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In this work, we study a cross-layer design of a spectrally efficient bidirectional relay communication in a three- node network using superposition encoding at the relay node. On the physical layer, a half-duplex relay node decodes-and- forwards the messages of two nodes in a two-phase protocol with optimal time-division. On the data link layer, we assume ergodic arrival processes at node 1 and 2 which have queues with infinite buffer length. At the beginning of each time-slot a centralized controller chooses the service rate pair which achieves the weighted rate sum maximum of the instantaneous achievable rate region for the block-fading channel state of the next time-slot with weights equal to the current buffer levels. To this end, the controller adjusts the time-division and relay power distribution. The policy is throughput optimal since the stability region is equal to the bidirectional ergodic rate region. This is because whenever the mean queue length is large, a negative drift of a quadratic Lyapunov function on the buffer levels can be proved.