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A signal is sent by a two-state Markov source through a noisy channel. The objective is to develop a decoding scheme to obtain a reconstruction of the original signal. Necessary and sufficient conditions are presented, in both a sequential and a nonsequential context, for the optimality of several decoding schemes, including the singlet decoding rule and the data-independent decoding rule. A generalization of the simple noise process given by Drake  is presented, and analogous results are derived.