  In this paper, we consider three transmit strategies for the fading
three-node, two-way relay network (TWRN) -- 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 demonstrated theoretically that DNC-Sup outperforms DNC-TS and CW-Sup in
terms of total average energy usage. More importantly, it is shown in
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.
