  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 Gel'fand-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 Gel'fand-Pinsker problem.
