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Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

Francisco Lázaro, Alexandre Graell i Amat, Gianluigi Liva, Balázs Matuz

Published Jan 1, 2019• 9 citations
Publisher

Abstract

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.

DOI
10.1109/globecom38437.2019.9013601

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IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•0 citations
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.
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.
A decoding algorithm forqqq-ary low-density parity-check codes over theqqq-ary symmetric channel is introduced. The exchanged messages are lists of symbols fromFq\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.
A simple decoder for q-ary low-density parity-check codes is studied, termed symbol message passing. The decoder passes hard decisions from a q-ary alphabet. For orthogonal modulations over the additive white Gaussian channel for which the modulation order and the field order q are equal, it is shown that the extrinsic messages can be modelled as observations of a q-ary symmetric channel, allowing to work out density evolution equations. A stability analysis is provided which emphasizes the influence of degree-3 variable nodes. Simulation results show performance gains for increasing q w.r.t. binary low-density parity-check codes with bit-interleaved coded modulation, and potential savings in decoding complexity.
A simple decoding algorithm, dubbed symbol message passing decoder, is studied for q-ary low-density parity-check codes over the q-ary Poisson pulse-position modulation channel. The messages in the decoder are symbols from the finite field Fq{\mathbb{F}_q}Fq​. To improve performance, a second decoder with an extended message set {E∪Fq}\left\{ {{\text{E}} \cup {\mathbb{F}_q}} \right\}{E∪Fq​} is also investigated, where E denotes an erasure. Thresholds within 1.3 dB from the Shannon limit are obtained for low field orders.