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

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5 Author(s)
Shengtian Yang ; Zhengyuan Xiaoqu 10-2-101, Hangzhou, China ; Thomas Honold ; Yan Chen ; Zhaoyang Zhang
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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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IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 11 )