Design of LDPC codes and reliable practical decoders for standard and non-standard channels

Ph.DDOCTOR OF PHILOSOPH

On the Design of Punctured Low Density Parity Check Codes for Variable Rate Systems

The authors face the problem of designing good LDPC codes for applications requiring variable, that is adaptive, rates. More precisely, the object of the paper is twofold. On one hand, we propose a deterministic (not random) procedure to construct good LDPC codes without constraints on the code dimension and rate. The method is based on the analysis and optimization of the local cycles length in the Tanner graph and gives the designer the chance to control complexity of the designed codes. On the other hand, we present a novel puncturing strategy which acts directly on the parity check matrix of the code, starting from the lowest rate needed, in order to allow the design of higher rate codes avoiding additional complexity of the co/decoding hardware. The efficiency of the proposed solution is tested through a number of numerical simulations. In particular, the puncturing strategy is applied for designing codes with rate variable between 0.715 and 0.906. The designed codes are used in conjunction with M-QAM constellations through a pragmatic approach that, however, yields very promising results

Bandwidth-efficient communication systems based on finite-length low density parity check codes

Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part

Analysis and improvement of GNSS navigation message demodulation performance in urban environments

Global Navigation Satellite Systems (GNSS) are increasingly present in our everyday life. Further operational needs are emerging, mainly in urban environments. In these obstructed environments, the signal emitted by the satellite is severely degraded due to the many obstacles. Consequently, the data demodulation and the user position calculation are difficult. GNSS signals being initially designed in an open environment context, their demodulation performance is thus generally studied in the associated AWGN propagation channel model. But nowadays, GNSS signals are also used in degraded environments. It is thus essential to provide and study their demodulation performance in urban propagation channel models. It is in this context that this PhD thesis is related, the final goal being to improve GNSS signals demodulation performance in urban areas, proposing a new signal. In order to be able to provide and study GNSS signals demodulation performance in urban environments, a simulation tool has been developed in this PhD thesis context: SiGMeP for ‘Simulator for GNSS Message Performance'. It allows simulating the entire emission/reception GNSS signal chain in urban environment. Existing and modernized signals demodulation performance has thus been computed with SiGMeP in urban environments. In order to represent this demodulation performance faithfully to reality, a new methodology adapted to urban channels is proposed in this dissertation. Then, to improve GNSS signals demodulation performance in urban environments, the research axis of this thesis has focused on the ‘Channel Coding' aspect. In order to decode the transmitted useful information, the receiver computes a detection function at the decoder input. But the detection function used in classic receivers corresponds to an AWGN propagation channel. This dissertation thus proposes an advanced detection function which is adapting to the propagation channel where the user is moving. This advanced detection function computation considerably improves demodulation performance, just in modifying the receiver part of the system. Finally, in order to design a new signal with better demodulation performance in urban environments than one of existing and future signals, a new LDPC channel code has been optimized for a CSK modulation. Indeed, the CSK modulation is a promising modulation in the spread spectrum signals world, which permits to free from limitation sin terms of data rate implied by current GNSS signals modulations

A Framework for Low-Complexity Iterative Interference Cancellation in Communication Systems

Thesis Supervisor: Gregory W. Wornell Title: ProfessorCommunication over interference channels poses challenges not present for the more traditional additive white Gaussian noise (AWGN) channels. In order to approach the information limits of an interference channel, interference mitigation techniques need to be integrated with channel coding and decoding techniques. This thesis develops such practical schemes when the transmitter has no knowledge of the channel. The interference channel model we use is described by r = Hx + w, where r is the received vector, H is an interference matrix, x is the transmitted vector of data symbols chosen from a finite set, and w is a noise vector. The objective at the receiver is to detect the most likely vector x that was transmitted based on knowledge of r, H, and the statistics of w. Communication contexts in which this general integer programming problem appears include the equalization of intersymbol interference (ISI) channels, the cancellation of multiple-access interference (MAI) in code-division multiple-access (CDMA) systems, and the decoding of multiple-input multiple-output (MIMO) systems in fading environments. We begin by introducing mode-interleaved precoding, a transmitter precoding technique that conditions an interference channel so that the pairwise error probability of any two transmit vectors becomes asymptotically equal to the pairwise error probability of the same vectors over an AWGN channel at the same signal-to-noise ratio (SNR). While mode-interleaved precoding dramatically increases the complexity of exact ML detection, we develop iterated-decision detection to mitigate this complexity problem. Iterateddecision detectors use optimized multipass algorithms to successively cancel interference from r and generate symbol decisions whose reliability increases monotonically with each iteration. When used in uncoded systems with mode-interleaved precoding, iterated-decision detectors asymptotically achieve the performance ofML detection (and thus the interferencefree lower bound) with considerably lower complexity. We interpret these detectors as low-complexity approximations to message-passing algorithms. The integration of iterated-decision detectors into communication systems with coding is also developed to approach information rates close to theoretical limits. We present joint detection and decoding algorithms based on the iterated-decision detector with modeinterleaved precoding, and also develop analytic tools to predict the behavior of such systems. We discuss the use of binary codes for channels that support low information rates, and multilevel codes and lattice codes for channels that support higher information ratesHewlett-Packard under the MIT/HPAlliance, the National Science Foundation, the Semiconductor Research Corporation, Texas Instruments through the Leadership Universities Program, and the Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship Program

