Gaussian Z-interference channel with a relay link: Type II channel and sum capacity bound

This paper studies the Gaussian Z-interference channel with a rate-limited digital relay link from one receiver to the other receiver. In a companion paper, we dealt with the Type I channel, where the relay link goes from the interference-free receiver to the interfered receiver. It was shown that in the weak interference regime, each relay bit can improve the sum capacity by up to one bit asymptotically in the high signal-to-noise-ratio and interference-to-noise-ratio limit. In this paper, we study the Type II channel where the relay link goes from the interfered receiver to the interference-free receiver. The capacity region for such a channel is established in the strong interference regime; achievable rate regions are established in the moderately strong and weak interference regimes. In the weak interference regime, we show that in contrast to the Type I channel, the sum capacity improvement due to relaying for the Type II channel is upper bounded by at most half a bit, even as the relay link rate goes to infinity.