Summary: IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 4, APRIL 2009 873
On Decoding Binary Perfect and Quasi-Perfect Codes over
Markov Noise Channels
Haider Al-Lawati and Fady Alajaji, Senior Member, IEEE
Abstract--We study the decoding problem when a binary
linear perfect or quasi-perfect code is transmitted over a bi-
nary 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.
Index Terms--Binary channels with memory, Markov noise,
maximum likelihood decoding, minimum Hamming distance
decoding, linear block codes, perfect and quasi-perfect codes.