Non-scaling conjecture for multi-hop interference networks with delayed CSI

Let $K$ users communicate over a layered $M$-hop interference network with delayed channel-state information (CSI), and let its network sum-DoF be the supremum of achievable sum-DoFs. The condition $M=o(K)$ means that $M/K\to 0$ as $K\to\infty$. Non-scaling conjecture. The DoF of the $K$-user $M$-hop interference network with delayed CSI and $M=o(K)$ does not scale with $K$. The paper establishes DoF scaling for certain multi-hop networks, including networks with $2K$ or more hops, and identifies determining the minimum number of hops and relays per hop needed for scaling as an open problem; this conjecture proposes that sublinear hop count is insufficient.