Necessary Conditions for K/2 Degrees of Freedom
Recep G\"ul, Helmut B\"olcskei, Shlomo Shamai (Shitz)
TL;DR
This paper establishes that the injectivity condition identified by Stotz et al. for achieving 1/2 degrees of freedom in K-user interference channels is not only sufficient but also necessary, fully characterizing when full degrees of freedom are attainable.
Contribution
It proves the injectivity condition is necessary, completing the characterization of interference channel matrices that enable full degrees of freedom.
Findings
Injectivity condition is necessary for full degrees of freedom.
Provides an exact characterization of matrices allowing full degrees of freedom.
Extends previous sufficient condition to a necessary and sufficient condition.
Abstract
Stotz et al., 2016, reported a sufficient (injectivity) condition for each user in a K-user single-antenna constant interference channel to achieve 1/2 degree of freedom. The present paper proves that this condition is necessary as well and hence provides an equivalence characterization of interference channel matrices allowing full degrees of freedom.
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