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Stochastic properties of the binary channel that describe the successes and failures of the transmission of a modulated signal over a time-correlated flat-fading channel are considered for investigation. This analysis is employed to develop κth-order Markov models for such a bunt channel. The order of the Markov model that generates accurate analytical models is estimated for a broad range of fading environments. The parameterization and accuracy of an important class of hidden Markov models, known as the Gilbert-Elliott channel (GEC), are also investigated. Fading rates are identified in which the κth-order Markov model and the GEC model approximate the fading channel with similar accuracy. The latter model is useful for approximating slowly fading processes, since it provides a more compact parameterization. [ABSTRACT FROM AUTHOR]