The capacity region of a class of deterministic state-dependent Z-interference channels

We consider the problem of communicating over the state-dependent Z-interference channel (S-D Z-IC), when the state is known noncausally only to the interfering transmitter. We present an achievability scheme and show that it is optimal for the injective deterministic S-D Z-IC. This scheme is simple in the sense that it does not involve rate-splitting. The idea of the scheme is that the interfering transmitter chooses its signal to be jointly typical with an auxilary coordination codebook that allows the unintended receiver to partly decode the resultant interference. We then investigate the special case of the modulo-additive S-D Z-IC in detail and show that in this case standard Gelfand-Pinsker coding for the interfering link and treating interference as noise at the second link is optimal. We also extend our main result to the deterministic state-dependent Z-channel (S-D Z-C) in which an additional message is transmitted on the cross-link.