11 problems

Consider a multiple-description lattice vector quantization system with $K$ descriptions, and let the side distortions be evaluated in the high-resolution regime as the lattice dim…

Let $K$ be the number of descriptions, let $L$ be the lattice dimension, and let $N$ and $us$ be the system parameters in the paper. For each pair of distinct description indices…

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

Let ${\boldsymbol{B}}_{14}(a)$ be the parameterized $14$-dimensional lattice generator, and let $f(v)$ be the polynomial defined in the paper. Let $v_0$ be the second positive root…

Let ${\boldsymbol{B}}_{13}(a_1,a_2,a_3)$ be the parameterized $13$-dimensional lattice generator, and let $f^B_2$ and $f^B_3$ be the two degree-$14$ polynomials defined in the pape…

Let ${\boldsymbol{B}}_{13}({\boldsymbol{a}})$ be the three-parameter family of $13$-dimensional lattice generators described in the paper, with ${\boldsymbol{a}}=[a_1,a_2,a_3]$. Op…

Let $a_{\text{opt}}$ be the parameter at which the necessary local-optimality condition $G'(a)=0$ holds, and let ${\boldsymbol{B}}_{14}(a)$ denote the parameterized $14$-dimensiona…

For each dimension $n=10,\ldots,16$, the authors numerically optimized lattices and, in five cases, identified the optimized lattice with an exact lattice. Optimality conjecture. T…

A lattice quantizer is a lattice in Euclidean space whose normalized second moment measures its mean square quantization error at fixed point density. The packing problem asks for…

Let $n=3$, and consider quantizers whose error distribution is uniform over the $n$-ball. The normalized entropy of such a quantizer is the quantity being optimized. Face-centered-…

Let $n$ be a positive integer, and let the Zador upper bound be the upper bound on normalized second moment for arbitrary quantizers in dimension $n$. Lattice-quantizer attainment…