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Abstract: In this work we are concerned with the problem of achieving max-min fairnessin Gaussian parallel channels with respect to a general performance function,including channel capacity or decoding reliability as special cases. As ourcentral results, we characterize the laws which determine the value of theachievable max-min fair performance as a function of channel sharing policy andpower allocation to channels and users. In particular, we show that themax-min fair performance behaves as a specialized version of the Lovaszfunction, or Delsarte bound, of a certain graph induced by channel sharingcombinatorics. We also prove that, in addition to such graph, merely a certain2-norm distance dependent on the allowable power allocations and usedperformance functions, is sufficient for the characterization of max-min fairperformance up to some candidate interval. Our results show also a specificrole played by odd cycles in the graph induced by the channel sharing policyand we present an interesting relation between max-min fairness in parallelchannels and optimal throughput in an associated interference channel.



Author: Marcin Wiczanowski, Holger Boche

Source: https://arxiv.org/







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