SCL Decoding of Non-Binary Linear Block Codes
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| Format: | Preprint |
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2025
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| _version_ | 1866914264729518080 |
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| author | Lin, Jingyu Chen, Li Ye, Xiaoqian |
| author_facet | Lin, Jingyu Chen, Li Ye, Xiaoqian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SCL Decoding of Non-Binary Linear Block Codes Lin, Jingyu Chen, Li Ye, Xiaoqian Information Theory 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. |
| title | SCL Decoding of Non-Binary Linear Block Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2511.11256 |