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PreprintCC BY 4.0arXiv

On the Multi-Weight Shift-Sum Iterative Decoding of Short BCH Codes

  • Yinglei Yang
  • Di Zhang
  • Aimin Li
  • Yifei Shen
  • Alexey Frolov
  • Bo Gu
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Abstract

This paper investigates a shift-sum decoding algorithm that employs dual codewords. Existing dual codeword shift-sum decoding schemes mainly rely on minimum-weight dual codewords. However, the number of such codewords is often limited, which restricts the amount of reliability information available to the decoder. To address this issue, we extend the component counting mechanism from minimum-weight dual codewords to dual codewords whose Hamming weights lie within a prescribed upper bound. We further introduce a normalized component counting rule to suppress the overcounting bias caused by the much larger populations of higher-weight classes. Based on this framework, we develop a hard-decision iterative error reduction decoder and a soft information-aided iterative error reduction decoder. Numerical results show that the proposed method consistently outperforms existing minimum-weight shift-sum baselines especially for short codes where additional dual codeword information is particularly valuable.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026multiweight,
  title = {{On the Multi-Weight Shift-Sum Iterative Decoding of Short BCH Codes}},
  author = {Yinglei Yang and Di Zhang and Aimin Li and Yifei Shen and Alexey Frolov and Bo Gu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17025},
  eprint = {2610.17025},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17025},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Multi-Weight Shift-Sum Iterative Decoding of Short BCH Codes
AU  - Yinglei Yang
AU  - Di Zhang
AU  - Aimin Li
AU  - Yifei Shen
AU  - Alexey Frolov
AU  - Bo Gu
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17025
UR  - https://arxiv.org/abs/2610.17025
AB  - This paper investigates a shift-sum decoding algorithm that employs dual codewords. Existing dual codeword shift-sum decoding schemes mainly rely on minimum-weight dual codewords. However, the number of such codewords is often limited, which restricts the amount of reliability information available to the decoder. To address this issue, we extend the component counting mechanism from minimum-weight dual codewords to dual codewords whose Hamming weights lie within a prescribed upper bound. We further introduce a normalized component counting rule to suppress the overcounting bias caused by the much larger populations of higher-weight classes. Based on this framework, we develop a hard-decision iterative error reduction decoder and a soft information-aided iterative error reduction decoder. Numerical results show that the proposed method consistently outperforms existing minimum-weight shift-sum baselines especially for short codes where additional dual codeword information is particularly valuable.
ER  -