises: acquiring a first number of reference data records, each reference data record indicating a fidelity index corre sponding to a respective set of encoding parameters; and executing a regression-analysis process to determine con stants S2, W, 0, O, e, and () defining an analytical function quantifying dependence of a file size on encoding parameters q, r, and (p, said first analytical function being of the form where q is a ratio of a minimum quantization step to a candidate quantization step, r is a ratio of a candidate display resolution to a maximum display resolution, and (p is a ratio of a candidate framerate to a maximum frame rate. 14. The method of claim 4 wherein said selecting com prises: acquiring a first number of reference data records, each reference data record indicating a file size corresponding to a respective set of encoding parameters; and May 21, 2015 US 2015/O 1393O2 A9 executing a regression-analysis process to determine con stants S2, W, 0, O, e, and () defining a second analytical function quantifying dependence of a relative bit rate on encoding parameters q, r, and (p, said second analytical function being of the form examining at least two entries of said sorted table, adjacent to said first entry, corresponding to candidate sets of encoding parameters compatible with said receiver char where q is a ratio of a minimum quantization step to a candidate quantization step, r is a ratio of a candidate display resolution to a maximum display resolution, and (p is a ratio of a candidate framerate to a maximum frame determining said preferred set of encoding parameters as one of said candidate sets of encoding parameters cor responding to a highest fidelity index. rate. 15. A method, implemented in an encoderhaving a proces Sor, comprising: acquiring a first signal; determining descriptors of said first signal; acquiring characteristics of a receiver, determining a permissible flow rate over a path from said encoder to said receiver; Selecting a preferred set of encoding parameters compat ible with said descriptors and said characteristics for encoding said first signal to produce a second signal of said permissible flow rate; and encoding said first signal according to said encoding parameters. 16. The method of claim 15 wherein said first signal is a Video signal, said set of encoding parameters comprises a quantization step, a display resolution, and a frame rate; and said selecting comprises: acquiring predetermined data records, each indicating a flow rate corresponding to one of a collection of sets of encoding parameters; identifying candidate data records each corresponding to: a flow rate not exceeding said permissible flow rate; and a set of encoding parameters compatible with said descriptors and said characteristics; and identifying one of said candidate data records correspond ing to a highest fidelity index. 17. The method of claim 15 further comprising generating: a first table, based on a first analytical function indicating fidelity indices corresponding to said second number of sets of encoding parameters, said second number exceeding said first number; a second table, based on a second analytical function, indi cating relative flow rates corresponding to a second number of sets of encoding parameters. 18. The method of claim 17 further comprising: examining said second table to identify candidate sets of encoding parameters compatible with said receiver char acteristics and corresponding to a flow rate not exceed ing said permissible flow rate; examining said first table to determine fidelity indices cor responding to said candidate encoding parameters; and determining said preferred set of encoding parameters as one of said candidate sets of encoding parameters hav ing a highest fidelity index. 19. The method of claim 18 further comprising: Sorting said second table in a descending order of relative flow rates to produce a sorted table; using bisecting search to determine a first entry of said sorted table corresponding to a relative flow rate nearest to and not exceeding said permissible flow rate; acteristics; examining said first table to determine fidelity indices cor responding to said candidate sets of encoding param eters; and 20. The method of claim 17 wherein: said first signal is a video signal, said set of encoding parameters comprises a quantization step, a display resolution, and a frame rate; said first analytical function is of the form said second analytical function being of the form B(q, r (p)=1-2+2xxqx(1+e'*)'xp'; where q is a ratio of a minimum quantization step to a candidate quantization step, r is a ratio of a candidate display resolution to a maximum display resolution, and (p is a ratio of a candidate framerate to a maximum frame rate, C, B, Y. Ö, m, S2, W, 0, O, e, and () are constants. 21. The method of claim 20 further comprising: acquiring a first number of reference data records, each reference data record indicating a fidelity index and a relative flow rate corresponding to a respective set of encoding parameters; executing a first regression-analysis process to determine constants C, B, Y., 8, and m defining said first analytical function relating fidelity index to encoding parameters q, r, and (p; and executing a second regression-analysis process to deter mine constants S2, W, 0, O, e, and () defining said second analytical function relating flow rate to encoding param eters q, r, and (p. 22. An apparatus for signal encoding comprising a proces sor and at least one memory device storing: reference data records, each reference data record indicat ing a fidelity index and a file size corresponding to one of a collection of sets of encoding parameters; processor-executable instructions devised to: define a first analytical model for determining fidelity indices and a second analytical model for determining file sizes based on said reference data records; and generate two tables of fidelity indices and file sizes cor responding to a number of sets of encoding param eters exceeding a number of said reference data records; processor-executable instructions for determining charac teristics of a target receiver of a video recording; and processor-executable instructions causing said processor to examine said tables to identify a set of encoding parameters compatible with said characteristics and cor responding to a highest fidelity index and a file size not exceeding a specified upper bound. 23. An apparatus for signal encoding comprising a proces sor and at least one memory device storing: reference data records, each reference data record indicat ing a fidelity index and a relative flow rate corresponding to one of a collection of sets of encoding parameters; US 2015/O 1393O2 A9 May 21, 2015 18 processor-executable instructions devised to: define a first analytical model for determining fidelity indices and a second analytical model for determining relative flow rates based on said reference data records; and generate two tables of fidelity indices and relative flow rates corresponding to a number of sets of encoding parameters exceeding a number of said reference data records; processor-executable instructions for determining charac teristics of a target receiver of a video recording; and processor-executable instructions causing said processor to examine said tables to identify a set of encoding parameters compatible with said characteristics and cor responding to a highest fidelity index and a flow rate not exceeding a specified upper bound. k k k k k