An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSC
AffiliationUniv Arizona, Dept Elect & Comp Engn
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CitationS. K. Chilappagari, M. Chertkov and B. Vasic, "An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSC," in IEEE Transactions on Information Theory, vol. 57, no. 7, pp. 4417-4426, July 2011, doi: 10.1109/TIT.2011.2146670.
RightsCopyright © 2011 IEEE.
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AbstractWe 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 equal to the transmitted codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which generates an error vector called the BSC-instanton. We prove that: (a) the LP decoder fails for any error pattern with support that is a superset of the support of an instanton; (b) for any input, the ISA outputs an instanton in the number of steps upper-bounded by twice the number of errors in the input error vector. We then find the number of unique instantons of different sizes for a given LDPC code by running the ISA sufficient number of times.
VersionFinal accepted manuscript