A framework for low-complexity iterative interference cancellation in communication systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 211-215).Communication over interference channels poses challenges not present for the more traditional additive white Gaussian noise (AWGN) channels. In order to approach the information limits of an interference channel, interference mitigation techniques need to be integrated with channel coding and decoding techniques. This thesis develops such practical schemes when the transmitter has no knowledge of the channel. The interference channel model we use is described by r = Hx + w, where r is the received vector, H is an interference matrix, x is the transmitted vector of data symbols chosen from a finite set, and w is a noise vector. The objective at the receiver is to detect the most likely vector x that was transmitted based on knowledge of r, H, and the statistics of w. Communication contexts in which this general integer programming problem appears include the equalization of intersymbol interference (ISI) channels, the cancellation of multiple-access interference (MAI) in code-division multiple-access (CDMA) systems, and the decoding of multiple-input multiple-output (MIMO) systems in fading environments. We begin by introducing mode-interleaved precoding, a transmitter preceding technique that conditions an interference channel so that the pairwise error probability of any two transmit vectors becomes asymptotically equal to the pairwise error probability of the same vectors over an AWGN channel at the same signal-to-noise ratio (SNR). While mode-interleaved precoding dramatically increases the complexity of exact ML detection, we develop iterated-decision detection to mitigate this complexity problem. Iterated-decision detectors use optimized multipass algorithms to successively cancel interference from r and generate symbol(cont.) decisions whose reliability increases monotonically with each iteration. When used in uncoded systems with mode-interleaved preceding, iterated-decision detectors asyrmptotically achieve the performance of ML detection (and thus the interference-free lower bound) with considerably lower complexity. We interpret these detectors as low-complexity approximations to message-passing algorithms. The integration of iterated-decision detectors into communication systems with coding is also developed to approach information rates close to theoretical limits. We present joint detection and decoding algorithms based on the iterated-decision detector with mode-interleaved precoding, and also develop analytic tools to predict the behavior of such systems. We discuss the use of binary codes for channels that support low information rates, and multilevel codes and lattice codes for channels that support higher information rates.by Albert M. Chan.Ph.D

Correlation decay and decentralized optimization in graphical models

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 213-229) and index.Many models of optimization, statistics, social organizations and machine learning capture local dependencies by means of a network that describes the interconnections and interactions of different components. However, in most cases, optimization or inference on these models is hard due to the dimensionality of the networks. This is so even when using algorithms that take advantage of the underlying graphical structure. Approximate methods are therefore needed. The aim of this thesis is to study such large-scale systems, focusing on the question of how randomness affects the complexity of optimizing in a graph; of particular interest is the study of a phenomenon known as correlation decay, namely, the phenomenon where the influence of a node on another node of the network decreases quickly as the distance between them grows. In the first part of this thesis, we develop a new message-passing algorithm for optimization in graphical models. We formally prove a connection between the correlation decay property and (i) the near-optimality of this algorithm, as well as (ii) the decentralized nature of optimal solutions. In the context of discrete optimization with random costs, we develop a technique for establishing that a system exhibits correlation decay. We illustrate the applicability of the method by giving concrete results for the cases of uniform and Gaussian distributed cost coefficients in networks with bounded connectivity. In the second part, we pursue similar questions in a combinatorial optimization setting: we consider the problem of finding a maximum weight independent set in a bounded degree graph, when the node weights are i.i.d. random variables.(cont.) Surprisingly, we discover that the problem becomes tractable for certain distributions. Specifically, we construct a PTAS for the case of exponentially distributed weights and arbitrary graphs with degree at most 3, and obtain generalizations for higher degrees and different distributions. At the same time we prove that no PTAS exists for the case of exponentially distributed weights for graphs with sufficiently large but bounded degree, unless P=NP. Next, we shift our focus to graphical games, which are a game-theoretic analog of graphical models. We establish a connection between the problem of finding an approximate Nash equilibrium in a graphical game and the problem of optimization in graphical models. We use this connection to re-derive NashProp, a message-passing algorithm which computes Nash equilibria for graphical games on trees; we also suggest several new search algorithms for graphical games in general networks. Finally, we propose a definition of correlation decay in graphical games, and establish that the property holds in a restricted family of graphical games. The last part of the thesis is devoted to a particular application of graphical models and message-passing algorithms to the problem of early prediction of Alzheimer's disease. To this end, we develop a new measure of synchronicity between different parts of the brain, and apply it to electroencephalogram data. We show that the resulting prediction method outperforms a vast number of other EEG-based measures in the task of predicting the onset of Alzheimer's disease.by Théophane Weber.Ph.D

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum