Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance

David Burshtein, Idan Goldenberg

Research output: Contribution to journalArticlepeer-review

Abstract

We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.

Original languageEnglish
Article number5955120
Pages (from-to)7386-7402
Number of pages17
JournalIEEE Transactions on Information Theory
Volume57
Issue number11
DOIs
StatePublished - Nov 2011

Keywords

  • Fractional distance
  • linear programming decoding
  • low-density parity-check (LDPC) codes
  • maximum likelihood (ML) decoding
  • minimum distance

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