5 problems

Time-average code-length conjecture. The time-average expected codeword lengths should satisfy

Let $X$ be a source alphabet with $|X|=2$, consisting of symbols $x_1$ and $x_2$, with probabilities $\text{p}(x_1)$ and $\text{p}(x_2)$. Let $\beta_T$, $\beta_0$,…

Let $R^*(D)$ denote the infimum mutual-information rate over generalized causal reproductions $\mathsf{GCR}$ whose long-term distortion is at most $D$, and let $R(D)$ denote the ra…

Variant I monotonicity conjecture. If $J>1$, then the optimal $n_i$ for Variant I CPCs increase monotonically with $i\in\mathcal{S}_1$ and decrease monotonically with…

Monotonicity conjecture. If $J>1$ and $E[\eta_\ell]$ is convex in $\ell$, then the optimal multiplicities $n_i$ for Variant II CPCs increase monotonically with $i$.