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

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2 Author(s)
Al-Lawati, H. ; Dept. of Math. & Stat., Queen''s Univ., Kingston, ON ; Alajaji, F.

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.

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Communications, IEEE Transactions on  (Volume:57 ,  Issue: 4 )