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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

On Tanner's Lower Bound for the Minimum Distance of Regular LDPC Codes Based on Combinatorial Designs

Tomoharu Shibuya, Masatoshi Onikubo, Kohichi Sakaniwa

Published Oct 1, 2003• 1 citation
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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.