VLSI Implementation of a Non-Binary Decoder Based on the Analog Digital Belief Propagation

This work presents the VLSI hardware implementation of a novel Belief Propagation (BP) algorithm introduced in [1] and named as Analog Digital Belief Propagation (ADBP). The ADBP algorithm works on factor graphs over linear models and uses messages in the form of Gaussian like probability distributions by tracking their parameters. In particular, ADBP can deal with system variables that are discrete and/or wrapped. A variant of ADBP can then be applied for the iterative decoding of a particular class of non binary codes and yields decoders with complexity independent of alphabet size M, thus allowing to construct ecient decoders for digital transmission systems with unbounded spectral eciency. In this work, we propose some simplifications to the updating rules for ADBP algorithm that are suitable for hardware implementation. In addition, we analyze the eect of finite precision on the decoding performance of the algorithm. A careful selection of quantization scheme for input, output and intermediate variables allows us to construct a complete ADBP decoding architecture that performs close to the double precision implementation and shows a promising complexity for large values of M. Finally, synthesis results of the main processing elements of ADBP are reported for 45 nm standard cell ASIC technology

Etude des décodeurs LDPC non-binaires

Binary Low-Density Parity-Check (LDPC) codes and turbo-codes are known to have near-capacity performance for long code lengths. However, these codes are less efficient for short and moderate code lengths. In addition, the combination of binary codes with high-order modulations requires a marginalization step to extract bits reliabilities from symbols reliablities. Thus, binary demodulation suffers from a loss of information that can be recovered using iterative demodulators at the expense of higher complexity. LDPC codes defined over finite fields of order q > 2 can be considered as a solution to these problems. Nevertheless, optimal decoding of non-binary LDPC codes suffers from extremely highcomplexity which almost prevents practical implementation. In this thesis we aim at proving the feasibility of using non-binary LDPC codes in modern communication systems by proposing on the one hand a low-complexity decoder architecture based on a sub-optimal decoding algorithm, and showing on the other hand the advantages of combining such codes with high-order modulations. In the first part of our thesis, we propose to simplify the Extended Min-Sum (EMS) algorithm by considering a limited number n_α 2 permettent de résoudre ces problèmes. Toutefois, lesdécodeurs optimaux associés ont une complexité très importante qui rend leur utilisation problématique.L’objectif de cette thèse est de valoriser les codes LDPC non binaires en proposant d’une part une architecture d’un décodeur à complexité réduite et en montrant d’autre part l’intérêt de les associer à des modulations d’ordre élevé. Dans la première partie de notre thèse, nous proposons de simplifier l’algorithme de décodage Extended Min-Sum (EMS) en considérant un nombre limité n_α << n_m des fiabilités intrinsèques lors de la mise à jour des messages par les nœuds de variable. Cette approche permet de réduire la taille de la mémoire dédiée au stockage des messages intrinsèques. De plus, pour améliorer l’effcacité des nœuds de parité nous proposons une variante simplifiée de l’algorithme L-Bubble Check et l’architecture associée. Enfin, nous montrons par l’intermédiaire d’un prototype sur une carte FPGA (Field Programmable Gate Array) que notre décodeur possède une faible complexité en le comparant avec un ancien décodeur EMS conçu par notre laboratoire de recherche dans le cadre du projet européen DAVINCI. Dans la deuxième partie, nous étudions l’association des codes LDPC non binaires avec une modulation par décalage cyclique de code (Cyclic Code-shift Keying, CCSK) de même ordre. Nous avons choisi cette modulation pour ses propriétés qui permettent de réduire la complexité du démodulateur. En effet, nous montrons qu’il est possible dans le cas d’un système de transmission mono-porteuse avec préfixe cyclique de fusionner le démodulateur et l’égaliseur dans un même bloc comportant une seule transformée de Fourier rapide et une seule transformée de Fourier rapide inverse. Les simulations montrent que ce système possède des performances comparables à un système de transmission multiporteuses de type OFDM (Orthogonal Frequency-Division Multiplexing). Elles montrent aussi que la modulation CCSK donne des performances meilleures que la modulation de Hadamard dans un canal en environnement intérieur sélectif en fréquence. Enfin, les simulations montrent que les codes LDPC non binaires sont nettement plus effcaces avec la modulation CCSK que les codes LDPC binaires même en considérant une démodulation itérative

D11.2 Consolidated results on the performance limits of wireless communications

Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin

Capacity -based parameter optimization of bandwidth constrained CPM

Continuous phase modulation (CPM) is an attractive modulation choice for bandwidth limited systems due to its small side lobes, fast spectral decay and the ability to be noncoherently detected. Furthermore, the constant envelope property of CPM permits highly power efficient amplification. The design of bit-interleaved coded continuous phase modulation is characterized by the code rate, modulation order, modulation index, and pulse shape. This dissertation outlines a methodology for determining the optimal values of these parameters under bandwidth and receiver complexity constraints. The cost function used to drive the optimization is the information-theoretic minimum ratio of energy-per-bit to noise-spectral density found by evaluating the constrained channel capacity. The capacity can be reliably estimated using Monte Carlo integration. A search for optimal parameters is conducted over a range of coded CPM parameters, bandwidth efficiencies, and channels. Results are presented for a system employing a trellis-based coherent detector. To constrain complexity and allow any modulation index to be considered, a soft output differential phase detector has also been developed.;Building upon the capacity results, extrinsic information transfer (EXIT) charts are used to analyze a system that iterates between demodulation and decoding. Convergence thresholds are determined for the iterative system for different outer convolutional codes, alphabet sizes, modulation indices and constellation mappings. These are used to identify the code and modulation parameters with the best energy efficiency at different spectral efficiencies for the AWGN channel. Finally, bit error rate curves are presented to corroborate the capacity and EXIT chart designs

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

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum