Informational Bottlenecks in Two-Unicast Wireless Networks with Delayed CSIT

TL;DR

This paper investigates how delayed channel state information affects the degrees-of-freedom in layered two-unicast wireless networks, introducing new graph-theoretic bounds and achieving a complete characterization of sum DoF.

Contribution

It introduces a novel graph-theoretic approach to bound DoF with delayed CSIT and characterizes the sum DoF for a class of networks, revealing infinite possible DoF values.

Findings

Delayed CSIT leads to a range of DoF values, including infinite sets.

New outer bounds based on bottleneck nodes are established.

Achievability schemes match the outer bounds, fully characterizing sum DoF.

Abstract

We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form $mD_1 + D_2 \leq m$. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless networks, which shows that, unlike in the case of instantaneous CSIT, the DoF of two-unicast networks with delayed CSIT can take an infinite set of values.