Bounds and capacity results for the cognitive Z channel

We study the discrete memoryless Z channel where the non-broadcasting transmitter is cognitive and knows both messages of the broadcasting transmitter. We call this the cognitive Z channel. We first propose inner and outer bounds on the capacity of the cognitive Z channel. The achievability scheme we propose consists of superposition encoding, Gel´fand-Pinsker encoding and Marton´s encoding scheme for the broadcast channel. We then show that our inner and outer bounds on the capacity region is tight when the the receiver without a crossover link sees a noiseless channel.