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

The problem of capacity achieving (optimal) input probability measure (p.m.) 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 p.m.’s, under which the optimal input p.m. is shown to be discrete with a finite number of probability mass points when peak power limited. Index Terms Channel capacity, discrete input, conditional output probability measure, real scalar channels