The trapping redundancy of linear block codes

Stefan Laendner, Thorsten Hehn, Olgica Milenkovic, Johannes B. Huber

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation (BP) decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640, 1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.

Original languageEnglish (US)
Pages (from-to)53-63
Number of pages11
JournalIEEE Transactions on Information Theory
Volume55
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Belief propagation (BP)
  • Low-density parity-check (LDPC) codes
  • Margulis codes
  • Projective geometry (PG) codes
  • Trapping redundancy
  • Trapping sets

ASJC Scopus subject areas

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

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