Topological interference management with decoded message passing: A polyhedral approach

We study the topological interference management problem with decoded message passing (TIM-MP) using a polyhedral approach. The TIM-MP problem considers partially-connected interference channels with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters, while the decoded messages at the receivers can be routed to other receivers via backhaul links to help cancel interference. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies for which orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. We are also able to prove the linear optimality of orthogonal access in terms of symmetric DoF for the networks up to four users with all possible network topologies (218 instances).