The Arbitrarily Varying Gaussian Relay Channel with Sender Frequency Division

TL;DR

This paper analyzes the capacity of the arbitrarily varying Gaussian relay channel with sender frequency division, providing bounds and conditions for capacity equality or disparity under various constraints.

Contribution

It determines the random and deterministic code capacities, establishes bounds, and identifies conditions for capacity equivalence in this specific relay channel model.

Findings

Deterministic capacity can be lower than random capacity under low power input.

Capacity bounds are established for primitive arbitrarily varying relay channels.

Deterministic and random capacities coincide in the primitive channel case.

Abstract

We consider the arbitrarily varying Gaussian relay channel with sender frequency division. We determine the random code capacity, and establish lower and upper bounds on the deterministic code capacity. It is observed that when the channel input is subject to a low power limit, the deterministic code capacity may be strictly lower than the random code capacity, and the gap vanishes as the input becomes less constrained. A second model addressed in this paper is the general case of primitive arbitrarily varying relay channels. We develop lower and upper bounds on the random code capacity, and give conditions under which the deterministic code capacity coincides with the random code capacity, and conditions under which it is lower. Then, we establish the capacity of the primitive counterpart of the arbitrarily varying Gaussian relay channel with sender frequency division. In this case, the deterministic and random code capacities are the same.