Capacity-achieving probability measure for a reduced number of signaling points

Putting bounding constraints on the input of a channel leads in many cases to a discrete capacity-achieving distribution with a finite support. Given a finite number of signaling points, we determine reduced subsets and the corresponding optimal probability measures to simplify the receiver design. The objective for the subset selection is to keep the channel quality high by maximizing mutual information and cutoff rate. Two approaches are introduced to obtain a capacity-achieving probability measure for the reduced subset. The first one is based on a preceded signaling point selection while the second one chooses the signaling points and corresponding probabilities simultaneously. Numerical results for both approaches show that using only a small number of signaling points achieves a very high mutual information compared to channels utilizing the full set of signaling points.