TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite

TL;DR

This paper proves that TDMA is optimal for all-unicast DoF regions in TIM networks precisely when the network topology graph is chordal bipartite, linking graph properties to interference management efficiency.

Contribution

It establishes a necessary and sufficient condition (chordal bipartite topology) for TDMA optimality in all-unicast DoF regions of TIM networks.

Findings

TDMA achieves the all-unicast DoF region if topology is chordal bipartite.

Results recover known optimality conditions for 1D convex networks.

The findings extend to the index coding problem's topological representation.

Abstract

The main result of this work is that an orthogonal access scheme such as TDMA achieves the all-unicast degrees of freedom (DoF) region of the topological interference management (TIM) problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem.