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

TL;DR

This paper establishes new sufficient conditions under which the optimal input probability measure for peak power limited channels is discrete with finitely many mass points, advancing the understanding of capacity-achieving measures.

Contribution

It introduces novel requirements for real scalar channels that guarantee the finiteness and discreteness of optimal input measures under peak power constraints.

Findings

Optimal input measures are discrete with finite support under new conditions.

Provides a theoretical framework for capacity-achieving measures with peak power limits.

Advances the general understanding of input distributions in constrained channel models.

Abstract

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.