In this thesis, we investigate the two-way relay channel (TWRC) and protocols such as amplify and forward (AF), decode and forward (DF) and physical-layer network coding (PNC) in order to analyze the achievable maximum sum rate in TWRC theoretically. Next, we investigate the algorithms and performances of the optimal power allocation and the optimal time allocation for two-way relay channel using DF and PNC to maximize the achievable sum rate. Optimal time allocation for TWRC using PNC has not been analyzed in the literature. Therefore, we propose an optimal time allocation scheme for two-way relay channel using the physical-layer network coding. In other words, we analytically determine the optimal transmit time durations for the first and the second time slot, which maximize the achievable sum rate under a sum time constraint for a given squared magnitude of the channel coefficients and transmit power values. The closed forms of the achievable sum rate gain of the proposed optimal time allocation over the equal time allocation scheme for some special cases are also derived. Numerical results show that the achievable sum rate for proposed optimal time allocation is greater than or equal to that for equal time allocation.