Sum degrees-of-freedom of two-unicast wireless networks
Ilan Shomorony, A. Salman Avestimehr · 2011
We consider two-source two-destination (i.e., two-unicast) multi-hop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are independently drawn from continuous distributions, then, with probability 1, two-unicast layered Gaussian networks can only have 1, 3/2 or 2 sum degrees-of-freedom. We provide necessary and sufficient conditions for each case based on the network topology and a new notion of source-destination paths with manageable interference.