Physical layer network coding for information exchange over a relay node

An information exchange problem between two source nodes over a network relay hub is considered where the downlink wireless broadcast channels from the hub to each node are asymmetrical, with different received SNRs. Conventional XOR network coding uses a single downlink FEC with a code rate that protects the node with the smaller received SNR, thereby penalizing the achievable information throughput to the node with larger received SNR. This paper presents an alternative physical network coding scheme that allows different downlink FECs from the hub to each node with different code rates and different data encoding lengths to achieve optimum capacity and information throughput results.