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In physical layer network coding, it has been argued that performance improvements of a few dBs can be achieved by decoding a linear combination of colliding frames at an intermediate relay. The best results have been achieved by directly decoding the necessary linear combination rather than decoding each of the colliding packets, but so far only rather impractical architectures have been proposed. We explore in this paper a more pragmatic approach, where some important problems have been solved. We show by simulation that the proposed system is able to outperform analog network coding, the only other known practical architecture in this area so far, with substantial gains especially when noise amplification at the relay can be particularly detrimental, for instance when spatial diversity is available or large networks are analyzed.