Weight distributions of multi-edge type LDPC codes

  • Authors:

  • Kenta Kasai;Tomoharu Awano;David Declercq;Charly Poulliat;Kohichi Sakaniwa

  • Affiliations:

  • Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan and ETIS ENSEA, University of Cergy-Pontoise, CNRS, Cergy, France;Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan;ETIS ENSEA, University of Cergy-Pontoise, CNRS, Cergy, France;ETIS ENSEA, University of Cergy-Pontoise, CNRS, Cergy, France;Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
  • Year:
  • 2009

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Abstract

For a (λ(x), ρ(x)) standard irregular LDPC code ensemble, the growth rate of the average weight distribution for small relative weight ω is given by log(λ′(0)ρ′(1))ω + O(ω2) in the limit of code length n. If λ′(0)ρ′(1) n tends to infinity. It is known that the condition coincides with the stability condition of density evolution over the erasure channels with the erasure probability 1. In this paper, we show that this is also the case with multi-edge type LDPC (MET-LDPC) codes. MET-LDPC codes are generalized structured LDPC codes introduced by Richardson and Urbanke. The parameter corresponding λ&prime(0)ρ′(1) appearing in the conditions for MET-LDPC codes is given by the spectral radius of the matrix defined by extended degree distributions.