2006/02/26 by Roxana Smarandache, Pascal O. Vontobel, Smarandache, Roxana +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #DNA and Biological Computing #Discrete Mathematics (cs.DM) #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.DM #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.cs/0602089
Submitted to IEEE Transactions on Information Theory, February 25, 2006
arxiv created 2006/02/26 · openalex publication_date 2006/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.