Error Correction Coding

This paper examines the arbitrage-induced in regimes (upper, inner and lower regime) price dynamics between Hushen 300 index spot and futures markets using a threshold cointegration analysis and Error Correction Model (ECM) on china stock market index.. The studies are carried out from 426 observations with samples selected from 04/16/2010 to 03/16/2012. We are interested to know what extent of mispricing would represent for profitable arbitrage opportunity. Futures prices would have a fluctuating effect within lower and upper thresholds by the factors of transaction costs and arbitrage risks, but no profitable arbitrage opportunities within this area.

... Parts of some chapters grew out of lecture notes based on these books and the connections will be obvious. ... 269 6.8.1 Equivalence of the Two Reed-Solomon Code Constructions .... ... 281 Resources and Implementation Suggestions Lab 7 programming the BCH Decoder ...

Error correcting codes are used for detection and correction of errors in digital communication system. Error correcting coding is based on appending of redundancy to the information message according to a prescribed algorithm. Reed Solomon codes are part of channel coding and withstand the effect of noise, interference and fading. Galois field arithmetic is used for encoding and decoding reed Solomon codes. Galois field multipliers and linear feedback shift registers are used for encoding the information data block. The design of Reed Solomon encoder is complex because of use of LFSR and Galois field arithmetic. The purpose of this paper is to design and implement Reed Solomon (255, 239) encoder with optimized and lesser number of Galois Field multipliers. Symmetric generator polynomial is used to reduce the number of GF multipliers. To increase the capability toward error correction, convolution interleaving will be used with RS encoder. The Design will be implemented on Xilinx FP...

In digital communication system error correction codes are used when channel is noisy. An error correction code removes errors induced in communication and make possible error free transmission. By use of such error correction code we can send signal at lower transmit power as compared to un-coded system. Convolutional code corrects both type of errors random and burst and used in deep space and wireless communication. This paper introduces convolutional encoders for various code rates and generator polynomials and calculates BER performance for coded and un-coded system. Generator polynomials were selected for code rate 1/2, 1/3, and 1/4 on the basis of BER performance. This paper presents the signal power gain achieved by convolutional code as compared to un-coded system.

In digital communication forward error correction methods have a great practical importance when channel is noisy. Convolutional error correction code can correct both type of errors random and burst. Convolution encoding has been used in digital communication systems including deep space communication and wireless communication. The error correction capability of convolutional code depends on code rate and constraint length. The low code rate and high constraint length has more error correction capabilities but that also introduce large overhead. This paper introduces convolutional encoders for various constraint lengths. By increasing the constraint length the error correction capability can be increased. The performance and error correction also depends on the selection of generator polynomial. This paper also introduces a good generator polynomial which has high performance and error correction capabilities.

In late 2014 an observer commented that I could improve my teaching by encouraging learners to rely less on the teacher for feedback, and I should think of ways to push students to work harder during this phase of a lesson.

It was through this process that I was introduced to the Cambridge English/English UK Action Research Scheme and subsequently peer assessment. Writing was chosen for two reasons. First, I felt it was the skill that was most neglected in my classroom and, despite lots of writing being done in the form of notes or practising grammatical structures, teaching writing and analysing it were not common practice. Second, writing covered a concrete opportunity for students to assess each other’s work at A2/pre-intermediate level, whereas an assessment of oral performance would be both too subjective and too diffcult. My hope was that through regular consultation with each other about their written work, students would move from a position of needing someone to point out their own errors to being able to see them for themselves. I was keen to use peer assessment as a way of fostering the students’ future autonomy. My interest was further piqued to learn about the relative scarcity of application of peer assessment in EFL.

My study took place at Eurocentres Bournemouth, a private language school o ering General English courses to students from 16 years of age. Over a 12-week period, 28 students, aged from 17 to 65, participated from 11 countries in an A2 class. Students stayed from between a week to 12 weeks.

This paper considers the prototyping of linear block codes encoder and decoder for sound data using National Instruments LabView software. Linear block codes can be defined by two parameters, which are code size n and information bit size k.  LabView is an easy to use, multipurpose software which has many features for designing and prototyping. This research is a preliminary research on channel coding implementation on LabView. In this research, Hadamard codes are used to implement the design. 16-bit sound data are used as test subjects for block code encoding, decoding, and error correction. The result shows that the design works well. The design can correct single bit error in any positions. Authors’ next project is to implement cyclic and more advanced code for error correcting implementation in LabView.

Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets,  approximate computing has become, not merely attractive, but even imperative. In this paper, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. We classify these techniques based on several key characteristics to emphasize their similarities and differences. The aim of this paper is to provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the  mainstream computing approach in future systems.

