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-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 R^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-l1 rate-distortion problem.

-||-   _|_ _|_     /    __|__   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: Sun May 16 15:02:23 CEST 2021