Multiple Unicast Capacity of 2-Source 2-Sink Networks

TL;DR

This paper investigates the capacity limits of 2-source, 2-sink multihop wireless networks, revealing how network structure and relay count influence degrees of freedom and achievable throughput.

Contribution

It characterizes the degrees of freedom for layered multihop X networks with various relay configurations and develops new achievability schemes using interference alignment and neutralization.

Findings

Degrees of freedom are 1, 4/3, 3/2, or 2 depending on network connectivity.

With unlimited relays, the DoF can reach 5/3.

Routing suffices for wired networks to achieve sum capacity.

Abstract

We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networks with arbitrary connectivity, the sum capacity is achieved simply by routing. For wireless networks, we explore the degrees of freedom (DoF) of multihop X networks with a layered structure, allowing arbitrary number of hops, and arbitrary connectivity within each hop. For the case when there are no more than two relay nodes in each layer, the DoF can only take values 1, 4/3, 3/2 or 2, based on the connectivity of the network, for almost all values of channel coefficients. When there are arbitrary number of relays in each layer, the DoF can also take the value 5/3 . Achievability schemes incorporate linear forwarding, interference alignment and aligned interference neutralization principles. Information theoretic converse arguments specialized for the connectivity of the network are constructed based on the intuition from linear dimension counting arguments.