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This paper considers the implementation of cyclic codes encoder and decoder for multimedia content in the form of sound data using National Instruments LabView software. Cyclic codes can be defined by two parameters, which are code size n and information bit size k.  LabView is an easy to use, multipurpose software which has many features for designing and prototyping. This research is a preliminary research on channel coding implementation on LabView. In this research, cyclic codes are used to implement the design. 16-bit sound data are used as test subjects for cyclic code encoding, decoding, and error correction. The result shows that the design works well. The design can correct short two-bit error in last n-k position of the codeword. Authors’ next project is to implement more advanced code for error correcting implementation in LabView.

This short article gives an introduction to binary linear block codes for error detection and error correction.  Various codes are discussed and compared, including repetition codes, Hamming codes, and Reed-Muller codes.

A version of this article was published by the Radio Society of Great Britain in their members' magazine/journal, 'RadCom'.

Encryption is the process of encoding messages in such a way, that they can only be decoded by the intended receiver. On the other hand, physical-layer (PHY) security exploits channel characteristics, such as noise and multipath fading, in order to ensure confidential transmission. Even though PHY security had initially been considered as an impractical theoretical concept with little application to reality, the continued improvement in the processing power of eavesdroppers’ devices has made encryption methods more vulnerable to cryptanalytic attacks. Therefore, both from an academic and an industrial point of view, PHY security has attracted considerable attention, due to its independence from the computational strength of the eavesdropper.
In this thesis, recent research efforts on PHY security are outlined, and novel mathematical expres- sions for problems related to PHY security are derived. Also, methods and algorithms are proposed, which aim to improve the performance of existing ones. The thesis is divided into three main parts.
The first part examines PHY security from an information-theoretic standpoint, by evaluating mea- sures, such as the secrecy capacity and the secrecy outage probability (SOP). Specifically, the impact of location uncertainty of the eavesdropper on PHY security in wireless systems is evaluated and quantified. A single-antenna downlink system with a single legitimate user and an eavesdropper is considered, and the eavesdropper’s location is modeled as a two-dimensional uniform distribution over a ring-shaped area around the base-station (BS). An exact, closed-form expression for the SOP is derived, as well as a simplified expression for the case of free-space transmission. Moreover, a closed-form expression for the SOP is derived for the case, where the distance between the BS and the eavesdropper is modeled as a one-dimensional uniform distribution from the inner to the outer radius of the ring. Insights are given and conclusions are drawn based on the offered results for the SOP. Next, the effect of interference on the SOP is investigated, in a single-antenna downlink system with a single legitimate user and an eavesdropper. An arbitrary number of broadcasting BSs, whose signals are treated by the legitimate receiver and the eavesdropper as interference, is assumed. Also, all the wireless links in the system are subject to Rayleigh fading. Under these assumptions, an exact, closed-form expression is derived for the SOP. Numerical results for the SOP are provided and conclusions are drawn.
The second part deals with PHY key exchange algorithms, and specifically ones that are based on multipath fading. First, a novel least-square channel thresholding process is presented, so that the transmitter and the legitimate receiver each generate a bit string, based on their respective channel responses. According to the principle of reciprocity, the two bit strings are almost identical. The proposed thresholding method leads to a larger number of series of consecutive ones in the generated bit strings, compared to the case where a constant threshold is used. It is demonstrated that, when this method is used in the context of a PHY key exchange algorithm, this property leads to better protection from eavesdropper attacks. Next, two error reconciliation methods are proposed, in order to correct the discrepancies between the bit strings generated by the transmitter and the legitimate receiver. The first method is based on a neural network, which is constructed and trained by the transmitter, so that inputs similar to its bit string are changed to the correct value. Afterwards, the receiver’s bit string is fed through the neural network, which corrects the bit discrepancies with the transmitter’s bit string. The second method uses block error correction coding, in order to perform error reconciliation. Also, the average number of consecutive ones is used in order to produce a mask, that increases the security of the method against brute-force attacks. The two methods are shown, through simulations, to have higher key agreement rates than other methods proposed in the literature.
The third part focuses on polar codes, and particularly the design of polar codes for the relay channel. An erroneous decoding detection method is proposed, which we refer to as “smart” relaying. This technique can be applied to a polar coding scheme, where successive cancellation decoding is used. Specifically, the log-likelihood ratios (LLRs) used at any point in the decoding process are compared with a threshold parameter, and if a decision is made by taking into consideration an LLR that is too close to 1, the decoded result is discarded. In this case, the relay does not retransmit the message, since it is more likely that the receiver will make the correct decision by only taking into consideration the information received from the direct source-destination channel. Otherwise, part of the information is re-encoded by the relay with a capacity-achieving polar code for the relay-destination channel, and re-transmitted to the destination. A combination of the information received by the source and the relay is used in order to reconstruct the original message. Furthermore, a condition is proven, that shows in which cases “smart” relaying yields a better block error rate, compared to the case where “smart” relaying is not used. An extension of this technique to multiple parallel relay systems is also proposed. Finally, simulation results are presented, in order to illustrate the performance of the proposed method.

