6 problems

Let $(N_1,N_2,u,q_1,q_2)$ denote positive channel and power parameters, and let the isotropic condition mean that the maximum in the stated theorem is achieved by isotropic Gaussia…

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

A general layered erasure channel has layers indexed by $l\in\{1,\dots,q\}$, and let Theorem $1$ denote the theorem giving an outer bound on its capacity region. The moderate-inter…

Consider the three-user semi-symmetric complex Gaussian interference channel … … … where $P_k=P$ for $k=1,2,3$, and write $\phi(g_1)$ and $\phi(g_2)$ for the phases of $g_1$ and…

Costa's corner-point conjecture. For reliable communication at both receivers, the following should hold: if $R_2\geq C_2-\varepsilon$ for an arbitrary $\varepsilon>0$, then

Let $h,p,v\in\mathbb{R}_+$, let $X_1^G\sim\mathcal{N}(0,p)$ and let $Z\sim\mathcal{N}(0,v)$ be independent of $X_1^G$. Let $X$ and $X_1$ be i.i.d. random variables with mean $0$ an…