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The authors consider the Gaussian N-relay diamond network, where a source wants to communicate to a destination node through a layer of N-relay nodes. They investigate the following question: What fraction of the capacity can they maintain by using only k out of the N available relays? They show that in every Gaussian N-relay diamond network, there exists a subset of k relays which alone provides approximately a fraction k/k+1 of the total capacity. The result holds independent of the number of available relay nodes N, the channel configurations and the operating SNR.
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