Provably efficient instanton search algorithm for LP decoding of LDPC codes over the BSC
Abstract
We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton. We prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of flips in the input. Repeated sufficient number of times, the ISA outcomes the number of unique instantons of different sizes.
Cite
@article{arxiv.0808.2515,
title = {Provably efficient instanton search algorithm for LP decoding of LDPC codes over the BSC},
author = {Shashi Kiran Chilappagari and Michael Chertkov and Bane Vasic},
journal= {arXiv preprint arXiv:0808.2515},
year = {2008}
}
Comments
Submitted to IEEE Transactions on Information Theory. 9 Pages, 4 Figures; Dr. Bane Vasic added as an author; Changes made to the introduction and abstract; Acknowledgment section added; Some references added; Figures modified to make them more clear;