Capacity of the Generalized Pulse-Position Modulation Channel

We show the capacity of a generalized pulse-position modulation (PPM) channel, where the input vectors may be any set that allows a transitive group of coordinate permutations, is achieved by a uniform input distribution. We derive a simple expression in terms of the Kullback–Leibler distance for the binary case, and find the asymptote in the PPM order. We prove a sub-additivity result for the PPM channel and use it to show PPM capacity is monotonic in the order.