Local-optimality guarantees for optimal decoding based on paths

Nissim Halabi*, Guy Even

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded in the Tanner graph of the code. Local-optimality implies both maximum-likelihood (ML) optimality and linear-programming (LP) decoding optimality. Also, an iterative message-passing decoding algorithm is guaranteed to find the unique locally-optimal codeword, if one exists. We demonstrate this proof technique by considering a definition of local optimality that is based on the simplest combinatorial structures in Tanner graphs, namely, paths of length h. We apply the technique of local optimality to a family of Tanner codes. Inverse polynomial bounds in the code length are proved on the word error probability of LP-decoding for this family of Tanner codes.

Original languageEnglish
Title of host publication2012 7th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2012
Pages205-209
Number of pages5
DOIs
StatePublished - 2012
Event2012 7th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2012 - Gothenburg, Sweden
Duration: 27 Aug 201231 Aug 2012

Publication series

NameInternational Symposium on Turbo Codes and Iterative Information Processing, ISTC
ISSN (Print)2165-4700
ISSN (Electronic)2165-4719

Conference

Conference2012 7th International Symposium on Turbo Codes and Iterative Information Processing, ISTC 2012
Country/TerritorySweden
CityGothenburg
Period27/08/1231/08/12

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