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On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes

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Executive Summary

In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular Doubly-Generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC and Generalized LDPC (GLDPC) codes. Ensembles with check or variable node minimum distance greater than 2 are shown to be having good growth rate behavior, while for other ensembles a fundamental parameter is identified which discriminates between an asymptotically small and an asymptotically large expected number of small linear-weight codewords. Also, in the latter case it is shown that the growth rate depends only on the check and variable nodes with minimum distance 2.

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