The Capacity Region of a Class of Z Channels With Degraded Message Sets

We study a two-transmitter two-receiver network where Receiver 1 can only hear the transmitted signal of Transmitter 1. Transmitter 1 has two messages, one of which is intended for Receiver 1 while both are intended for Receiver 2. Transmitter 2 has one message which is intended for Receiver 2. We call this channel model the Z channel with degraded message sets. For networks with the element of distributed encoding, it has been shown that when the multiple access link between the two encoders and the decoder satisfies the conditions proposed by Liu and Goldsmith, capacity results can be obtained for a variety of problems. In this paper, we generalize these conditions and show that for a larger class of multiple access links, the capacity region of the Z channel with degraded message sets can be characterized despite the presence of distributed encoding.