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Generalization of Tanner′s Minimum Distance Bounds for LDPC Codes  

Shin Min Ho (연세대학교 전기ㆍ전자공학과 부호 및 정보이론 연구실)
Kim Joon Sung (연세대학교 전기ㆍ전자공학과 부호 및 정보이론 연구실)
Song Hong Yeop (연세대학교 전기ㆍ전자공학과 부호 및 정보이론 연구실)
Publication Information
The Journal of Korean Institute of Communications and Information Sciences / v.29, no.10C, 2004 , pp. 1363-1369 More about this Journal
Abstract
LDPC(Low Density Parity Check) codes are described by bipartite graphs with bit nodes and parity-check nodes. Tanner derived minimum distance bounds of the regular LDPC code in terms of the eigenvalues of the associated adjacency matrix. In this paper we generalize the Tanner's results. We derive minimum distance bounds applicable to both regular and blockwise-irregular LDPC codes. The first bound considers the relation between bit nodes in a minimum-weight codeword, and the second one considers the connectivity between parity nodes adjacent to a minimum-weight codeword. The derived bounds make it possible to describe the distance property of the code in terms of the eigenvalues of the associated matrix.
Keywords
LDPC codes; bit-oriented bound; parity-oriented bound; Tanner graph;
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