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Most investigations on the effect of channel memory on the performance of block codes use a two-state Gilbert-Elliott (GE) model to describe the channel behavior. As there are circumstances that the channel of concern can not be properly described by the GE model, there are some recent works on coded performance that characterize the channel behavior by a general finite-state Markov chain. This letter presents a new efficient systematic approach to analyze the performance of block codes in such a hidden Markov channel (HMC). An application example is given to predict codeword error probability performance of an RS-coded system in a channel with memory. Numerical results are also provided to validate our analytic results.