Capacity Bounds Via Duality: A Phase Noise Example

Lapidoth and Moser have recently proposed a general technique for obtaining upper bounds on channel capacity via a dual expression in which the maximization over probability distributions on the channel input alphabet is replaced with a minimization over probability distributions on the channel output alphabet. They have also introduced the notion of “capacity achieving input distributions that escape to infinity” in order to study channel capacity at high signal-to-noise (SNR) ratios. In this partly tutorial paper we shall demonstrate the use of these ideas by applying them to the study of communication over discrete-time channels impaired by additive Gaussian noise and phase noise.