High resolution quantization and entropy coding of jump processes

TL;DR

This paper investigates the quantization and entropy coding errors for jump processes with Poisson-like jump counts, revealing distinct error rates and focusing on compound Poisson processes in multi-dimensional spaces.

Contribution

It provides new insights into the quantization of jump processes with general distributions and correlations, including the specific case of compound Poisson processes in .

Findings

Entropy coding error and quantization error have different rates in many cases.

Quantization of -valued compound Poisson processes is analyzed.

Jump processes with Poisson bounds on jump counts are effectively studied.

Abstract

We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and correlated. We show in particular that in many cases entropy coding error and quantization error have distinct rates. Finally, we investigate the quantization problem for the special case of $\mathbb{R}^d$-valued compound Poisson processes.