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In this paper, we consider three transmit strategies for the fading three-node two-way relay network, namely, physical-layer network coding (PNC), digital network coding (DNC), and codeword superposition (CW-Sup). The aim is to minimize the total average energy needed to deliver a given pair of required average rates. Full channel state information is assumed to be available at all transmitters and receivers. The optimization problems corresponding to the various strategies in fading channels are formulated, solved, and compared. For the DNC-based strategies, a simple time sharing of transmission of the network-coded message and the remaining bits of the larger message (DNC-TS) is considered first. We extend this approach to include a superposition strategy (DNC-Sup), in which the network-coded message and the remainder of the longer source message are superimposed before transmission. It is theoretically demonstrated that DNC-Sup outperforms DNC-TS and CW-Sup in terms of total average energy usage. More importantly, it is shown in the simulation that DNC-Sup performs better than PNC if the required rate is low and worse otherwise. Finally, an algorithm to select the optimal strategy in terms of energy usage subject to different rate pair requirements is presented.

Fading Two-Way Relay Channels: Physical-Layer Versus Digital Network Coding