Superposition encoding and partial decoding is optimal for a class of Z-interference channels

We apply a technique introduced by Korner and Marton to the converse of a class of Z-interference channels. This class has the properties that, for the transmitter-receiver pair that suffers from interference, 1) the conditional output entropy is invariant with respect to the input and, 2) the maximum output entropy is achieved by a single input distribution irrespective of the interference distribution. We show that for this class of channels, superposition encoding and partial decoding is optimal. We thus provide a single-letter characterization for the capacity region, which was previously unknown.