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Allerton Conference on Communication, Control, and Computing

Graph Codes for Dual-Parameter Barrier Channels

Yuval Ben-Hur, Saar Stern, Yoav Cohen, Yuval Cassuto

Published Sep 24, 2024• 1 citation
Publisher

Abstract

A ternary barrier channel is a non-symmetric error model defined previously to address emerging applications. Conveniently, it admits a code-construction method comprising two binary constituent codes. In this paper we propose a decoding algorithm that decodes the two constituent codes jointly by message passing on a graph representing the two codes' parity-check constraints. The messages exchanged by the algorithm are likelihoods calculated from incoming messages, and they are derived in the paper based on the exact dependence between the binary values of the two codewords. Simulation results demonstrate that the proposed decoder has superior error-rate performance compared to prior decoding approaches.

DOI
10.1109/allerton63246.2024.10735324

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A ternary barrier channel is a non-symmetric error model defined previously to address emerging applications. Conveniently, it admits a code-construction method comprising two binary constituent codes. In this paper we propose a decoding algorithm that decodes the two constituent codes jointly by message passing on a graph representing the two codes' parity-check constraints. The messages exchanged by the algorithm are likelihoods calculated from incoming messages, and they are derived in the paper based on the exact dependence between the binary values of the two codewords. Simulation results demonstrate that the proposed decoder has superior error-rate performance compared to prior decoding approaches.
Barrier-error channels have been suggested as a model for non-binary channels that are milder than symmetric-error channels. Such channels are motivated by practical applications in data storage and communications. The barrier-error model allows errors only to (downward) and from (upward) a specific symbol within the alphabet. We study a generalization of prior barrier-error models that considers different numbers of downward and upward errors. The results of this paper include a sufficient condition for error correction, code-size upper and lower bounds, a code construction decomposing to just two constituent symmetric-error codes (prior ones used many), and a decoding algorithm that decodes the two codes jointly. The decoder is shown empirically to achieve better block error rates when compared to previous algorithms.
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.
Binary and a ternary message passing decoding algorithms for generalized low-density parity-check codes are defined and analyzed. In all algorithms, the variable nodes exploit soft channel information. However, the exchanged messages between variable and check nodes are binary or ternary. Two types of local decoders are assumed at the check nodes, namely an optimum a-posteriori probability soft-input soft-output decoder, and a more practical bounded distance decoder. A density evolution analysis for irregular code ensembles is developed for all the introduced algorithms, which allows obtaining the scaling coefficients needed for the variable node operation. Finite-length simulation results confirm the validity of the asymptotic analysis.
A ternary message passing (TMP) decoding algorithm for low-density parity-check codes is developed. All messages exchanged between variable and check nodes have a ternary alphabet, and the variable nodes exploit soft information from the channel. A density evolution analysis is developed for unstructured and protograph-based ensembles. For unstructured ensembles the stability condition is derived. Optimized ensembles for TMP decoding show asymptotic gains of up to 0.6 dB with respect to ensembles optimized for binary message passing decoding. Finite length simulations of codes from TMP-optimized ensembles show gains of up to 0.5 dB under TMP compared to protograph-based codes designed for unquantized belief propagation decoding.
We present a novel decoding algorithm for q-ary low-density parity- check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature.
We present a novel decoding algorithm for q-ary low-density parity- check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature.