14 problems

Let $\mathcal{X}$ and $\mathcal{Y}$ be finite alphabets, let $d(x,y)$ be a distortion measure, let $P$ be a probability distribution on $\mathcal{X}$, and let $R(\Delta|P)$ denote…

Consider a symmetric $n$-channel multiple-description lattice vector quantization system under the high-resolution assumptions, with side distortions determined by the lattice scal…

Common-randomness conjecture. The large amount of high-quality common randomness required to achieve the rate-distortion-perception function under the strong realism constraint is…

Let $R_{\epsilon}^{\phi_s}(D)$ denote the rate-distortion function at average distortion constraint $D$ when the initial sampling phase is $\phi_s$, and let $R_{\epsilon}^{0}(D)$ d…

Finite-alphabet and fixed-length conjecture. The assumptions that the auxiliary variable $V$ is finite-valued and that the codes are fixed-length are not restrictive.

Let $\alpha$ denote the measure concentrated on the unit circle, and let $\nu^*=\alpha$ be the optimal measure for the rate-distortion problem. A Lebesgue density is a density with…

Let the DT Ångström–Brockett (Å-B) scheme operate with sampling interval $\tau>0$, and let its rate-distortion performance be compared with that of the corresponding CT Å-B scheme.…

Ru bearing-precision conjecture. For some unknown reason, the early Muslims were not able to determine the bearing to the reconstruction point $Ru$ with the same precision as the m…

Let a continuous-time memoryless wide-sense cyclostationary Gaussian process have a cyclostationary variance, and sample it asynchronously with sampling interval $T_{\rm s}$ and sa…

Let $k=2$, let $\bfX\in\{0,1\}^n$ be the label vector, and let a querying scheme use $m$ same cluster' queries, each involving two elements ($\Delta=2$). A scheme is $(1-\delta)$-g…

The vector Gaussian rate-distortion problem with variable side information under trace distortion, denoted ${\textsc{RDTr}}$, is considered together with its Minimax and Maximin lo…

Binary auxiliary-variable conjecture. A binary auxiliary variable $U$ is sufficient to achieve the rate-distortion function, and the proposed bound $R_{bound}(d)$ is tight.

Let $d=\langle d^{n'}\rangle_1^\infty$ be a permutation-invariant distortion function, and let $R^P_U(D)$ and $R^P_U(D,\inf)$ be the rate-distortion quantities defined in the paper…

SPARC rate-distortion conjecture. SPARCs achieve the optimal rate-distortion trade-off for all rates with minimum-distance encoding.