On the Capacity of the Interference Channel with a Cognitive Relay

Abstract: The InterFerence Channel with a Cognitive Relay (IFC-CR) consists of the classical interference channel with two independent source-destination pairs whose communication is aided by an additional node, referred to as the cognitive relay, that has a priori knowledge of both sources' messages. This a priori message knowledge is termed cognition and idealizes the relay learning the messages of the two sources from their transmissions over a wireless channel. This paper presents new inner and outer bounds for the capacity region of the general memoryless IFC-CR that are shown to be tight for a certain class of channels. The new outer bound follows from arguments originally devised for broadcast channels among which Sato's observation that the capacity region of channels with non-cooperative receivers only depends on the channel output conditional marginal distributions. The new inner bound is shown to include all previously proposed coding schemes and it is thus the largest known achievable rate region to date. The new inner and outer bounds coincide for a subset of channel satisfying a strong interference condition. For these channels there is no loss in optimality if both destinations decode both messages. This result parallels analogous results for the classical IFC and for the cognitive IFC and is the first known capacity result for the general IFC-CR. Numerical evaluations of the proposed inner and outer bounds are presented for the Gaussian noise case.