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PreprintarXiv licencearXiv

Improved Rate-versus-Distance Upper Bounds for LDPC Codes

  • Chong Shangguan
  • Yulin Yang
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Abstract

LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we develop a local-growth argument for estimating ball sizes in the coset graphs of LDPC codes. Rather than estimating coset balls directly, we use a local-growth analysis to bound the coset-weight generating function of linear spaces spanned by low-weight vectors. This approach sharpens the previous ball-size estimates of Iceland and Samorodnitsky. Combined with a general method of Friedman and Tillich that relates balls in coset graphs to sizes of error-correcting codes, it further improves the upper bounds on the rate of LDPC codes for a significant range of relative distances.

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Cite

BibTeXRIS
BibTeX
@misc{shangguan2026improved,
  title = {{Improved Rate-versus-Distance Upper Bounds for LDPC Codes}},
  author = {Chong Shangguan and Yulin Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.01213},
  eprint = {2605.01213},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.01213},
}
RIS
TY  - UNPB
TI  - Improved Rate-versus-Distance Upper Bounds for LDPC Codes
AU  - Chong Shangguan
AU  - Yulin Yang
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2605.01213
UR  - https://arxiv.org/abs/2605.01213
AB  - LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we develop a local-growth argument for estimating ball sizes in the coset graphs of LDPC codes. Rather than estimating coset balls directly, we use a local-growth analysis to bound the coset-weight generating function of linear spaces spanned by low-weight vectors. This approach sharpens the previous ball-size estimates of Iceland and Samorodnitsky. Combined with a general method of Friedman and Tillich that relates balls in coset graphs to sizes of error-correcting codes, it further improves the upper bounds on the rate of LDPC codes for a significant range of relative distances.
ER  -