Increasing signaling power not necessarily improves channel capacity

This work 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 we 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 is also relevant for other information processing applications. Even for the equiprobable mixture of two Gaussians no simple analytical expression is known. For 2-PAM signaling we investigate two simpler noise distributions, the triangular and chopped uniform one, and determine the capacity of the corresponding channels. While in the first case capacity increases monotonically as signaling points become further apart, in the second monotonicity does not hold. We finally conjecture that monotonicity can be concluded from the behavior of the equivalent binary asymmetric channel.