The ergodic fading interference channel with an on-and-off relay

We consider the ergodic fading Gaussian interference relay channel (EF-GIFRC) with individual power constraints at the nodes. Aiming at design insights to emerge from the optimal power allocation, we focus on scenarios similar to that of the degraded/reversely degraded relay channels. In particular, we focus on models where the source-to-relay (S - R) links are either stronger than direct links, or completely blocked, i.e., with an "on-and-off" relay. To characterize the capacity of EF-GIFRC with an on-and-off relay, we first investigate the parallel interference relay channel. We propose an achievable scheme based on partial decode-and-forward (DF) strategy and show that the capacity for the parallel IFRC can be achieved under strong interference and degradedness conditions. Based on the achievable rate region for parallel IFRC, we propose an achievable rate region for EF-GIFRC, and present the properties of optimal power allocation. We also present a sum capacity result when the EF-GIFRC satisfies certain channel conditions.