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

## TL;DR

This paper introduces a new symbol message passing decoding algorithm for q-ary low-density parity-check codes, extending existing binary algorithms to nonbinary cases, with proven thresholds and improved performance.

## Contribution

It presents a novel decoding algorithm for q-ary LDPC codes that generalizes binary message passing, with derived density evolution equations and verified performance improvements.

## Key findings

- Density evolution equations for q-ary symmetric channel
- Computed thresholds for regular LDPC ensembles
- Verified performance gains via Monte Carlo simulations

## 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.