Degrees of Freedom Region for an Interference Network with General Message Demands

TL;DR

This paper derives the degrees of freedom region for a general interference network with multiple transmitters and receivers, extending interference alignment techniques to arbitrary message demands and analyzing the geometric shape of the region.

Contribution

It generalizes interference alignment to networks with arbitrary message demands and characterizes the DoF region for such systems.

Findings

Derived the DoF region for the general interference network.

Extended interference alignment schemes to arbitrary message demands.

Analyzed the geometric shape of the DoF region.

Abstract

We consider a single hop interference network with $K$ transmitters and $J$ receivers, all having $M$ antennas. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. This generalizes the well-known $K$-user $M$-antenna interference channel, where each message is requested by a unique receiver. For our setup, we derive the degrees of freedom (DoF) region. The achievability scheme generalizes the interference alignment schemes proposed by Cadambe and Jafar. In particular, we achieve general points in the DoF region by using multiple base vectors and aligning all interferers at a given receiver to the interferer with the largest DoF. As a byproduct, we obtain the DoF region for the original interference channel. We also discuss extensions of our approach where the same region can be achieved by considering a reduced set of interference alignment constraints, thus reducing the time-expansion duration needed. The DoF region for the considered system depends only on a subset of receivers whose demands meet certain characteristics. The geometric shape of the DoF region is also discussed.