A Fresh Look at Coding for q-ary Symmetric Channels

TL;DR

This paper introduces a practical LDPC-based coding scheme for q-ary symmetric channels that is efficient, theoretically optimal, and adaptable to various channel types, with a focus on low complexity and code optimization.

Contribution

It proposes a simple, practical decoding scheme for q-ary channels based on binary LDPC codes, extending applicability and efficiency over existing methods.

Findings

The layered scheme is shown to be theoretically optimal.

The decoding complexity is linear in log2(q).

The scheme is adaptable to a broader class of q-ary channels.

Abstract

This paper studies coding schemes for the $q$-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size $q=2^m$, $m\in\mathbb{N}$, thus complementing some recently proposed packet-based schemes requiring large $q$. First, theoretical optimality of a simple layered scheme is shown, then a practical coding scheme based on a simple modification of standard binary LDPC decoding is proposed. The decoder is derived from first principles and using a factor-graph representation of a front-end that maps $q$-ary symbols to groups of $m$ bits connected to a binary code. The front-end can be processed with a complexity that is linear in $m=\log_2 q$. An extrinsic information transfer chart analysis is carried out and used for code optimization. Finally, it is shown how the same decoder structure can also be applied to a larger class of $q$-ary channels.