2014/04/19 by Ilan Shomorony, Shomorony, Ilan, A. Salman Avestimehr +1
Computer Science · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1404.4995
A shorter version of this paper will appear in the Proceedings of ISIT 2014
arxiv created 2014/04/19 · arxiv updated 2014/04/22
We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for deterministic networks, a recent result relating the capacity of AWGN KxKxK networks and the capacity of a deterministic counterpart allows us to establish an outer bound to the DoF of KxKxK wireless networks with general connectivity. This bound is tight in the case of the "adjacent-cell interference" topology, and yields graph-theoretic necessary and sufficient conditions for K DoF to be achievable in general topologies.