Abstract
In this paper, we investigate the problem of optimizing the expurgated upper bound to the probability of error associated with transmission over discrete memoryless channels. We find a general sufficient condition under which, for a given value of the parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\varrho \varepsilon [1, \infty)</tex> , the channel input distribution that leads to the optimal exponent corresponds to a constant memoryless source. We then derive a necessary and sufficient condition that the above property holds for all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 \leq \varrho < \infty</tex> (even then, different values of o would, in general, induce different optimal input distributions). Finally, we define a class of equidistant channels that includes all binary input channels, and show that for this class and all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\varrho \varepsilon [1, \infty)</tex> the optimal expurgated exponent is attained by the uniform distribution over the inputs.
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