  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.
