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

The main result of this paper is that an orthogonal access scheme, such as time division multiple access achieves the all-unicast degrees of freedom (DoF) region of the topological interference management 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.