Pseudo-Codeword Analysis of Tanner Graphs from Projective and Euclidean Planes

Details Pseudo-Codeword Analysis of Tanner Graphs from Projective and Euclidean Planes Pseudo-Codeword Analysis of Tanner Graphs from Projective and Euclidean Planes

2006-02-26

arxiv.org/abs/cs/0602089v1

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory, February 25, 2006

Scientific paper

In order to understand the performance of a code under maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's attention needs to be shifted to the pseudo-codewords, in particular to the minimal pseudo-codewords, and their pseudo-weights. In this paper we investigate some families of codes that have good properties under LP decoding, namely certain families of low-density parity-check (LDPC) codes that are derived from projective and Euclidean planes: we study the structure of their minimal pseudo-codewords and give lower bounds on their pseudo-weight.

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