We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide upper and lower bounds on the capacity of this channel. We then show that, when the channel
of the transmitter-receiver pair that does not face interference is noiseless, the two bounds coincide and therefore yield the capacity region. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gelfand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity result for a generalized Gelfand-Pinsker problem.
