"Physical-layer network coding (PNC) is an attractive approach to increasing the network throughput by exploiting the broadcast nature of wireless channels. This thesis focuses on the application of PNC in a class of wireless networks known as multi-way relay channels (MRWC), where multiple users share information through a single relay. The primary objective of the thesis is to develop new uplink and downlink schemes for PNC in MWRC, with the main focus on signal detection and power allocation. First, we propose a novel signal detection scheme for PNC in MWRC from the perspective of sequential multi-user detection. The extraction of the network codes from the superimposed user signals at the relay node is formulated as an under-determined linear system. To solve this problem with low decoding complexity, the proposed method combines successive interference cancellation (SIC) with Babai estimation for regularized integer least squares (ILS). We develop a power allocation scheme to enhance the performance of both SIC and ILS steps, and discuss an optimal user pairing strategy based on the average decoding error probability. The performance of the proposed method improves the relay's capability of extracting network codes from multiple superimposed user signals, as demonstrated by the numerical results. Next, we address the design of power allocation schemes for PNC in downlink MWRC. The power allocation is formulated as a constrained optimization problem, where the aim is to maximize the probability of successfully decoding a chain of network codes, so-called success probability, under a total power constraint when using Babai estimation for signal detection. Three aggregate measures of success probability are considered over the participating user terminals, i.e., arithmetic mean, geometric mean, and maximin, and the solutions are obtained based on the concavity of the related problems. Results demonstrate the effectiveness of the proposed schemes in improving the success probability in the reception of a chain of network codes. Finally, we propose a new power allocation scheme based on the success probability of SIC detection for PNC in uplink MWRC. We develop a generalized expression for the closed-form success probability of the SIC detection at the relay in the case of pulse-amplitude modulation (PAM). A constraint optimization is formulated over this probability subject to the transmit power constraints at the user terminals. We develop an evolutionary particle swarm optimization (PSO) algorithm to solve the problem, whose cost function is relatively complex and not necessarily concave. Results show that the proposed method can improve the quality of network code extraction at the relay"--