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The authors consider physical network coding on a two-way relay channel. Two source nodes send their packets simultaneously over time-varying MIMO channels to a relay node. Assuming that the relay employs the joint decode-and-forward strategy, the relay must be able to decode the individual source packets. This task requires a robust estimation of the source-to-relay channels. They design a message passing algorithm based on factor-graphs to solve this problem efficiently. The use of network coding in wireless networks has attracted considerable interest during the last decade. They consider the two-way relay channel with half-duplex constraint (i.e. a node cannot transmit and receive at the same time).
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