Joint opportunistic scheduling and network coding for bidirectional relay channel

In this paper, we consider a two-way communication system in which two users communicate with each other through an intermediate relay over block-fading channels. We investigate the optimal opportunistic scheduling scheme in order to maximize the long-term average transmission rate in the system assuming symmetric information flow between the two users. Based on the channel state information, the scheduler decides that either one of the users transmits to the relay, or the relay transmits to a single user or broadcasts to both users a combined version of the two users' transmitted information by using linear network coding. We obtain the optimal scheduling scheme by using the Lagrangian dual problem. Furthermore, in order to characterize the gains of network coding and opportunistic scheduling, we compare the achievable rate of the system versus suboptimal schemes in which the gains of network coding and opportunistic scheduling are partially exploited.