On feedback in Gaussian multi-hop networks

The study of feedback has been mostly limited to single-hop communication settings. In this paper, we consider Gaussian networks where sources and destinations can communicate with the help of intermediate relays over multiple hops. We assume that links in the network can be bidirected providing opportunities for feedback. We ask the following question: can the information transfer in both directions of a link be critical to maximizing the end-to-end communication rates in the network? Equivalently, could one of the directions in each bidirected link (and more generally at least one of the links forming a cycle) be shut down and the capacity of the network still be approximately maintained? We show that in any arbitrary Gaussian network with bidirected edges and cycles, and unicast, multiple-access or broadcast traffic, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. On the other hand, with multicast and multiple unicast traffic bidirected flow across links can be critical to maximizing the end-to-end capacity.