Francisco A . Monteiro

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to efficiently decode classical random linear codes (RLCs) performing near the maximum rate of the finite blocklength regime. By using noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, provided that a simple code membership test exists. These conditions are particularly suitable for quantum systems, and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum-GRAND, this work shows that it is possible to decode QECCs that are easy to adapt to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum-GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding. INDEX TERMS GRAND, ML decoding, quantum error correction codes, short codes, syndrome decoding.

Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for low-latency communications, as it supports error correction codes that generate short codewords. GRAND estimates transmitted codewords by guessing the error patterns that altered them during transmission. The guessing process requires the testing of error patterns that are arranged in increasing order of Hamming weight. This approach is fitting for binary transmission over additive white Gaussian noise channels. This letter considers transmission of coded and modulated data over block fading channels and proposes a more computationally efficient variant of GRAND, which leverages information on the modulation scheme and the fading channel. In the core of the proposed variant, referred to as symbol-level GRAND, is an expression that approximately computes the probability of occurrence of an error pattern and determines the order with which error patterns are tested. Analysis and simulation results demonstrate that symbol-level GRAND produces estimates of the transmitted codewords faster than the original GRAND at the cost of a small increase in memory requirements.

A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G’s polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency.

A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.

A fully-quantum network implies the creation of quantum entanglement between a given source node and some other destination node, with a number of quantum repeaters in between. This paper tackles the problem of quantum entanglement distribution by solving the routing problem over an infrastructure based on quantum repeaters and with a finite number of pairs of entangled qubits available in each link. The network model considers that link purification is available such that a nested purification protocol can be applied at each link to generate entangled qubits with higher fidelity than the original ones. A low-complexity multi-objective routing algorithm to find the shortest path between any two given nodes is proposed and assessed for random networks, using a fairly general path extension mechanism that can fit a large family of particular technological requirements. Different types of quantum protocols require different levels of fidelity for the entangled qubit pairs. For that reason, the proposed algorithm identifies the shortest path between two nodes that assures an end-to-end fidelity above a specified threshold. The minimum requirements for the end-to-end entanglement fidelity depend on the whole extension of the paths, and cannot be looked at as a local property of each link. Moreover, one needs to keep track not only of the shortest path, but also of longer paths holding more entangled qubits than the shorter paths in order to satisfy the fidelity criterion. Thus, standard single parameter shortest-path algorithms do not necessarily converge to the optimal solution. The problem of finding the best path in a network subject to multiple criteria (known as multi-objective routing) is, in general, an NP-hard problem due to the rapid growth of the number of stored paths. This work proposes a metric that identifies and discards paths that are objectively worse than others. By doing so, the time complexity of the proposed algorithm scales near-to-linearly with respect to the number of nodes in the network, showing that the shortest-path problem in quantum networks can be solved with a complexity very close to the one of the classical counterparts. That is analytically proved for the case where all the links of a path have the same fidelity (homogeneous model). The algorithm is also adapted to a particular type of path extension, where different links along a path can be purified to different degrees, asserting its flexibility and near-to-linearity even when heterogeneous fidelities along the sections of a path are considered.

Wireless networks beyond 5G will mostly be serving myriads of sensors and other machine-type communications (MTC), with each device having different requirements in respect to latency, error rate, energy consumption, spectral efficiency or other specifications. Multiple-input multiple-output (MIMO) systems remain a central technology towards 6G, and in cases where massive antenna arrays or cell-free networks are not possible to deploy and only moderately large antenna arrays are allowed, the detection problem at the base-station cannot rely on zero-forcing or matched filters and more complex detection schemes have to be used. The main challenge is to find low complexity, hardware feasible methods that are able to attain near optimal performance. Randomized algorithms based on Gibbs sampling (GS) were proven to perform very close to the optimal detection, even for moderately large antenna arrays, while yielding an acceptable number of operations. However, their performance is highly dependent on the chosen “temperature” parameter (TP). In this paper, we propose and study an optimized variant of the GS method, denoted by triple mixed GS, and where three distinct values for the TP are considered. The method exhibits faster convergence rates than the existing ones in the literature, hence requiring fewer iterations to achieve a target bit error rate. The proposed detector is suitable for symmetric large MIMO systems, however the proposed fixed complexity detector is highly suitable to spectrally efficient adaptively modulated MIMO (AM-MIMO) systems where different types of devices upload information at different bit rates or have different requirements regarding spectral efficiency. The proposed receiver is shown to attain quasi-optimal performance in both scenarios.

