Upper Bound on the Capacity of Gaussian Channels with Noisy Feedback

TL;DR

This paper establishes an upper bound on the capacity of Gaussian channels with noisy feedback by formulating a convex optimization problem and analyzing the limit under stationarity assumptions, providing insights into feedback capacity limits.

Contribution

It introduces a convex optimization framework to bound the capacity of Gaussian channels with noisy feedback and characterizes the asymptotic limit under stationarity.

Findings

Derived an upper bound on the n-block capacity for Gaussian channels with noisy feedback.

Proved the limit of the n-block upper bound equals the noisy feedback capacity under stationarity.

Provided a convex optimization approach to evaluate capacity bounds.

Abstract

We consider an additive Gaussian channel with additive Gaussian noise feedback. We derive an upper bound on the n-block capacity (defined by Cover [1]). It is shown that this upper bound can be obtained by solving a convex optimization problem. With stationarity assumptions on Gaussian noise processes, we characterize the limit of the n-block upper bound and prove that this limit is the upper bound of the noisy feedback (shannon) capacity.