3 problems

Deterministic-maximizer conjecture. For all $\alpha,\lambda\in\mathbb{R}_+$, the vectors $\mathbf{a}_\alpha^*$ and $\mathbf{b}_\alpha^*$ that maximize…

Consider a variable-length feedback code with $M=2^K$ messages, target error probability $P_e$, expected decoding time $\mathbb{E}[T]$, rate $\overline{R}$, channel capacity $C$, f…

Extended-test optimality conjecture. If $S_n^{*+}$ satisfies $\bar{l}<\infty$, $v_2>-2$, and $v_l\geq 0$ for all $3\leq l\leq\bar{l}$, then the test is optimal in terms of the gene…