Reducing the number of signaling points keeping capacity and cutoff rate high

Imposing so called peak power constraints on the input of a channel in many cases leads to a discrete capacity-achieving distribution with finite support. Given a finite number of signaling points ab initio, in this paper we determine reduced subsets in order to simplify the receiver design. The objective is to still keep the channel quality high. Two criteria are maximized, channel capacity and cutoff rate. By considering a uniform distribution over all signaling points, a lower bound to the general problem of finding an optimum signaling constellation in a bounded set and simultaneously the optimum input distribution is obtained. By semidefinite programming we show that even if only a small number of signaling points is selected the capacity and cutoff rate of the channel can be kept high.