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This paper addresses the design and performance evaluation of a pilot-aided turbo-coded system to achieve reliable PSK communication in frequency-flat, time-selective fading, with a relatively high Doppler rate. We introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude fading. The forward-backward algorithm is used to determine both the maximum a posteriori probability (MAP) value for each bit in the data sequence, and the MAP channel phase in each iteration. Soft information is exchanged between the phase and data estimation modules. Using a turbo-code and joint iterative decoding and channel estimation, performance is demonstrated to approach an upper bound to the capacity of a Markov-phase channel.