On decoding binary perfect and quasi-perfect codes over Markov noise channels

Authors:
Haider Al-Lawati;Fady Alajaji
Affiliations:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada;Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada
Venue:
IEEE Transactions on Communications
Year:
2009

Citing 1
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Analysis of low-density parity-check codes for the Gilbert-Elliott channel

IEEE Transactions on Information Theory

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Abstract

We study the decoding problem when a binary linear perfect or quasi-perfect code is transmitted over a binary channel with additive Markov noise. After examining the properties of the channel block transition distribution, we derive sufficient conditions under which strict maximum-likelihood decoding is equivalent to strict minimum Hamming distance decoding when the code is perfect. Additionally, we show a near equivalence relationship between strict maximum likelihood and strict minimum distance decoding for quasi-perfect codes for a range of channel parameters and the code's minimum distance. As a result, an improved (complete) minimum distance decoder is proposed and simulations illustrating its benefits are provided.