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The characterization of binary communication channels using functions of finite-state Markov chains is considered. Two distributions which are relevant to code evaluation, i.e., the error-free run and error-cluster distributions, are derived. It is shown for an -state model, partitioned into a group of error-free states and error states, that the general form of the error-free run distribution is the weighted sum of at most exponentials, and that of the error-cluster distribution the weighted sum of at most exponentials. As evidence of the capability of such models to characterize real communication channels, a simple class of models is investigated and shown experimentally to be capable of representing HF radio statistics.