Provably efficient instanton search algorithm for LP decoding of LDPC codes over the BSC

Chilappagari, Shashi Kiran; Chertkov, Michael; Vasic, Bane

Provably efficient instanton search algorithm for LP decoding of LDPC codes over the BSC

Authors

Chilappagari, Shashi Kiran

Chertkov, Michael

Vasic, Bane

Description

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.
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;