On the minimal pseudo-codewords of codes from finite geometries
Vontobel, P.O.
Smarandache, R.
Kiyavash, N.
Teutsch, J.
Vukobratovic, D.
Dept. of ECE, Wisconsin Univ., Madison, WI;
This paper appears in: Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on
Publication Date: 4-9 Sept. 2005
On page(s): 980-984
Location: Adelaide, SA,
ISBN: 0-7803-9151-9
INSPEC Accession Number: 9045184
Digital Object Identifier: 10.1109/ISIT.2005.1523484
Current Version Published: 2005-10-31
Abstract
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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