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

  • Authors:
  • Shashi Kiran Chilappagari;Bane Vasic

  • Affiliations:
  • Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ;Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

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 ≥ 5 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.