Related papers: On the best lattice quantizers
The optimal lattice quantizer is the lattice which minimizes the (dimensionless) second moment $G$. In dimensions $1$ to $8$, it has been proven that the optimal lattice quantizer is one of the classical lattices, or there is good evidence…
Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards…
We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6, ..., 48, and also has a smaller mean squared error compared to known lattice…
New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent…
For uniform scalar quantization, the error distribution is approximately a uniform distribution over an interval (which is also a 1-dimensional ball). Nevertheless, for lattice vector quantization, the error distribution is uniform not over…
This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices $\mathcal{E}_{m}$ and $\mathcal{G}_{m}$. By explicitly linking…
40 years ago, Conway and Sloane proposed using the highly symmetrical Coxeter-Todd lattice $K_{12}$ for quantization, and estimated its second moment. Since then, all published lists identify $K_{12}$ as the best 12-dimensional lattice…
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…
This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We address the problem of indirect quantization of a source subject to a mean-squared error distortion constraint. A well-known result of Wolf and Ziv is that the problem can be reduced to a standard (direct) quantization problem via a…
We present analytical expressions for optimal entropy-constrained multiple-description lattice vector quantizers which, under high-resolutions assumptions, minimize the expected distortion for given packet-loss probabilities. We consider…
In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…
We propose a randomized lattice algorithm for approximating multivariate periodic functions over the $d$-dimensional unit cube from the weighted Korobov space with mixed smoothness $\alpha > 1/2$ and product weights…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
We present an algorithm for the exact computer-aided construction of the Voronoi cells of lattices with known symmetry group. Our algorithm scales better than linearly with the total number of faces and is applicable to dimensions beyond…
We study the error of the number of points of a lattice $L$ that belong to a rectangle, centred at $0$, whose axes are parallel to the coordinate axes, dilated by a factor $t$ and then translated by a vector $X \in \mathbb{R}^{2}$. When we…
The problem of designing a multiple description vector quantizer with lattice codebook Lambda is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical…