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.Index Terms-Binary channels with memory, Markov noise, maximum likelihood decoding, minimum Hamming distance decoding, linear block codes, perfect and quasi-perfect codes.

The performance of Reed-Solomon codes over the binary additive Markov noise channel (BAMNC) is analyzed.A recursive expression for the probability of Ñ error symbols in a block of Ò symbols is derived using the generating series approach, thus facilitating the exact calculation of the probability of codeword error under bounded distance decoding. An approximation to this probability is obtained, and it is shown to be tight when the noise correlation is not very large. In this case, interleaving the channel at the symbol level can be avoided. Furthermore, a wide range of channel conditions, under which channel interleaving at the bit level can be avoided, is identified.

No abstract

No abstract