Capacity of the broadcasting phase of time-varying two-way relaying

In this paper, we mainly focus on the problem about the channel capacity and power allocation of the downlink process of a wireless two-way relay channel which is time-varying while the relay node has a total awareness of the channel side information. For situations differing about how receiving nodes know about messages for the other, we accordingly determine the channel capacities and the coding process using techniques such as network coding, superposition coding and nested coding; also the relay node should make corresponding strategies about power allocation with channel side information to attain the best average channel capacity, whose optimal solution in closed form is achieved using KKT conditions.