Eigenvalue bounds on the pseudocodeword weight of expander codes

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August 2007, 1(3): 287-306. doi: 10.3934/amc.2007.1.287

Eigenvalue bounds on the pseudocodeword weight of expander codes

Christine A. Kelley ^1, and Deepak Sridhara ^2,

1.	Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States
2.	Seagate Technology, 1251 Waterfront Place, Pittsburgh, PA 15222, United States

Received September 2006 Revised July 2007 Published July 2007

Abstract
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Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. These bounds are compared with the known eigenvalue-based lower bounds on the minimum distance of expander codes. Furthermore, Tanner's parity-oriented eigenvalue lower bound on the minimum distance is generalized to yield a new lower bound on the minimum pseudocodeword weight. These bounds are useful in predicting the performance of LDPC codes under graph-based iterative decoding and linear programming decoding.

Keywords: pseudocodeword weight, pseudocodewords, iterative decoding., LDPC codes, Expander graphs.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Christine A. Kelley, Deepak Sridhara. Eigenvalue bounds on the pseudocodeword weight of expander codes. Advances in Mathematics of Communications, 2007, 1 (3) : 287-306. doi: 10.3934/amc.2007.1.287

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