# On General Lattice Quantization Noise

## TL;DR

This paper investigates how to design lattices for quantization noise that closely match a wide range of target distributions, especially as the lattice dimension increases.

## Contribution

It demonstrates that high-dimensional lattice quantization noise can asymptotically approximate a broad family of distributions with i.i.d. components.

## Key findings

- Quantization noise can approach various distributions in high dimensions.
- Lattice construction techniques enable control over the noise distribution.
- Asymptotic results hold as the lattice dimension tends to infinity.

## Abstract

The problem of constructing lattices such that their quantization noise approaches a desired distribution is studied. It is shown that asymptotically is the dimension, lattice quantization noise can approach a broad family of distribution functions with independent and identically distributed components.