Canonical Conditions for K/2 Degrees of Freedom

TL;DR

This paper establishes a precise condition under which each user in a K-user interference channel can achieve half the degrees of freedom, encompassing all channel topologies and linking interference alignment to a generic injectivity criterion.

Contribution

It introduces a necessary and sufficient condition for 1/2 degrees of freedom per user in all channel configurations, and provides codebook constructions to achieve this performance.

Findings

Condition applies to all channel topologies

Guarantees separability of signal and interference

Provides explicit codebook constructions

Abstract

We present a necessary and sufficient condition for $1/2$ degree of freedom for each user in constant $K$-user single-antenna interference channels. This condition applies to all channel topologies, i.e., to fully-connected channels as well as channels that have individual links absent, reflected by corresponding zeros in the channel matrix. Moreover, it captures the essence of interference alignment by virtue of being expressed in terms of a generic injectivity condition that guarantees separability of signal and interference. Finally, we provide codebook constructions achieving $1/2$ degree of freedom for each user for all channel matrices satisfying our condition.