The Gaussian Interference Relay Channel with a Potent Relay

We consider the Gaussian interference channel with an intermediate relay. The relay is assumed to have abundant power and is named potent for that reason. A main reason to consider this model is to find good outerbounds for the Gaussian interference relay channel (GIFRC) with finite relay power. By setting the power of the relay constraint to infinity, we show that the capacity region is asymptotically equivalent to the case when the relay-destination links are noiseless and orthogonal to other links. The capacity region of the latter provides an outerbound for the GIFRC with finite relay power. We then show the capacity region of the former can be upper bounded by a single-input-multiple-output interference channel with an antenna common to both receivers. To establish the sum capacity of this channel, we study the strong and the weak interference regimes. For both regimes, we show that the upperbounds we find are achievable, thus establishing the sum capacity of GIFRC with the potent relay. Both results, in turn, serve as upperbounds for the sum capacity of the GIFRC with finite relay power. Numerical results show that the upperbounds are close to the known achievable rates for many scenarios of interest.