Explicit and almost sure conditions for K/2 degrees of freedom

TL;DR

This paper establishes explicit conditions on channel matrices for achieving K/2 degrees of freedom in K-user interference channels and constructs asymptotically optimal input distributions, leveraging fractal geometry techniques.

Contribution

It provides the first explicit conditions on channel matrices for K/2 DoF and constructs optimal input distributions, advancing understanding of interference channel capacity.

Findings

Explicit conditions for K/2 DoF are identified.

Constructs asymptotically DoF-optimal input distributions.

Uses fractal geometry to derive technical results.

Abstract

It is well known that in K-user constant single-antenna interference channels K/2 degrees of freedom (DoF) can be achieved for almost all channel matrices. Explicit conditions on the channel matrix to admit K/2 DoF are, however, not available. The purpose of this paper is to identify such explicit conditions, which are satisfied for almost all channel matrices. We also provide a construction of corresponding asymptotically DoF-optimal input distributions. The main technical tool used is a recent breakthrough result by Hochman in fractal geometry.