Capacity of Strong and Very Strong Gaussian Interference Relay-without-delay Channels

TL;DR

This paper investigates the capacity of Gaussian interference channels with a relay that can transmit instantaneously, proposing an achievable scheme that is exactly optimal under certain power conditions, which is a novel result.

Contribution

It introduces a new capacity-achieving scheme for strong and very strong Gaussian interference relay channels with instantaneous relaying, surpassing typical asymptotic optimality.

Findings

The scheme achieves exact capacity when relay power exceeds a threshold.

Outer bounds are established for strong and very strong interference cases.

The proposed method is simple and practically useful.

Abstract

In this paper, we study the interference relay-without-delay channel which is an interference channel with a relay helping the communication. We assume the relay's transmit symbol depends not only on its past received symbols but also on its current received symbol, which is an appropriate model for studying amplify-and-forward type relaying when the overall delay spread is much smaller than the inverse of the bandwidth. For the discrete memoryless interference relay-without-delay channel, we show an outer bound using genie-aided outer bounding. For the Gaussian interference relay-without-delay channel, we define strong and very strong interference relay-without-delay channels and propose an achievable scheme based on instantaneous amplify-and-forward (AF) relaying. We also propose two outer bounds for the strong and very strong cases. Using the proposed achievable scheme and outer bounds, we show that our scheme can achieve the capacity exactly when the relay's transmit power is greater than a certain threshold. This is surprising since the conventional AF relaying is usually only asymptotically optimal, not exactly optimal. The proposed scheme can be useful in many practical scenarios due to its optimality as well as its simplicity.