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The authors provide a geometric solution to the problem of optimal relay positioning to maximize the multicast rate for low-SNR networks. The network they consider consists of a single source, multiple receivers and the only intermediate and locatable node as the relay. They construct network the hypergraph of the system nodes from the underlying information theoretic model of low-SNR regime that operates using superposition coding and FDMA in conjunction (which they call the "Achievable hypergraph model").
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