Analysis of low-density parity-check codes for the Gilbert-Elliott channel

  • Authors:
  • A. W. Eckford;F. R. Kschischang;S. Pasupathy

  • Affiliations:
  • Edward S. Rogers Sr. Dept. of Electr. & Comput. Eng., Univ. of Toronto, Ont., Canada;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2005

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Abstract

Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains.