On the Secrecy Capacity of the Z-Interference Channel

The two-user Z-interference channel with an additional secrecy constraint is considered. The two transmitterreceiver pairs wish to reliably transmit their messages; however the transmission of the first pair both interferes with the transmission of the second pair and is also required to be completely secure from the second receiver. The focus here is on the capacity region of the above Z-interference channel in the Gaussian case under the standard power constraints. The maximum rates of the two users in this setting are described, and although the maximum rate of the transmission of the first pair has a single-letter expression, due to Wyner’s secrecy capacity expression, its maximization is non-trivial. The significance of a stochastic encoder for the second transmitter, encoding a message which is not required to comply with any secrecy constraints, is noted. It is shown explicitly that constraining this encoder to be deterministic reduces the capacity region. Finally, a Satotype outer bound on the capacity region is obtained under this additional deterministic encoder constraint.