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There has recently been growing interest in using physical layer network coding techniques to facilitate information transfer in wireless relay networks. The physical layer network coding technique takes advantage of the additive nature of wireless signals by allowing two terminals to transmit simultaneously to the relay node. This technique has several performance benefits, such as improving utilization and throughput of wireless channels and reducing delay. In this thesis, we present an algorithm for joint decoding of two unsynchronized transmitters to a modulo-2 sum of their transmitted messages. We address the problems that arise when the boundaries of the signals do not align with each other and when their phases are not identical. Our approach uses a state-based Viterbi decoding scheme that takes into account the timing offsets between the interfering signals. As a future research plan, we plan to utilize software-defined radios (SDRs) as a testbed to show the practicality of our approach and to verify its performance. Our simulation studies show that the decoder performs well with the only degrading factor being the noise level in the channel.