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Evaluation of expurgated bound exponents

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1 Author(s)

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 \varrho \varepsilon [1, \infty ) , 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 1 \leq \varrho < \infty (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 \varrho \varepsilon [1, \infty ) the optimal expurgated exponent is attained by the uniform distribution over the inputs.

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Information Theory, IEEE Transactions on  (Volume:14 ,  Issue: 3 )