Abstract — As the adoption of Information and Communication Technology (ICT) tools in production and service rendering sectors increases, the demand for digital data storage with large storage capacity also increases. Higher storage media systems reliability and fault tolerance are among the key factors that the existing systems sometimes fail to meet and therefore, resulting into data loss. Forward error correction is one of the techniques applied to reduce the impact of data loss problem in digital data storage. This paper presents a survey conducted in different digital data storage companies in Dar es Salam, Tanzania. Data were collected and analyzed using Statistical Package for Social Sciences (SPSS). Secondary data were captured from user and manufacturer technical reports. It was revealed that data loss is still a predominant challenge in the digital data storage industry. Therefore, the study proposes the new storage media FEC model using locked convolutional encoder with the enhanced NTC Viterbi decoder.

Index Terms—Storage Media, FEC, NTC, Viterbi, RS

https://sites.google.com/site/ijcsis/

This paper is an attempt to ascertain the suitability of computers for second and foreign language (SL/FL) error correction, especially those made by SL/FL learners. For this purpose, the handling of such errors proposed in Second Language Acquisition (SLA) literature will be examined. Subsequently the technologies capable of evaluating student output and identifying and correcting Non-Native Speaker (NNS) errors will be examined. Though it will be made quite clear that the computer cannot substitute a human being in total language processing, some strengths of artificial intelligence in partial language processing will be pointed out and their suitability for L2 error correction will be highlighted. The article will conclude emphasizing that the use of high quality multimedia applications and programmes stimulates and fosters language learning.

Key words: computer, language errors, error correction, second language (L2), Computer Assisted Language Learning (CALL), Intelligent CALL (ICALL).

With the exception of some households that have been able to recycle their Yagi-Uda antennas (VHF, UHF or Dualband types) for reception of ATSC most North American households will continue to have television reception quality far below what the 8VSB signal transmission system is capable of achieving.

Historically : NTSC, PAL or SECAM fadeout events generally are "long duration" events due to the continuous wave nature of the traditional TV transmission signal.

These fadeout events were tolerable (or at least interesting) to the traditional analogue television viewer.

ATSC 8VSB fadeout events in the digital television era are generally catastrophic and random.

These fadeout events alienate less technically inclined television viewers, as the cause of reception failure is often not obvious.

Viewers in general expect digital television (regardless of how it is transmitted) to be more reliable than analogue television. This reliability has not yet been achieved.

Most 8VSB set top box decoders (as of the mid to late 2010s) only possess "2nd generation" adaptive reception chipsets.

These chipsets [and their associated receiver subsystems] have on average only adequate sensitivity to weak signals.

These receivers possess only a limited ability to cope with
instantaneous fade out events.

Longer duration fade out events are at best "coped with" generally with variable degrees of success.

The most up to date 3rd and 4th generation 8VSB adaptive reception chipsets often do not perform as optimally as their designers originally hoped.

There are a myriad of subtle (and gross) design and transmission issues that these receivers must cope with that are beyond the ability of a laboratory to simulate adequately.

Currently the ATSC HDTV viewer is left only with ongoing frustration.

Most 8VSB decoders uniformly fail to tell the viewer that the received signal is unhealthy before a link loss event.

Long duration fade events (as with analogue television) don't really happen with 8VSB as the digital television transmitters use 2/3rds to 1/3rd less power than their previous analogue relative.

Essentially, fractal antennas are the only way to make 8VSB HDTV reception reliable again, at the lowest possible cost to all parties involved.

In satelite communication there are so many different noise characteristics which causes of errors. In this work to facilitate the error free satelite communication we examined the causes of the errors and seeked the ways of reduction the effects of these errors. Furthermore, main study is to make an FPGA core for Forward Error Correcting codes which can be used for Telecommand(TC) Space Data Link Protocol is defined by Consultative Committee for Space Data Systems (CCSDS). The modified special code Bose-Chaudhuri-Hocquenghem(BCH) using a data unit called the Communications Link Transmission Unit (CLTU), which consists of a Start Sequence, BCH Codeblocks, and a Tail Sequence was implemented by VHDL , simulations were also done for one , two and three bit errors in fifty six bits of data. The simulations show us this code detects and corrects one bit error and shows the location of the error , for more bit errors it only detects the error. For datarate and error correction simplicity of TC link this code has optimum performance .

