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 Citations (Scopus)

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 publicationIEEE International Symposium on Information Theory - Proceedings
Pages1648-1652
Number of pages5
DOIs
StatePublished - 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Other

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

Fingerprint

Polytope
Linear programming
Decoding
Lowest
Log-concave
Binary codes
Nonconvex Optimization
Binary Code
Gaussian White Noise
Cost functions
Convex function
Cost Function
Heuristics
Formulation
Output

ASJC Scopus subject areas

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

Cite this

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

Polytope of correct (linear programming) decoding and low-weight pseudo-codewords. / Chertkov, Michael; Stepanov, Mikhail.

IEEE International Symposium on Information Theory - Proceedings. 2011. p. 1648-1652 6033824.

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

Chertkov, M & Stepanov, M 2011, Polytope of correct (linear programming) decoding and low-weight pseudo-codewords. in IEEE International Symposium on Information Theory - Proceedings., 6033824, pp. 1648-1652, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 7/31/11. https://doi.org/10.1109/ISIT.2011.6033824
Chertkov M, Stepanov M. Polytope of correct (linear programming) decoding and low-weight pseudo-codewords. In IEEE International Symposium on Information Theory - Proceedings. 2011. p. 1648-1652. 6033824 https://doi.org/10.1109/ISIT.2011.6033824
Chertkov, Michael ; Stepanov, Mikhail. / Polytope of correct (linear programming) decoding and low-weight pseudo-codewords. IEEE International Symposium on Information Theory - Proceedings. 2011. pp. 1648-1652
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