Conjecture on the unbounded uMAT–MAT DoF gap for any number of cells

Consider the $(L,C)$ MISO interference broadcast channel in the setting of the paper's inner-bound theorem. Let $d^{(\mathrm{uMAT})}$ be the degrees of freedom achieved by the uncoupled MAT scheme and let $d^{(\mathrm{MAT})}$ be the degrees of freedom obtained by applying MAT with time sharing between cells. Define

$$\epsilon=d^{(\mathrm{uMAT})}-d^{(\mathrm{MAT})}.$$

For $C=2$, the paper proves that

$$\lim_{L\rightarrow\infty}\epsilon=\infty.$$

uMAT–MAT gap conjecture. For the same scenario, the DoF gap defined above holds for any number of cells $C$.

The conjecture extends the established two-cell asymptotic result to arbitrary $C$. It is based on the reported results and is not proved in the source.