Error-correction capability of column-weight-three LDPC codes

Shashi Kiran Chilappagari, Bane Vasic

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ≥ errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any α > 0, ∃ N such that ∀ n > N, no code in the ensemble of column-weight-three codes can correct all αn or fewer errors. The results are extended to the bit flipping algorithms.

Original languageEnglish (US)
Pages (from-to)2055-2061
Number of pages7
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 2009


  • Error-correction capability
  • Gallager A algorithm
  • Low-density parity-check (LDPC) codes
  • Tanner graph
  • Trapping sets

ASJC Scopus subject areas

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


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