Eigenvalue bounds on the pseudocodeword weight of expander codes

TL;DR

This paper derives new eigenvalue-based lower bounds on the pseudocodeword weight of expander LDPC codes, enhancing understanding of their decoding performance and generalizing existing bounds on minimum distance.

Contribution

It introduces four methods to obtain bounds on pseudocodeword weight from expander graphs and generalizes Tanner's eigenvalue bound to pseudocodewords.

Findings

Derived lower bounds on pseudocodeword weight for expander LDPC codes

Compared pseudocodeword bounds with minimum distance bounds

Generalized Tanner's eigenvalue bound to pseudocodewords

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.