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IEEE Transactions on Communications

Decoding of Low-Density Parity-Check Codes Over Finite-State Binary Markov Channels

Javier Garcia‐Frias

Published Nov 1, 2004• 53 citations
Publisher

Abstract

We propose a modified algorithm for decoding of low-density parity-check codes over finite-state binary Markov channels. The proposed approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, even when the channel parameters are not known a priori at the decoder.
DOI
10.1109/tcomm.2004.836568

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We propose a modified algorithm for decoding of low-density parity check codes over finite-state binary Markov channels. The hidden Markov model representing the channel is incorporated into the bipartite graph of the low-density parity check code, and the message passing algorithm is modified accordingly. This approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, allowing reliable communication at rates which are above the capacity of a memoryless channel with the same stationary bit error probability as the Markov channel. Moreover, we introduce a joint estimation/decoding method that allows the estimation of the parameters of the channel when they are not known a priori.
This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.
Here we have proposed two decoding strategies of low-density parity-check (LDPC) codes over Markov noise channels with bit flipping noise. The sum-product algorithm used for decoding LDPC codes over memoryless channels is extended to include channel estimation and how much gain we obtain by doing so is simulated and verified. LDPC codes have been studied for years over memoryless channels and are known to have excellent performance. However, these codes over channels with memory is the topic of current research. Here, channels with memory are characterized by Markov modeling which is a useful busty channel model. With sufficient no. of states, they are able to model sufficient noise characteristics. We have gone for a two-state system as it shows a good compromise between complexity and performance.
An improved decoding algorithm for low-density parity-check code(LDPC) on finite-state Markov channels was presented and the corresponding factor graph representation was given.It consists of two parts: standard sum-product algorithm(SPA) for LDPC and forward-backward(FB) algorithm for Markov channel.After each iteration for SPA,FB re-estimated the channel likelihood ratio for the next iteration of SPA based on soft decisions for noise bits from SPA.Considering more cycles in the factor graph with the introduction of the Markov channel node,the probabilistic schedule was used to update the message during the iterations for decoding.Simulation results show that the algorithm not only performs much better than the standard sum-product algorithm,but also outperforms the algorithm based on hard decisions for noise bits.
A decoding algorithm for qqq -ary low-density parity-check codes over the qqq -ary symmetric channel is introduced. The exchanged messages are lists of symbols from Fq\mathbb{F}_{q}Fq​ . A density evolution analysis for maximum list sizes 1 and 2 is developed. Thresholds for selected regular low-density parity-check code ensembles are computed showing gains with respect to a similar algorithm in the literature. Finite-length simulation results confirm the asymptotic analysis.