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 challenging. 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. An r-step decoding path sorting strategy is further proposed to facilitate the decoding. Simulation results on 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.

翻译：非二进制线性分组码（NB-LBCs）是一类重要的纠错码，在纠正突发错误方面表现出色，在现代通信和存储系统中具有广泛应用。然而，这些码的高效软判决译码仍具挑战性。本文针对定义在特征为二的有限域（即F_{2^r}，其中r为扩展次数）上的非二进制线性分组码，提出了连续删除列表（SCL）译码方法。通过建立每个非二进制码字的二进制组成与r个二进制极化码码字之间的一对r映射，对r个极化码进行SCL译码的复杂度可低于码长的二次方。为进一步优化译码过程，本文还提出了一种r步译码路径排序策略。在扩展里德-所罗门（eRS）码和非二进制扩展BCH（NB-eBCH）码上的仿真结果表明，SCL译码能以更少的有限域算术运算超越现有最先进的软判决译码性能。对于长度为16的eRS码，采用适中的列表大小即可逼近其最大似然（ML）译码性能。