On Lossy Compression of Generalized Gaussian Sources

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

doi:10.1109/ICSEE.2018.8646192

On Lossy Compression of Generalized Gaussian Sources

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

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 language	English (US)
Title of host publication	2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781538663783
DOIs	https://doi.org/10.1109/ICSEE.2018.8646192
State	Published - Jul 2 2018
Event	2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018 - Eilat, Israel Duration: Dec 12 2018 → Dec 14 2018

Publication series

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

Conference

Conference	2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018
Country/Territory	Israel
City	Eilat
Period	12/12/18 → 12/14/18

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

Access to Document

10.1109/ICSEE.2018.8646192

Cite this

Dytso, A., Bustin, R., Poor, H. V., & Shitz, S. S. (2018). On Lossy Compression of Generalized Gaussian Sources. In 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018 Article 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

Dytso, Alex ; Bustin, Ronit ; Poor, H. Vincent et al. / On Lossy Compression of Generalized Gaussian Sources. 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018. Institute of Electrical and Electronics Engineers Inc., 2018. (2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018).

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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.",

author = "Alex Dytso and Ronit Bustin and Poor, {H. Vincent} and Shitz, {Shlomo Shamai}",

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Dytso, A, Bustin, R, Poor, HV & Shitz, SS 2018, 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., 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018, Eilat, Israel, 12/12/18. https://doi.org/10.1109/ICSEE.2018.8646192

On Lossy Compression of Generalized Gaussian Sources. / Dytso, Alex; Bustin, Ronit; Poor, H. Vincent et al.
2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018. Institute of Electrical and Electronics Engineers Inc., 2018. 8646192 (2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - 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.

AB - 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.

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Dytso A, Bustin R, Poor HV, Shitz SS. On Lossy Compression of Generalized Gaussian Sources. In 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018. Institute of Electrical and Electronics Engineers Inc. 2018. 8646192. (2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018). doi: 10.1109/ICSEE.2018.8646192

On Lossy Compression of Generalized Gaussian Sources

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