On the construction of structured LDPC codes free of small trapping sets

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

Research output: Contribution to journalArticle

69 Scopus citations

Abstract

We present a method to construct low-density parity-check (LDPC) codes with low error floors on the binary symmetric channel. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the trapping set ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum-product algorithm by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets. We apply this method to construct structured LDPC codes. To facilitate the discussion, we give a new description of structured LDPC codes whose parity-check matrices are arrays of permutation matrices. This description uses Latin squares to define a set of permutation matrices that have disjoint support and to derive a simple necessary and sufficient condition for the Tanner graph of a code to be free of four cycles.

Original languageEnglish (US)
Article number6169192
Pages (from-to)2280-2302
Number of pages23
JournalIEEE Transactions on Information Theory
Volume58
Issue number4
DOIs
StatePublished - Apr 2012

Keywords

  • Error floor
  • Latin squares
  • structured low-density parity-check codes
  • trapping sets

ASJC Scopus subject areas

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

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