Capacity Achieving Peak Power Limited Probability Measures: Sufficient Conditions for Finite Discreteness

The problem of capacity achieving (optimal) input probability measures has been widely investigated for several channel models with constrained inputs. So far, no outstanding generalizations have been derived. This paper does a forward step in this direction, by introducing a set of new requirements, for the class of real scalar conditional output probability measures, under which the optimal input probability measure is shown to be discrete with a finite number of probability mass points, when peak power limited.