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The authors propose two practical power- and bandwidth-efficient systems based on amplify-and-forward and decode-and-forward schemes to address the problem of information exchange via a relay. The key idea is to channel encode each source's message by using a high-performance non-binary turbo code based on partial unit memory codes to enhance the bit-error-rate performance, then reduce the energy consumption and increase spectrum efficiency by using network coding (NC) to combine individual nodes' messages at the relay before forwarding to the destination. Two simple and low complexity physical layer NC schemes are proposed based on combinations of received source messages at the relay. The authors also present the theoretical limits and numerical analysis of the proposed schemes. Simulation results under additive white Gaussian noise confirm that the proposed schemes achieve significant bandwidth savings and fewer transmissions over the benchmark systems which do not resort to NC. Theoretical limits for capacity and signal-to-noise ratio behaviour for the proposed schemes are derived. This study also proposes a cooperative strategy that is useful when insufficient combined messages are received at a node to recover the desired source messages, thus enabling the system to retrieve all packets with significantly fewer retransmission request messages.