Abstract

We study rate-distortion problems of a Poisson process using a
group theoretic approach. By describing a realization of a Poisson
point process with either point timings or inter-event
(inter-point) intervals and by choosing appropriate distortion
measures, we establish rate-distortion problems of a homogeneous
Poisson process as ball- or sphere-covering problems for
realizations of the hyperoctahedral group in $\Reals^n$.
Specifically, the realizations we investigate are a hypercube and
a hyperoctahedron. Thereby we unify three known rate-distortion
problems of a Poisson process (with different distortion measures,
but resulting in the same rate-distortion function) with the
Laplacian-$\ell_1$ rate-distortion problem.

Keywords

Hyperoctahedral group, natural choice of distortion measure,
Poisson point processes, rate-distortion function, sphere
covering.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Mon Feb 28 12:21:03 CET 2022