9 problems

Capacity-region equality conjecture. The capacity regions are identical in all cases, including the remaining open regime:

Inner-bound optimality conjecture. In the remaining open regime, the inner bound is tight, so that

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…

MLP-bound looseness conjecture. The bound on the multi-letter portion in the converse is too loose.

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 $\mathbf{C}(H)$ denote the capacity region of the Gaussian interference channel with common information for channel parameters $H$, and let the outer bounds proposed in the cit…

Let a MIMO broadcast channel have $J$ users, with each user having multiple receive antennas. Let ${\cal R}(i)$ denote its capacity region in channel state $i$, and let the corresp…

Convexity conjecture. For the degraded CMLOBCs described above, the capacity region is strictly concave ($\cap$) if and only if

Symmetric-input conjecture. The boundary of the capacity region is obtained by taking the joint distribution $p(U,X)$ induced by a $7$-ary symmetric channel…