Interference Channel With a Causal Relay Under Strong and Very Strong Interference

In this paper, we study a two-user interference channel with a causal relay, where the relay´s transmit symbol depends not only on its past received symbols, but also on its present received symbol. This is an appropriate model for studying amplify-and-forward type relaying when the bandwidth delay-spread product is much smaller than one. For the discrete memoryless interference channel with a causal relay, we derive a genie-aided outer bound. For the Gaussian interference channel with a causal relay, we define strong and very strong interference conditions and propose an outer bound for each case. We also propose an achievable scheme based on instantaneous amplify-and-forward (AF) relaying for the Gaussian interference channel with a causal relay and so it achieves capacity under some conditions. Our result extends the previous result by El Gamal, Hassanpour, and Mammen on the optimality of instantaneous AF relaying for the Gaussian relay channel with a causal relay to that of the Gaussian interference channel with a causal relay under strong and very strong interference.