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.

翻译：非二进制线性分组码是一类重要的纠错码，特别适用于纠正突发错误，在现代通信和存储系统中具有广泛应用。然而，这类码的高效软判决译码方法仍有待进一步发展。本文针对定义在特征为二的有限域（即F_{2^r}，其中r为扩张次数）上的非二进制线性分组码，提出了连续删除列表译码方法。通过建立每个非二进制码字的二进制构成与r个二进制极化码码字之间的一对r映射，可在码字长度的亚二次复杂度下实现对r个极化码的SCL译码。为进一步优化译码过程，本文还提出了一种简化的路径排序方法。在短码长的扩展里德-所罗门码和非二进制扩展BCH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当前最先进的软判决译码性能。对于长度为16的扩展RS码，采用中等列表规模即可逼近其最大似然译码性能。