SCL Decoding of Non-Binary Linear Block Codes

TL;DR

This paper introduces a successive cancellation list decoding method for non-binary linear block codes over F_{2^r}, achieving near-ML performance with reduced complexity by mapping non-binary codewords to multiple binary polar codes.

Contribution

It develops a novel SCL decoding approach for NB-LBCs over F_{2^r} using a binary mapping, improving decoding efficiency and performance over existing methods.

Findings

SCL decoding outperforms state-of-the-art soft-decision decoding.

Decoding complexity is sub-quadratic in code length.

Near-ML performance achieved for length-16 extended Reed-Solomon codes.

Abstract

Non-binary linear block codes (NB-LBCs) are an important class of error-correcting codes that are especially competent in correcting burst errors. They have broad applications in modern communications and storage systems. However, efficient soft-decision decoding of these codes remains to be further developed. This paper proposes successive cancellation list (SCL) decoding for NB-LBCs that are defined over a finite field of characteristic two, i.e., F_{2^r}, where r is the extension degree. By establishing a one-to-r mapping between the binary composition of each non-binary codeword and $r$ binary polar codewords, SCL decoding of the r polar codes can be performed with a complexity that is sub-quadratic in the codeword length. A simplified path sorting is further proposed to facilitate the decoding. Simulation results on short-length extended Reed-Solomon (eRS) and non-binary extended BCH (NB-eBCH) codes show that SCL decoding can outperform their state-of-the-art soft-decision decoding with fewer finite field arithmetic operations. For length-16 eRS codes, their maximum-likelihood (ML) decoding performances can be approached with a moderate list size.