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

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

2008-08-26

arxiv.org/abs/0808.3504v1

Computer Science

Information Theory

10 pages, 1 figure, presented at the 46th Annual Allerton Conference on Communication, Control and Computing (this version inc

Scientific paper

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. Assuming that there exist check and variable nodes with minimum distance 2, it is shown that the growth rate depends only on these nodes. An important connection between this new result and the stability condition of D-GLDPC codes over the BEC is highlighted. Such a connection, previously observed for LDPC and GLDPC codes, is now extended to the case of D-GLDPC codes.

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