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This paper introduces a new and effective information theoretic test of the accuracy of the Markov property of block errors in fading channels. We apply the test to verify the validity of a first-order Markov model for block error processes on Rayleigh and Ricean fading channels. Unlike previous work, we address the effects of maximal ratio diversity-combining at the receiver. As a second application, we investigate the behavior of the block success/failure process in transmission systems that incorporate closed-loop power control. This topic is of great interest in the design of next-generation wireless networks. Numerical results show that our approach provides significant improvements in accuracy over previously proposed methods.