Abstract-The main result of this work is that fractional coloring (orthogonal access) achieves the all-unicast capacity (degrees of freedom (DoF)) region of the index coding (topological interference management (TIM)) problem if and only if the bipartite network topology graph (with sources on one side and destinations on the other, and edges identifying presence of nontrivial channels whose communication capacity is not zero or infinity) is chordal, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast capacity (DoF) region includes the capacity (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-capacity (DoF) of one-dimensional convex networks are recovered as a special case.
It was shown in REF that TDMA can be used to achieve the all-unicast DoF region if and only if the bipartite network topology graph is chordal, i.e., every cycle that can contain a chord has one.
Fractional Coloring (Orthogonal Access) achieves All-unicast Capacity (DoF) Region of Index Coding (TIM) if and only if Network Topology is Chordal
ArXiv
ArXiv
Mathematics Computer Science