Detection of binary Markov sources over channels with additive Markov noise

We consider maximum a posteriori (MAP) detection of a binary asymmetric Markov source transmitted over a binary Markov channel. The MAP detector observes a long (but finite) sequence of channel outputs and determines the most probable source sequence. In some cases, the MAP detector can be implemented by simple rules such as the “believe what you see” rule or the “guess zero (or one) regardless of what you see” rule. We provide necessary and sufficient conditions under which this is true. When these conditions are satisfied, the exact bit error probability of the sequence MAP detector can be determined. We examine in detail two special cases of the above source: (i) binary independent and identically distributed (i.i.d.) source and (ii) binary symmetric Markov source. In case (i), our simulations show that the performance of the MAP detector improves as the channel noise becomes more correlated. Furthermore, a comparison of the proposed system with a (substantially more complex) traditional tandem source-channel coding scheme portrays superior performance for the proposed scheme at relatively high channel bit error rates. In case (ii), analytical as well as simulation results show the existence of a “mismatch” between the source and the channel (the performance degrades as the channel noise becomes more correlated). This mismatch is reduced by the use of a simple rate-one convolutional encoder