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The design of modulation schemes for the physical layer network-coded two way relaying scenario was studied. It was shown that every network coding map that satisfies the exclusive law is represent able by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. But, only the scenario in which the end nodes use M-PSK signal sets is addressed. In this paper, the authors address the case in which the end nodes use M-QAM signal sets. In a fading scenario, for certain channel conditions, termed singular fade states, the MA phase performance is greatly reduced.
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