Non-orthogonal multiple access (NOMA) concatenated with multiple-input multiple-output (MIMO) or with massive MIMO, has been under scrutiny for both broadband and machinetype communications (MTC), even though it has not been adopted in the latest 5G standard (3GPP Release 16), being left for beyond 5G. This paper dwells on the problems causing such cautiousness, and surveys different NOMA proposals for the downlink in cellcentered systems. Because acquiring channel state information at the transmitter (CSIT) may be hard, open-loop operation is an option. However, when users clustering is possible, due to some common statistical CSI, closed-loop operation should be exploited. The paper numerically compares these two operating modes. The users are clustered in beams and then successive interference cancellation (SIC) separates the power-domain NOMA (PD-NOMA) signals at the terminals. In the precoded closedloop system, the Karhunen-Loève channel decomposition is used assuming that users within a cluster share the same slowly changing spatial correlation matrix. For a comparable number of antennas the two options perform similarly, however, while in the open-loop downlink the number of antennas at the BS is limited in practice, this restriction is waived in the precoded systems, with massive MIMO allowing for a larger number of clusters.

A low complexity receiver which was devised in previous papers proved there to be quasioptimum over additive gaussian noise and also showed low power penalty with flat Rayleigh fading, i.e., with random phase, and despite the fact that one of three reduced complexity blocks of that receiver relies on symmetries on signal's phase transitions. This letter analyzes the origin of that error resilience during the derivation of the metrics.

This paper explores the feasible limits for complexity reduction of a very simple front-end block for the calculus of phase transition metrics on a continuous phase modulation (CPM) receiver. A quasi-optimum receiver of very low complexity is attained by splitting the function of the optimum receiver bank filters in two blocks: calculus of projections coefficients on a low dimensional space of Walsh functions followed by simple matrix calculus. A sequence detection algorithm follows this block. The presented approach enables the reduction of the matched filters or correlators to just two integrators, regardless of the CPM scheme. Research on the reduction limits of the space dimension is conducted using catastrophic M-ary CPM schemes, taking advantage of their very low number of phase states. Performance of 1REC h=1/2 16-ary scheme is for the fist time presented. A rule is defined concerning the number of Walsh functions that must be used. That outcome proves to be valid for two CPM schemes of high power gain. The receiver is tested under additive white gaussian noise (AWGN).

In this article a simulation environment for digital transmission systems is presented. Its application in digital transmission experimental learning is possible by allowing key parameters influence study through a graphical interface. It is possible to visualise some points of the system, modify structures and transmission parameters. Equivalent lowpass of BPSK and QPSK with limited Nyquist spectrum and nonlimited spectrum (finite time impulses) are considered. Fast BER curve estimation is obtained by a semi-analytical procedure.

Future networks are expected to depart from traditional routing schemes in order to embrace network coding (NC)-based schemes. These have created a lot of interest both in academia and industry in recent years. Under the NC paradigm, symbols are transported through the network by combining several information streams originating from the same or different sources. This special issue contains thirteen papers, some dealing with design aspects of NC and related concepts (e.g., fountain codes) and some showcasing the application of NC to new services and technologies, such as data multi-view streaming of video or underwater sensor networks. One can find papers that show how NC turns data transmission more robust to packet losses, faster to decode, and more resilient to network changes, such as dynamic topologies and different user options, and how NC can improve the overall throughput. This issue also includes papers showing that NC principles can be used at different layers of the networks (including the physical layer) and how the same fundamental principles can lead to new distributed storage systems. Some of the papers in this issue have a theoretical nature, including code design, while others describe hardware testbeds and prototypes.

The role of interference in wireless networks has recently been profoundly rethought with the emergence of new techniques for combating it and exploit it to maximize the use efficiency of the physical resources. This paper presents a two-way relay channel using a lattice-based physical layer network coding scheme, a massive MIMO array, and in-band full-duplex, taking into account the residual self-interference that results after applying recently developed cancellation techniques for the loopback interference. The proposed scheme is able to ultimately exchange information across the TWRC in only one time slot, whereas four time slots would be needed in a conventional TWRC. The system's performance is shown to be mostly dependent on the number of antennas at the relay, and also dependent on the channel state information of all the channel matrices, including the one describing the loopback interference at the relay. For base-stations and relays with a few hundred antennas, the proposed scheme is feasible for wireless systems.
Index Terms—In-band full-duplex, massive multiple-input multiple-output (MIMO), Physical Layer Network Coding (PLNC), Two-way Relay Channel.

