5 problems

Gaussian-case conjecture. In the Gaussian case, the surfaces of $\mathcal{R}_{in}$ and $\mathcal{R}_{out}$ are

Let $(S,X)$ follow a non-degenerate joint Gaussian distribution, and consider indirect quadratic lossy source coding, with or without observed source reconstruction. Quadratic Gaus…

Gaussian privacy conjecture. The form of $pi(rho)$ should be piecewise affine in $rho$, and the achievability scheme in the Gaussian privacy theorem should have the same structure—…

Entropy-region conjecture for three vector-valued Gaussians. The closure of $G_3^{\mathrm{Gauss}}$ is characterized by the following inequalities. If $\tilde y\leq 0$, then

Berger–Tung Gaussian auxiliary-variable conjecture. Choosing the auxiliary random variables to be Gaussian should result in the optimal rate-distortion region for reconstructing bo…