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Abstract: Many communication channels with discrete input have non-uniform capacityachieving probability mass functions PMF. By parsing a stream of independentand equiprobable bits according to a full prefix-free code, a modu-lator cangenerate dyadic PMFs at the channel input. In this work, we show that fordiscrete memoryless channels and for memoryless discrete noiseless channels,searching for good dyadic input PMFs is equivalent to minimizing theKullback-Leibler distance between a dyadic PMF and a weighted version of thecapacity achieving PMF. We define a new algorithm called Geometric HuffmanCoding GHC and prove that GHC finds the optimal dyadic PMF in Om \log msteps where m is the number of input symbols of the considered channel.Furthermore, we prove that by generating dyadic PMFs of blocks of consecutiveinput symbols, GHC achieves capacity when the block length goes to infinity.

Autor: Georg Böcherer, Rudolf Mathar


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