5 problems

LMI-rate tightness conjecture. The asymptotic conditional entropy of the entropy-coded matching-codeword index equals the LMI rate:

Let $Q$ and $P$ be the target and proposal distributions for AD coding, and suppose that the likelihood ratio $dQ/dP$ is unimodal. Let $D_{\infty}\infdivx{Q}{P}$ denote the relevan…

Let $Q$ and $P$ be the target and proposal distributions passed to DAD coding, and let $D_{\infty}\infdivx{Q}{P}$ denote the relevant order-infinity divergence between them. Based…

Let an entropy encoder receive a sequence of $n$ numbers from the alphabet $\{0,1,\ldots,\sigma-1\}$. The redundancy is the difference between the number of bits produced by the en…

Exponential-order conjecture. The orders on the right-hand side, respectively, are the correct ones; namely, in the uniform $[0,1]^d$ case and the uniform Cantor-set case, the disp…