# American Institute of Mathematical Sciences

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

## Eigenvalue bounds on the pseudocodeword weight of expander codes

 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

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.
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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