Sum capacity of the deterministic interference channel with an out-of-band half-duplex relay

We consider the linear deterministic model for the two user interference channel (IC) with an out-of-band relay (OBR). In this model, each user has access to two orthogonal bands, where one band forms the IC, and the other band is assisted by a half-duplex relay, i.e., the relay receives and transmits in orthogonal bands. The channel is assumed to be symmetric. We first derive new outerbounds using genie arguments, and then construct optimal relaying strategies. As a result, we characterize the sum capacity of this model for all channel parameters. In particular, it is shown that similar to the case of the IC with output feedback (and without a relay), the "W" curve for the sum capacity of the IC becomes "V" curve as the strength of the links in the OBRC grows. The interference links are classified as extremely strong, very strong, strong, moderate, weak, and very weak. For the IC without the relay, it is known that some signal spaces are left unused for the sum-capacity-optimal transmission strategy. We show that, with an OBR, these spaces can be utilized to achieve the sum capacity of this model improving upon that of the IC without the OBR. We show that for very strong and extremely strong interference, the interference is useful to improve the achievable rates. For weak or very weak interference, the unused signal spaces of the IC can be utilized to transmit new information bits.