Polytope of correct (linear programming) decoding and low-weight pseudo-codewords

Michael Chertkov, Mikhail Stepanov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We analyze Linear Programming (LP) decoding of graphical binary codes operating over soft-output, symmetric and log-concave channels. We show that the error-surface, separating domain of the correct decoding from domain of the erroneous decoding, is a polytope. We formulate the problem of finding the lowest-weight pseudo-codeword as a non-convex optimization (maximization of a convex function) over a polytope, with the cost function defined by the channel and the polytope defined by the structure of the code. This formulation suggests new provably convergent heuristics for finding the lowest weight pseudo-codewords improving in quality upon previously discussed. The algorithm performance is tested on the example of the Tanner [155,64,20] code over the Additive White Gaussian Noise (AWGN) channel.

Original languageEnglish (US)
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages1648-1652
Number of pages5
DOIs
StatePublished - Oct 26 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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    Chertkov, M., & Stepanov, M. (2011). Polytope of correct (linear programming) decoding and low-weight pseudo-codewords. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 (pp. 1648-1652). [6033824] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6033824