Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields
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Publication:5272251
DOI10.1109/TIT.2011.2162642zbMATH Open1365.94533arXiv1010.2030MaRDI QIDQ5272251
Thomas Honold, Zhaoyang Zhang, Yan Chen, Pei-Liang Qiu, Shengtian Yang
Publication date: 12 July 2017
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average weight distribution are proved. Based on this analysis, a general result, including all previous results as special cases, is established for the minimum distance of individual codes in a regular LDPC code ensemble.
Full work available at URL: https://arxiv.org/abs/1010.2030
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05)
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