On trapping sets and guaranteed error correction capability ofLDPC codes and GLDPC codes

Shashi Kiran Chilappagari, Dung Viet Nguyen, Bane Vasic, Michael W. Marcellin

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

The relation between the girth and the guaranteed error correction capability of γ-left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3γ/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed error correction capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed error correction capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.

Original languageEnglish (US)
Article number5437420
Pages (from-to)1600-1611
Number of pages12
JournalIEEE Transactions on Information Theory
Volume56
Issue number4
DOIs
StatePublished - Apr 1 2010

Keywords

  • Bit flipping algorithms
  • Error correction capability
  • Fixed sets
  • Generalized low-density parity-check (LDPC) codes
  • Low-density parity-check (LDPC) codes
  • Trapping sets

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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