4 problems

Nair's conjecture. For keeping the states of a linear system uniformly bounded over a DMC, the zero-error feedback capacity of the channel has to be larger than the topological ent…

Weighted-capacity optimization conjecture. For every $(c_1,c_2)\in\Delta^1$, $R(\mathcal{O}_f;c_1,c_2)$ equals the optimum of

Let a channel have a representation by unit vectors $\{\tilde{\bm{\psi}}_x\}$, and let $\tilde{\bm{\psi}}_x^\dagger\tilde{\bm{\psi}}_{x'}$ denote the inner product of the vectors c…

Conjectured optimal-policy form. The optimal policy of Player 1 is a stochastic matrix satisfying