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The problem of finding the optimum output quantizer for a given discrete memory-less channel is investigated, where the quantizer output has fewer values than the channel output. While mutual information has received attention as an objective function for optimization, the focus of this paper is use of the random coding exponent, which was originally derived by Gallager, as criteria. Two problems are addressed, where one problem is a partial problem of the other. The main result is a quantizer design algorithm, and a proof that it finds the optimum quantizer in the partial problem. The quantizer design algorithm is based on a dynamic programming approach, and is an extension of a mutual-information maximization method.
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