The rapid growth of wireless communication technology has motivated novel approaches into improving performance. A major avenue of research investigates the benefit of relaying, where wireless devices outside radio range of each other communicate by passing information through a device in between. Traditionally, devices communicating through a relay transmit at separate times to avoid interfering with each other. Physical-layer network coding is a recent technique that improves throughput by allowing devices to transmit at the same time to the relay, deliberately interfering. This dissertation develops a system performing physicallayer network coding in the topology where two devices exchange information through a single relay. Many signaling techniques require synchronized carrier phases and frequencies for all three devices, which can be challenging to achieve in some scenarios. To alleviate the need for synchronization, this work develops a noncoherent system that requires only frame and symbol synchronization and relaxes the need for carrier synchronization. To combat the degrading effects of the wireless channel, the system utilizes bit-interleaved coded modulation (BICM) along with powerful iterative LDPC and turbo coding. The modulation considered, M-ary frequency-shift keying, is suitable for noncoherent reception and has constant envelope and high energy efficiency. Two formulations of demodulation are developed, one that requires knowledge of the fading amplitudes, and the other that requires only knowledge of the average power. The LDPC codes are optimized for the particular scheme by using extrinsic information transfer (EXIT) charts to identify promising variable-node degree distributions. Simulation results illustrate the efficacy of the proposed demodulator when it is combined with the optimized LDPC codes. The simulation results agree with the coded modulation (CM) capacities, which are also developed. Throughout this work, the capacity and error rate performance of the developed receiver is compared against conventional network coding where the end nodes avoid interfering by transmitting in different times or bands. iii Acknowledgements I have been extremely fortunate to be surrounded by inspiring individuals who made this contribution possible. Dr. Matthew Valenti is a patient, supportive mentor and friend who recognized my passion for creative challenges. I would like to thank my committee for their unwavering dedication. Dr. Brian Woerner made tremendous efforts to ensure that I was supported while performing research. The past and present students of the Wireless Communications Research Lab at WVU provided endless encouragement. Most of all I would like to thank my parents, who sacrificed deeply for me and taught me the value of persistence. My results could not have been produced without support from several generous sources. Various stages of my assistantship were supported by National Science Foundation (NSF) Award No. CNS-0750821 and Army Research Laboratory Contract W911NF-10-0109. Const...