An Efficient Instanton Search Algorithm for LP Decoding of LDPC Codes Over the BSC
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An Efficient Instanton Search ...
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Final Accepted Manuscript
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Univ Arizona, Dept Elect & Comp EngnIssue Date
2011-06-20
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IEEECitation
S. 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.Rights
Copyright © 2011 IEEE.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.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 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.ISSN
0018-9448Version
Final accepted manuscriptae974a485f413a2113503eed53cd6c53
10.1109/tit.2011.2146670