6 problems

Csiszár–Narayan factorization conjecture. A necessary condition for $C_{\textnormal{0-u}}=C$ is that the channel law admit such a factorization on some capacity-achieving subset of…

Consider an unstable scalar process with instability parameter $\lambda$, controlled over a channel. A controller has finite memory when its control action depends on only finitely…

For $q\geq 2$, let $R({\mathcal E})$ be the average channel capacity of the two-user union channel without feedback, and let $R({\mathcal O}_f)$ be the average zero-error capacity…

Consider the two-user binary adder channel with complete feedback, and let $R({\mathcal O}_f)$ denote its average zero-error capacity. Binary adder-channel conjecture. The average…

Let $\Phi_{\theta}$ be the channel considered above, and for each $n>1$ let $\varepsilon_n>0$ be the threshold such that $\bar{Q}_0(\Phi^{\otimes n}_{\theta})=0$ for…

Let ${\mathcal N}\in\mathcal C({\mathcal H},{\mathcal K})$ have a decomposition … where each ${\mathcal N}_s$ is extremal in ${\mathcal C}({\mathcal H},{\mathcal K})$ and $q(s)>0$…