|Author||Chilappagari, Shashi Kiran ♦ Chertkov, Michael ♦ Vasic, Bane|
|Date of Submission||2008-08-18|
|Subject Domain (in DDC)||Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics|
|Subject Keyword||Computer Science - Information Theory ♦ Condensed Matter - Statistical Mechanics ♦ cs ♦ math ♦ physics:cond-mat|
|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.|
|Learning Resource Type||Article|
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