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

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

2008-08-19

arxiv.org/abs/0808.2515v2

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory. 9 Pages, 4 Figures; Dr. Bane Vasic added as an author; Changes made to t

Scientific paper

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.

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