A Counterexample to Cover's 2P Conjecture on Gaussian Feedback Capacity

TL;DR

This paper presents a counterexample disproving Cover's conjecture that the feedback capacity of a Gaussian channel is always less than or equal to the nonfeedback capacity at double the power constraint.

Contribution

The paper provides a specific counterexample showing that Cover's 2P conjecture does not hold universally for Gaussian feedback channels.

Findings

Counterexample invalidates Cover's 2P conjecture

Feedback capacity can exceed nonfeedback capacity at doubled power

Challenges existing assumptions about Gaussian channel capacities

Abstract

We provide a counterexample to Cover's conjecture that the feedback capacity $C_\textrm{FB}$ of an additive Gaussian noise channel under power constraint $P$ be no greater than the nonfeedback capacity $C$ of the same channel under power constraint $2P$, i.e., $C_\textrm{FB}(P) \le C(2P)$.