Eigenvalue bounds on the pseudocodeword weight of expander codes

Details Eigenvalue bounds on the pseudocodeword weight of expander codes Eigenvalue bounds on the pseudocodeword weight of expander codes

2007-08-18

arxiv.org/abs/0708.2462v1

Journal on Advances of Mathematics of Communications, vol. 1, no. 3, pp. 287 -- 307, Aug. 2007

Computer Science

Information Theory

Journal on Advances of Mathematics of Communications, vol. 1, no. 3, pp. 287 -- 307, Aug. 2007

Scientific paper

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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