Detection of Binary Sources Over Discrete Channels with Additive Markov Noise

Abstract

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.<P>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.<P>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.