Optimal quantizers for some absolutely continuous probability measures

TL;DR

This paper investigates optimal quantization strategies for absolutely continuous probability measures on various geometric domains, providing explicit calculations of optimal sets and quantization errors for specific numbers of means.

Contribution

It offers explicit solutions for optimal quantizers and errors for measures on discs, squares, and the real line, advancing understanding of quantization in these settings.

Findings

Explicit optimal sets of n-means computed for specific n

Quantization errors calculated for measures on different domains

Enhanced understanding of quantization for absolutely continuous measures

Abstract

The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit discs, squares, and the real line. For these probability measures the optimal sets of $n$-means and the $n$th quantization errors are calculated for some positive integers $n$.