Implementarea, în limbajul de descriere hardware Verilog, a modulului Error Correction Code bazat pe codul Hamming, pe 32 de biți. Documentația conține o introducere, cerințe de sistem, descrierea funcționalității modulului, detalii legate de implementare propriu-zisă, pseudocod, erori întâmpinate, testbench și bibliografie.

This paper considers the prototyping of linear block codes encoder and decoder for sound data using National Instruments LabView software. Linear block codes can be defined by two parameters, which are code size n and information bit size k.  LabView is an easy to use, multipurpose software which has many features for designing and prototyping. This research is a preliminary research on channel coding implementation on LabView. In this research, Reed-Muller codes are used to implement the design. 16-bit sound data are used as test subjects for block code encoding, decoding, and error correction. The result shows that the design works well. The design can correct single bit error in any positions. Authors’ next project is to implement cyclic and more advanced code for error correcting implementation in LabView.

In the field of language teaching and learning, one of the most difficult and challenging skills to acquire is writing. Most teachers of writing struggle over which approaches, methods and classroom activities are the most effective to fulfill the writing course objective. The general aim of teachers of writing, especially at the college level, is, generally, to lead students to produce a coherent, well-thought, and well-articulated piece of writing. Therefore, one way to help students and guide them to achieve this goal is the response to students' written errors. In this regard, the present study endeavors to investigate the role of Written Corrective Feedback (WCF) on the development of EFL learners' writing skills. With special reference to the English department in Rabat, this study purports to reveal to what extent WCF can impact the writing skills of EFL learners at the university. A further objective of this study is to show which method of WCF is more effective in the development of university students' writing skills.

This research was aimed to find out the kind of errors and the dominant error at the first grade students of SMP Swasta Kartika 1-2 Medan in constructing negative and interrogative sentences by using simple present tense in academic year 2019/2020. In this research, the subject was only VII-3s’ class with 28 students in one class. This research was a qualitative research with a descriptive method. The data obtained from the errors made by the students in written test which consisted of 20 questions. In this study, the result of analyzed the data by calculating the errors, there were 554 case of errors with 4 types of errors made by the students in their written test of using simple present tense, they were: 197 (35,55%) case of errors on misformation; 177 (31,94%) case of errors on omission; 165 (29,78%) case of errors on addition; and 15 (2,70%) case of errors on misordering, where error of misformation as a type of dominant error.

The performance of a communication system is mainly depending on channel between the receiver and the transmitter in the system. Therefore, the most important thing for communication is the channel which is affected by parameters such as noise, fading, shadowing, and interference. These effects complicate for the receiver to obtain the transmitted signal. Communication systems use coding and interleaving techniques to reduce or eliminate the disturbing effect of these channels. The graphical user interface (GUI) is a graphical development environment that provides designers with a variety of tools and facilities for their convenience. Recently, GUI based applications have been preferred in vocational and technical education. The development of such applications accelerates the learning process of the students by showing the effects of system's case changes. MATLAB is software that has proven its importance in vocational and technical education with its useful interface, the speed of calculations, and the ability to visualize data. The GUI, which is a component of MATLAB, decreases the complexity of the code in software and increases the clarity of the subject. In this study, a GUI based communication system training platform was realized in MATLAB according to the near to real time parameters. The results show that the developed training application instantly displays changes to the channel and is user-friendly for students. In addition, it is thought that the use of GUI interface in vocational and technical education will provide a tangible benefit.

This study investigates the efficacy of written corrective feedback on two groups of first-semester JFL students’ homework. The treatment group was required to respond to “dynamic written corrective feedback (WCF),” which is modeled after a study by Hartshorn, K. J., Evans, W. N., Merrill, F. P., Sudweeks, R. R., Strong-Krause, D., and Anderson, J. N.. (2010), by continuously correcting/revising their homework by using metalinguistic error codes, answer keys, and maintaining an error log. In contrast, the control group was required to correct/revise the homework only once by looking at the answer keys. The research investigated dynamic/non-dynamic WCF in terms of (1) the accuracy rate of particles and predicates in grammar exercises and essay writing, (2) the overall quality of students’ essay writing, and (3) students’ perception of dynamic WCF. The Wilcoxon rank-sum test concluded that the median accuracy rate of the particle usage was significantly different (p<.05) in grammar tests, but not significant in essay writing. For accurate use of predicates, a significant difference was observed in essay writing, but not in grammar tests despite observable improvement in the latter. As for the overall quality of essay writing, the two groups did not differ significantly. The qualitative data, on the other hand, indicated the necessity to implement metalinguistic error codes and the tally sheet with sufficient planning and caution to make best use of the practice.

