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.