Eigenvalue bounds on the pseudocodeword weight of expander codes

Christine A. Kelley; Deepak Sridhara

doi:10.3934/amc.2007.1.287

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2007, Volume 1, Issue 3: 287-306. Doi: 10.3934/amc.2007.1.287

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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
2.
Seagate Technology, 1251 Waterfront Place, Pittsburgh, PA 15222

Received: August 31, 2006

Revised: June 30, 2007

Published: July 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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