Tez çalışması, uydu haberleşme sistemleri aracılığıyla yapılan sayısal video yayınlarının alıcı tarafında kulanılan ileri hata düzeltme birimi tasarımı ve gerçeklemesini kapsamaktadır. Bu kapsamda Avrupa Telekominikasyon Standardı Enstitüsü (ETSI) tarafından İkinci Nesil Sayısal Video Yayını (DVB-S2) için belirtilen standartlar göz önüne alınmıştır. Alıcı tarafı DVB-S2 ileri hata kod çözücü birimi standartlar incelenerek ve daha önceki çalışmalar dikkate alınarak tasarlanmış ve VHDL kodları yazılarak donanımsal olarak gerçeklenmiş MODELSIM yardımıyla benzetimleri yapılmış ve MATLAB yardımıyla da doğrulanmıştır.
BCH kod çözücüsü tasarımında hızlı aynı zamanda kapladığı alan açısından da az ve esnek bir yapı oluşturulmuştur. Dışarıdan set edilebilen parametrelerle değişik veri uzunluklarına uyumlu bir tasarım yapılmıştır. Hata belirteci(syndrome) hesaplamada paralel GF çarpıcıları kullanılırak hızlı olması sağlanmıştır. Anahtar eşitlik çözücüde gecikmenin ve kritik yol beklemesinin(Critical path delay) en az olması için RiBM (Reformulated inverse-free Berlekamp-Massey) algoritması kullanılmıştır. Fifo büyüklükleri dışarıdan set edilebilecek şekilde esnek yapılmıştır.
LDPC kod çözücü yapısında hızlı haberleşme sistemleri için ideal olan belief propagation yöntemi seçilmiş literatürden farklı olarak karmaşıklığı ve kapladığı alanı azaltmak amacıyla min-sum algoritması kullanılmıştır. Tekrar hız açısından verimli olması amacıyla düzenli H matrisi güvenilir bir kaynaktan kenar tablosu alınarak oluşturulmuştur. İterasyon sayısı, mod kodu, veri uzunlukları dışarıdan girilebilecek şekilde yapılarak hertürlü(yer ya da hız) kısıt için optimum ayarlanabilecek bir tasarım oluşturulmuştur. Gerek hız gerek yer açısından bit ve kontrol noktaları RAM leri 360 bitlik gruplara ayrılarak kısmi paralel bir yapı oluşturulmuştur. Hesaplanan LLR değerlerinden sadece 2 si tutularak literatürdekilere göre yerden kazanç sağlanmıştır. Yumuşak karar LDPC kodu kullanılarak yerden tasarruf sağlanmış kodlama performansı artırılmıştır.

Приведены результаты сравнения производительности многопоточной реализации  декодера  турбокода  на  базе  процессоров  Intel  и  графических  процессоров nVidia  выпуска 2010–2013  гг . Показано, что  внутри одного поколения и  ценовой категории процессоров использование технологии CUDA позволяет получить вы-
игрыш  по  быстродействию  в  3…10  раз  относительно  центрального  процессора. Определены  факторы,  ограничивающие  область  применения  технологии  CUDA
при реализации турбодекодера.

We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in PG(4,q) to find information about the LDPC codes defined by Q (4,q), ${\mathcal{W}(q)}$ and ${\mathcal{H}(3,q^{2})}$ . For ${\mathcal{W}(q)}$ , and ${\mathcal{H}(3,q^{2})}$ , we are able to describe small weight codewords geometrically. For ${\mathcal{Q}(4,q)}$ , q odd, and for ${\mathcal{H}(4,q^{2})^{D}}$ , we improve the best known lower bounds on the minimum distance, again only using geometric arguments. Similar results are also presented for the LDPC codes LU(3,q) given in [Kim, (2004) IEEE Trans. Inform. Theory, Vol. 50: 2378–2388]

One of the key technologies for future IoT/M2M systems are low power wide area networks, which are designed to support a massive number of low-end devices often in the unlicensed shared spectrum using random access protocols. However these usually operate without centralised control and since Automatic Repeat request and acknowledgement mechanisms are not very effective due to the strict duty cycles limits and high interference in the shared bands, many packets are lost from collisions. In this paper we analyse a recently proposed application layer coding scheme, which aims to recover lost packets by introducing redundancy in the form of a fountain code. We show how latency and decoding complexity is affected by the packet loss rate but also prove that there is a limit to what can be achieved by introducing more redundancy. The analysis is backed up by simulation results