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We describe parallel concatenated codes for communications over continuous hidden Markov channels. We present three decoding systems that utilize the a priori statistics of the channel and clearly outperform systems based on the traditional approach of using a channel interleaver to create a channel which is assumed to be memoryless. Moreover, for each one of these systems, we develop a joint estimation/decoding method that allows the estimation of the parameters of the model without the need for training sequences. This joint estimation/decoding method involves little or no sacrifice in performance relative to the case where the Markov channel parameters are provided to the receiver as a priori information.