List Message Passing Decoding of Non-binary Low-Density Parity-Check Codes

TL;DR

This paper introduces a list message passing decoding algorithm for non-binary LDPC codes over the q-ary symmetric channel, demonstrating improved thresholds and confirming results through finite-length simulations.

Contribution

It presents a novel list message passing decoding method for non-binary LDPC codes with density evolution analysis and improved thresholds over existing algorithms.

Findings

Thresholds for regular LDPC ensembles are improved.

Finite-length simulations confirm asymptotic analysis.

Maximum list size impacts decoding performance.

Abstract

A decoding algorithm for $q$-ary low-density parity-check codes over the $q$-ary symmetric channel is introduced. The exchanged messages are lists of symbols from $\Fq$. 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.