Lossy source-channel communication over a phase-incoherent interference relay channel

We study the lossy communication of a bivariate Gaussian source over an interference channel with the presence of a helping relay. We assume that the wireless links introduce random phase shifts which are unknown to the transmitters (including the relay) and call the channel a phase incoherent interference relay channel (PI-IRC). We derive inner and outer bounds for the achievable distortion region, where the inner bound is derived under specific strong interference conditions as well as strong gain conditions between transmitters and the relay. When the sources are correlated, we find an approximate achievable distortion region in the high SNR regime. In case of independent sources, the bounds are tight and by explicitly providing the achievable distortion region, we show that a separation theorem results for the PI-IRC under strong interference conditions. By removing the relay, the result also specializes to an interference channel.