Quantization of Discrete Probability Distributions

TL;DR

This paper investigates the quantization of discrete probability distributions, linking it to the covering problem for the unit simplex, and introduces an asymptotically optimal algorithm with performance analysis.

Contribution

It reduces the quantization problem to the covering problem for the unit simplex and proposes a simple, asymptotically optimal algorithm.

Findings

Asymptotic characterization in the high-rate regime

Development of a simple, optimal quantization algorithm

Performance comparison with existing solutions

Abstract

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit simplex. This setting yields precise asymptotic characterization in the high-rate regime. We also describe a simple and asymptotically optimal algorithm for solving this problem. Performance of this algorithm is studied and compared with several known solutions.