  The study considers a three-node, two-way relaying network (TWRN) over a
multi-carrier system, aiming to minimize the total power consumption of all the
transmit and receiver activities. By employing digital network coding (DNC) and
physical-layer network coding (PNC), respectively, as well as a novel hybrid
PNC/DNC switching scheme, the total transmission power of the considered
multi-carrier TWRN system is firstly analyzed; and the derived analytical
expressions are then used to formulate a set of nonconvex optimization
problems. We will show how those nonconvex functions are convexified for better
computational tracbility. It is observed in the numerical results that, the PNC
scheme generally consumes less power than DNC but becomes worse in the very low
SNR regime. The proposed hybrid PNC/DNC switching scheme that takes advantage
of both, is shown to outperform in all SNR regimes.
