Capacity outer bounds for the cognitive Z channel

This paper considers the so-called cognitive Z channel, where two users transmit two independent messages to their respective receivers through a Z interference channel. User 1 (primary user) interferes with receiver 2 while user 2 (secondary user) does not interfere with receiver 1. In addition, user 2 overhears the transmission of user 1 through a noisy channel, hence the term 'cognitive'. We proposed two nontrivial capacity outer bounds, which established a capacity region corner point for certain parameter regimes. These outer bounds, together with previously proposed achievable rate region, shed light on the usefulness of the causal cooperation under certain channel conditions. Numerical examples are also given.