Stochastic decoding of low-density parity-check codes

Low-Density Parity-Check (LDPC) codes are one of the most powerful classes of error-control codes known to date. These codes have been considered for many recent digital communication applications. In this dissertation, we propose stochastic decoding of state-of-the-art LDPC codes and demonstrate it as a competitive approach to practical LDPC decoding algorithms.In stochastic decoding, probabilities are represented as streams of random bits using Bernoulli sequences in which the information is contained in the statistics of the bit stream. This representation results in low hardware-complexity processing nodes that perform computationally-intensive operations. However, stochastic decoding is prone to the acute problem of latching. This problem is caused by correlated bit streams within cycles in the code's factor graph, and significantly deteriorates the performance of stochastic LDPC decoders.We propose edge memories, tracking forecast memories, and majority-based tracking forecast memories to address the latching problem. These units efficiently extract the evolving statistics of stochastic bit streams and rerandomize them to disrupt latching. To the best of our knowledge, these methods are the first successful methods for stochastic decoding of state-of-the-art LDPC codes.We present novel decoder architectures and report on several hardware implementations. The most advanced reported implementation is a stochastic decoder that decodes the (2048,1723) LDPC code from the IEEE 802.3an standard. To the best of our knowledge, this decoder is the most silicon area-efficient and, with a maximum core throughput of 61.3 Gb/s, is one of the fastest fully parallel soft-decision LDPC decoders reported in the literature. We demonstrate the performance of this decoder in low bit-error-rate regimes.In addition to stochastic LDPC decoding, we propose the novel application of the stochastic approach for joint decoding of LDPC codes and partial-response channels that are considered in practical magnetic recording applications. Finally, we investigate the application of the stochastic approach for decoding linear block codes with high-density parity-check matrices on factor graphs. We consider Reed-Solomon, Bose-Chaudhuri-Hocquenghem, and block turbo codes. %%%%A ce jour, les codes Low-Density Parity-Check (LDPC) font partie des codes correcteurs d'erreurs les plus performants. Ces codes sont inclus dans differents standards de communications numeriques. Dans ce manuscrit, nous proposons d'utiliser le decodage stochastique pour les codes LDPC. D'autre part, nous demontrons que pour les codes LDPC, le decodage stochastique represente une alternative realiste aux algorithmes de decodage existants.Dans le processus de decodage stochastique, les probabilites sont representees sous forme de sequences de Bernoulli. L'information est contenue dans la statistique de ces flux binaires aleatoires. Cette representation particuliere permet d'executer des calculs intensifs avec une faible complexite materielle. Cependant le decodage stochastique…