On the capacity region of the semi-deterministic Z channel

We study a class of discrete memoryless Z channels, where there are some deterministic components in the channel configuration. We call this channel the semi-deterministic Z channel. We first provide an outer bound on the capacity region. Then the known achievable rate region for the general Z channel is specialized to the semi-deterministic case. Noting the similarity between the inner and outer bounds, we identify special classes of semi-deterministic Z channels where the two bounds coincide and therefore establish their capacity regions.