Detection of Binary Sources Over Discrete Channels with Additive Markov Noise

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We consider the problem of directly transmitting a binary source with an inherent redundancy over a binary channel with additive stationary ergodic Markov noise. Out objective is to design an optimum receiver which fully utilizes the source redundancy in order to combat the channel noise.

We investigate the problem of detecting a binary iid non-uniform source transmitted across the Markov channel. Two maximum a posteriori (MAP) formulations are considered: a sequence MAP detection and an instantaneous MAP detection. The two MAP detection problems are implemented using a modified version of the Viterbi decoding algorithm and a recursive algorithm. Necessary and sufficient conditions under which the sequence MAP detector becomes useless as well as simulation results are presented. A comparison between the performance of the proposed system with that of a (substantially more complex) traditional tandem source-channel coding scheme exhibits a better performance for the proposed scheme at relatively high channel bit error rates.

The same detection problem is then analyzed for the case of a binary symmetric Markov source. Analytical and simulation results show the existence of a "mismatch" between the source and the channel. This mismatch is reduced by the use of a rate-one convolutional encoder. Finally, the detection problem is generalized for the case of a binary non-symmetric Markov source.