In-band full-duplex transmission allows a relay station to theoretically double its spectral efficiency by simultaneously receiving and transmitting in the same frequency band, when compared to the traditional half-duplex or out-of-band full-duplex counterpart. Consequently, the induced self-interference suffered by the relay may reach considerable power levels, which decreases the signal-to-interference-plus-noise ratio (SINR) in a decode-and-forward (DF) relay, leading to a degradation of the relay performance. This paper presents a technique to cope with the problem of self-interference in broadband multiple-input multiple-output (MIMO) relays. The proposed method uses a time-domain cancellation in a DF relay, where a replica of the interfering signal is created with the help of a recursive least squares (RLS) algorithm that estimates the interference frequency-selective channel. Its convergence mean time is shown to be negligible by simulation results, when compared to the length of a typical orthogonal-frequency division multiplexing (OFDM) sequences. Moreover, the bit-error-rate (BER) and the SINR in a OFDM transmission are evaluated, confirming that the proposed method extends significantly the range of self-interference power to which the relay is resilient to, when compared with other mitigation schemes.

With the help of an in-band full-duplex relay station, it is possible to simultaneously transmit and receive signals from multiple users. The performance of such system can be greatly increased when the relay station is equipped with a large number of antennas on both transmitter and receiver sides. In this paper, we exploit the use of massive arrays to effectively suppress the loopback interference (LI) of a decode-and-forward relay (DF) and evaluate the performance of the end-to-end (e2e) transmission. This paper assumes imperfect channel state information is available at the relay and designs a minimum mean-square error (MMSE) filter to mitigate the interference. Subsequently, we adopt zero-forcing (ZF) filters for both detection and beamforming. The performance of such system is evaluated in terms of bit error rate (BER) at both relay and destinations, and an optimal choice for the transmission power at the relay is shown. We then propose a complexity efficient optimal power allocation (OPA) algorithm that, using the channel statistics, computes the minimum power that satisfies the rate constraints of each pair. The results obtained via simulation show that when both MMSE filtering and OPA method are used, better values for the energy efficiency are attained.

In general, lattice problems are simple to describe but rather hard to solve optimally. Several suboptimal solutions have been proposed for the closest vector problem (CVP), which is central in multiple-input multiple-output (MIMO) communication systems. It is known that some lattices have a trellis representation, however, those lattices require very particular geometries that are not found in lattices randomly generated. In this paper we show that for the typical number of dimensions used in MIMO communication, with high probability, there exists a synthetic lattice that is a member of the family of lattices that have a trellis representation and which is sufficiently close to any given random lattice. For that purpose we present a method to find a trellis-oriented basis for a given random lattice. The basis vectors of the synthetic lattice and the basis vectors of the original lattice are close and for finite alphabets the two lattices are roughly the same in the region of interest. Therefore, the optimal decision (Voronoi) regions of both lattices chiefly overlap. A linear transformation then focuses the original lattice onto the synthetic one, known to have a trellis representation. This minimizes the distortion of the Voronoi regions associated with maximum-likelihood detection and therefore the performance attained in the MIMO-CVP is close to optimal.

The superposition of waves caused by multipath propagation was for a long time considered an unavoidable nuisance in radio communication links. The discovery that multipath interference was central to enable much larger data rates was a breakthrough at the turn of the century. Multipleinput multiple-output (MIMO) spatial multiplexing (SM) allows unprecedented efficiency in the use of the radio spectrum, however, this comes at the cost of high complexity at the receiver because the underlying symbol detection problem belongs to the class of problems of highest computational complexity. In general, lattice problems are simple to describe but rather hard to solve optimally; finding algorithms to deal with the problem has been a central topic in the last decade of research in MIMO SM. This paper contributes to a deeper understanding of the most important types of receivers for SM with a unifying lattice perspective. Capitalising on that, two novel receivers are proposed. The geometric relation between the primal and the dual lattice is clarified, leading to the proposal of a preprocessing technique that greatly reduces the number of candidate solutions via geometric considerations. Then, looking at lattices from a group theory perspective, it is shown that it is possible to approximate the typical lattices encountered in MIMO by a lattice having a trellis representation, translating the problem for the first time into one manageable by the Viterbi algorithm, well known to the semiconductor industry.

