Rate-Distortion Problems of the Poisson Process based on a Group-Theoretic Approach

Hui-An Shen; Stefan M. Moser; Jean-Pascal Pfister

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arXiv · 2202.13684

Rate-Distortion Problems of the Poisson Process based on a Group-Theoretic Approach

Hui-An Shen·Stefan M. Moser·Jean-Pascal Pfister

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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 $\mathbb{R}^n$. 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-$\ell_1$ rate-distortion problem.

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Hui-An Shen, Stefan M. Moser, Jean-Pascal Pfister. 2022-02-28. Rate-Distortion Problems of the Poisson Process based on a Group-Theoretic Approach. https://arxiv.org/abs/2202.13684

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