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

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    Author
    Chilappagari, Shashi Kiran
    Chertkov, Michael
    Vasic, Bane
    Affiliation
    Univ Arizona, Dept Elect & Comp Engn
    Issue Date
    2011-06-20
    
    Metadata
    Show full item record
    Publisher
    IEEE
    Citation
    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.
    Journal
    IEEE Transactions on Information Theory
    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
    0018-9448
    DOI
    10.1109/tit.2011.2146670
    Version
    Final accepted manuscript
    ae974a485f413a2113503eed53cd6c53
    10.1109/tit.2011.2146670
    Scopus Count
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    UA Faculty Publications

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