# Topological Interference Management with Decoded Message Passing

## TL;DR

This paper explores a new approach to interference management in uplink cellular networks by leveraging message passing at receivers, modeling interference with conflict digraphs, and establishing conditions where orthogonal access is optimal for maximizing degrees-of-freedom.

## Contribution

It introduces a novel TIM-MP framework, linking interference alignment to orthogonal access, and characterizes network topologies where this approach is optimal, including linear optimality proofs for small networks.

## Key findings

- Orthogonal access achieves optimal DoF in certain network classes.
- Message passing enables interference alignment to reduce to orthogonal access.
- Optimality proven for networks with up to four users across all topologies.

## Abstract

The topological interference management (TIM) problem studies partially-connected interference networks with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters. In this paper, we consider a similar problem in the uplink cellular networks, while message passing is enabled at the receivers (e.g., base stations), so that the decoded messages can be routed to other receivers via backhaul links to help further improve network performance. For this TIM problem with decoded message passing (TIM-MP), we model the interference pattern by conflict digraphs, connect orthogonal access to the acyclic set coloring on conflict digraphs, and show that one-to-one interference alignment boils down to orthogonal access because of message passing. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies where orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. The relation to the conventional index coding with simultaneous decoding is also investigated by formulating a generalized index coding problem with successive decoding as a result of decoded message passing. The properties of reducibility and criticality are also studied, by which we are 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). Practical issues of the tradeoff between the overhead of message passing and the achievable symmetric DoF are also discussed, in the hope of facilitating efficient backhaul utilization.