State-dependent Gaussian Z-interference channel: New results

A class of Gaussian Z-interference channels with state is investigated in the regime of high state power in which two transmitters communicate two independent messages through a “dirty” Z-interference channel. Transmitter 1 (primary user) interferes with receiver 2 while transmitter 2 (secondary user) does not interfere with receiver 1. In addition, receiver 2 suffers from a random state sequence which is non-causally known only at transmitter 1. For this setup, which is also investigated by Duan et al. in [1], first we characterize the capacity region for the deterministic case and then by the obtained insight from analyzing the deterministic case, we establish sufficient conditions under which lattice-based transmission schemes meet the capacity region outer bound. In general, we show that lattice codes can achieve the capacity region to within 1over2 log (3) ≈ 0.79 bit of the outer bound for all values of channel parameters.