Capacity Bounds for a Class of Interference Relay Channels

The capacity of a class of interference relay channels (IRCs)-the injective semideterministic IRC where the relay can only observe one of the sources-is investigated. We first derive a novel outer bound and two inner bounds which are based on a careful use of each of the available cooperative strategies together with the adequate interference decoding technique. The outer bound extends Telatar and Tse´s work, whereas the inner bounds contain several known results in the literature. Our main result is the characterization of the capacity region of the Gaussian class of IRCs studied within a fixed number of bits per dimension, constant gap. The proof relies on the use of the different cooperative strategies in specific SNR regimes due to their complexity. As a matter of fact, this issue reveals the complex nature of the Gaussian IRC where the combination of a single coding scheme for the Gaussian relay and interference channel may not lead to a good coding scheme for this problem, even when the focus is only on capacity within a constant gap over all possible fading statistics.