Abstract This paper presents a lattice detection strategy for spatial multiplexing (SM) which takes advantage of a pre-processing stage based on the geometric relations between the points in the primal lattice and the ones in the dual lattice. The first part of the paper clarifies this geometric relationship that will be exploited later on in the design of a pre-processing stage for the proposed receiver. This pre-processing finds a set of successive minima in the dual lattice, and is only required at each channel update.

This paper explores the feasible limits for complexity reduction of a very simple front-end block for the calculus of phase transition metrics on a continuous phase modulation (CPM) receiver. A quasi-optimum receiver of very low complexity is attained by splitting the function of the optimum receiver bank filters in two blocks: calculus of projections coefficients on a low dimensional space of Walsh functions followed by simple matrix calculus. A sequence detection algorithm follows this block The presented approach enables the reductiou of the matched filters or correlators to just two integrators, regardless of the CPM scheme. Research ou the reduction limits of the space dimension is conducted using catastrophic Wary CPM schemes, taking advantage of their very low number of phase states. Performance of lREC h=1/2 16-ary scheme is for the fist time presented. A rule is defined concerning the number of Walsh functions that must be used. That outcome proves to be valid for two CPM schemes of high power gain. The receiver is tested under additive white gaussian noise (AWGN).

Neste artigo apresenta-se um simulador de um sistema de transmissão digital, DigiLab, desenvolvido em ambiente Matlab . A utilização é feita através de uma interface gráfica. Consideram-se modulações de fase binária e quaternária com espectro limitado e ilimitado. As simulações são realizadas através do equivalente passa-baixo e o desempenho é obtido de forma semi-analítica. A ferramenta encontra aplicação no ensino e na análise de novos sistemas.

The maximum likelihood detection of multiple input multiple output (MIMO) spatial multiplexing systems is strongly limited by its complexity. We propose that a quantized version of this problem permits the multiplications involved in the numerous calculations of Euclidean distances to be replaced by the use of a small look-up table storing all the exact possible distance components in each dimension of the quantized receive space. The number of pre-stored elements is as small as the number of quantization levels per dimension. This paper presents an approximate analysis of the quantization error which allows us to understand the results from simulations performed over fast flat fading channels for different MIMO systems.

The paper shows that some continuous phase modulation (CPM) schemes have some properties that allow a near optimum reception with very low complexity. The proposed reception method applies simultaneously three techniques for complexity reduction of CPM receivers, which have been previously object of separate analysis with additive white Gaussian noise (AWGN). These techniques are: first-quadrant metrics calculus on a F-dimensional Walsh space, derivation of the other quadrant metrics using a no loss derivation algorithm and finally the use of constrained complexity maximum likelihood sequence detection (MLSD) using the M-algorithm. The cumulative effect on total performance loss is negligible and no more than the sum of the partial losses due to the Walsh space and the M-algorithm, known to be negligible when observing the respective standalone rules for the complexity reduction limits.

This paper presents some results on teletraffic for environments with a dominant vehicular user profile in GSM. A model permitting exclusive channels for handover traffic is used and a discussion on the number of reserved channels for handover traffic is made. Blocking, handover failure and call dropping probabilities are examined for a typical traffic case on a GSM base station. For the analysed situation, 78 traffic channels, it is shown that a single dedicated channel is enough for a good quality of service.

Either in communication or in control applications, multiple-input multiple-output systems often assume the knowledge of a matrix that relates the input and output vectors. For discrete inputs, this linear transformation generates a multidimensional lattice. The same lattice may be described by an infinite number of generator matrixes, even if the rotated versions of a lattice are not considered. While obtaining the Gram matrix from a given generator matrix is a trivial operation, the converse is not obvious for non-square matrixes and is a research topic in algorithmic number theory. This paper proposes a method to execute such a conversion and applies it in a novel MIMO system implementation where most of complexity is taken from the receiver to the transmitter. Additionally, given the symmetry of the Gram matrix, the number of elements required in the feedback channel is nearly halved.