On Lossy Compression of Generalized Gaussian Sources

Alex Dytso, Ronit Bustin, H. Vincent Poor, Shlomo Shamai Shitz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers a problem of lossy compression of generalized Gaussian (GG) sources (i.e., sources with the probability density functions proportional to \mathrm {e}^{-\frac {|x|^{\mathrm {S}}}{2}}, s \gt 0) with an \ell {r}, r \gt 0, distortion measure.It is shown that an optimal reconstruction distribution always exists and properties of this distribution are studied. In particular, it is shown that if s \leq r-1 then an optimal reconstruction must have unbounded support and for s \gt r an optimal reconstruction must have bounded support. Further, it is shown that Shannon's lower bound is achievable if and only if r = s \in (0,1] \cup \{2\}, or in other words when the GG distribution is self-decomposable. Finally, conditions are shown under which an optimal reconstruction is discrete with finitely many mass points.

Original languageEnglish (US)
Title of host publication2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538663783
DOIs
StatePublished - Feb 20 2019
Event2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018 - Eilat, Israel
Duration: Dec 12 2018Dec 14 2018

Publication series

Name2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018

Conference

Conference2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018
CountryIsrael
CityEilat
Period12/12/1812/14/18

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Dytso, A., Bustin, R., Poor, H. V., & Shitz, S. S. (2019). On Lossy Compression of Generalized Gaussian Sources. In 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018 [8646192] (2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICSEE.2018.8646192