Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes
Smarandache, R.
Vontobel, P.O.
San Diego State Univ., San Diego;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: July 2007
Volume: 53,
Issue: 7
On page(s): 2376-2393
ISSN: 0018-9448
INSPEC Accession Number: 9598908
Digital Object Identifier: 10.1109/TIT.2007.899563
Current Version Published: 2007-06-25
Abstract
We consider coded data transmission over a binary-input output-symmetric memoryless channel using a binary linear code. In order to understand the performance of 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. Besides this main focus, we also present some results that hold for pseudo-codewords and minimal pseudo-codewords of any Tanner graph, and we highlight how the importance of minimal pseudo-codewords under LP decoding varies depending on which binary-input output-symmetric memoryless channel is used.
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