Rate-Distortion Problems of the Poisson Process: a Group-Theoretic Approach
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2021
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Conference Paper
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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-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 Rn. 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.
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2021 IEEE Information Theory Workshop (ITW)
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9611405
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IEEE
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2021 IEEE Information Theory Workshop (ITW 2021)
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03529 - Lapidoth, Amos / Lapidoth, Amos