Improved Rate-versus-Distance Upper Bounds for LDPC Codes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910184984543232 |
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| author | Shangguan, Chong Yang, Yulin |
| author_facet | Shangguan, Chong Yang, Yulin |
| contents | 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 introduce a new framework for estimating ball sizes in the coset graphs of LDPC codes. The key new object is the coset-weight generating function, which encodes the minimum Hamming weights of all cosets of a linear code. Rather than estimating coset balls directly, we upper-bound this generating function through a local growth analysis for codes spanned by low-weight vectors. This framework sharpens the previous ball-size estimate 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Rate-versus-Distance Upper Bounds for LDPC Codes Shangguan, Chong Yang, Yulin Information Theory Combinatorics 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 introduce a new framework for estimating ball sizes in the coset graphs of LDPC codes. The key new object is the coset-weight generating function, which encodes the minimum Hamming weights of all cosets of a linear code. Rather than estimating coset balls directly, we upper-bound this generating function through a local growth analysis for codes spanned by low-weight vectors. This framework sharpens the previous ball-size estimate 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. |
| title | Improved Rate-versus-Distance Upper Bounds for LDPC Codes |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2605.01213 |