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An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSC

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3 Author(s)
Shashi Kiran Chilappagari ; Marvell Semiconductor Inc, Santa Clara, CA, USA ; Michael Chertkov ; Bane Vasic

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 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.

Published in:

IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 7 )