Comment on "quasi-cyclic low density parity check codes from circulant permutation matrices"

  • Authors:

  • Manabu Hagiwara;Marc P. C. Fossorier

  • Affiliations:

  • National Institute of Advanced Industrial Science and Technology, Research Center for Information Security, Tokyo, Japan and Center for Research and Development Initiative, Chuo University, Tokyo, ...;3ETIS ENSEA/UCP/CNRS UMR, Cergy Pontoise, France

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

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Abstract

While preparing [H. Hagiwara et al., 2006], we realized that the proof of [M. Fossorier, 2004, Theorem 2.3] was leading to confusion as written. More precisely, only e1 = o2 directly follows from o1 + e1 and o2 + e2 = e. The other equality o1 = e2 follows from e1 = e2 and the fact that the sum of the (distinct) Delta's between the two rows considered has to be zero. Actually, a much concise proof can be obtained by directly observing that for J = p = 2m, {Delta1,2 (I) mod p, 0 < I < L - 1} = {0,1,..., L - 1} from [M. Fossorier, 2004, Theorem 2.1], so that SigmaI=0L-1 Delta1,2 (I) = m mod p ne 0. Since Ruwei Chen recently pointed out this issue, we decided to clarify this point.