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The authors consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. They prove that a moderate deviation principle holds for all convergence rates between the large deviation and the central limit theorem regimes. In block channel coding, there is a fundamental interplay between the rate, i.e., the amount of information transmitted per channel use, the block length, i.e., the total number of channel uses, and the probability of error. In this paper, they analyze the interplay between these three parameters for the best block codes.
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