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arXiv:1010.2030 · IEEE Transactions on Information Theory

Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields

Shengtian Yang, Thomas Honold, Yan Chen, Zhaoyang Zhang, Peiliang Qiu

Published Aug 3, 2011• 10 citations
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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.

DOI
10.1109/tit.2011.2162642

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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.
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