Improved Rate-versus-Distance Upper Bounds for LDPC Codes

Chong Shangguan; Yulin Yang

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arXiv · 2605.01213

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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Chong Shangguan, Yulin Yang. 2026-05-02. Improved Rate-versus-Distance Upper Bounds for LDPC Codes. https://arxiv.org/abs/2605.01213

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