On feedback in Gaussian multi-hop networks

TL;DR

This paper investigates the role of feedback in Gaussian multi-hop networks, showing that in many cases, acyclic subnetworks can approximate the original network's capacity, but feedback may be essential for certain traffic types.

Contribution

It demonstrates that acyclic subnetworks can often preserve capacity in multi-hop Gaussian networks, extending feedback insights from single-hop to complex multi-hop scenarios.

Findings

Acyclic subnetworks can approximately maintain capacity in arbitrary Gaussian networks.

For certain traffic types, feedback across links is crucial for maximizing capacity.

Results generalize feedback usefulness from single-hop to multi-hop Gaussian networks.

Abstract

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 traffic, we can always identify a directed acyclic subnetwork that approximately maintains the capacity of the original network. For Gaussian networks with multiple-access and broadcast traffic, an acyclic subnetwork is sufficient to achieve every rate point in the capacity region of the original network, however, there may not be a single acyclic subnetwork that maintains the whole capacity region. For networks with multicast and multiple unicast traffic, on the other hand, bidirected information flow across certain links can be critically needed to maximize the end-to-end capacity region. These results can be regarded as generalizations of the conclusions regarding the usefulness of feedback in various single-hop Gaussian settings and can provide opportunities for simplifying operation in Gaussian multi-hop networks.