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This paper is inspired by the general question of how to choose signaling points from a bounded set such that capacity of the corresponding channel is maximized. Since, subject to peak power constraints capacity achieving distributions become discrete, this question is most relevant for practical application. However, a solution seems to be difficult in general. In this paper, the authors confine ourselves to determining optimum signaling points for selected schemes. As a key problem, determining the entropy of mixture distributions is identified, which is of interest in itself and has applications in many engineering applications.
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