  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.
