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IEEE International Symposium on Information Theory (ISIT)

Second Support Weight Distribution of Regular LDPC Code Ensembles

Takayuki Itsui, Kenta Kasai, Ryoji Ikegaya, Tomoharu Shibuya, Kohichi Sakaniwa

Published Jul 1, 2006• 0 citations
Publisher

Abstract

The support weight distribution of a code is the number of unique subspaces of the code with specified dimension and support weight. In this paper, we formulate the average second support weight distribution and its asymptotic exponent of regular LDPC code ensembles
DOI
10.1109/isit.2006.261666

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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.