On the capacity region of the Gaussian Z-channel

We investigate the capacity region of the Gaussian Z-channel with a small crossover link gain, i.e. α≤1. For the case of α<1, we provide an achievable region, and the converse for most of the achievable region. We also derive lower and upper bounds for the part of the region where the capacity boundary is unclear. For the case of α=1, we determine the capacity region exactly.