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Many communication channels with discrete input have non-uniform capacity achieving Probability Mass Functions (PMF). By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modulator can generate dyadic PMFs at the channel input. In this paper, the authors show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF.
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