On the Minimal Pseudo-Codewords of Codes from Finite Geometries

Details On the Minimal Pseudo-Codewords of Codes from Finite Geometries On the Minimal Pseudo-Codewords of Codes from Finite Geometries

2005-08-02

arxiv.org/abs/cs/0508019v1

Computer Science

Information Theory

To appear in Proc. 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 2005

Scientific paper

In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal pseudo-codewords. This paper studies the minimal codewords and minimal pseudo-codewords of some families of codes derived from projective and Euclidean planes. Although our numerical results are only for codes of very modest length, they suggest that these code families exhibit an interesting property. Namely, all minimal pseudo-codewords that are not multiples of a minimal codeword have an AWGNC pseudo-weight that is strictly larger than the minimum Hamming weight of the code. This observation has positive consequences not only for LP decoding but also for iterative decoding.

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