On the capacity region of a class of Z Channels with cooperation

In this paper, we consider Z Channel (ZC) with cooperation, where there are two senders and two receivers. The first sender transmits information to both receivers and also to the second sender. The first receiver and the second sender cooperate with the first sender in sending messages to the second receiver. The second sender transmits information only to its intended receiver. We first establish an achievable rate region for the general cooperative ZC. The coding scheme is based on rate splitting technique. At the receivers, we use joint decoding strategy. To illustrate the tightness of the proposed inner bound, we define degraded cooperative ZC. We derive an outer bound to the capacity region of the degraded cooperative ZC. It will be shown that the two bounds coincide and determine the capacity region of the degraded cooperative ZC.