TY - GEN

T1 - On Lossy Compression of Generalized Gaussian Sources

AU - Dytso, Alex

AU - Bustin, Ronit

AU - Poor, H. Vincent

AU - Shitz, Shlomo Shamai

N1 - Funding Information:
The work of A. Dytso and H.V. Poor was supported by the National Science Foundation under Grant CNS-1702808. The work of R. Bustin and S. Shamai has been supported by the European Union’s Horizon 2020 Research and Innovation Programme, grant agreement no. 694630.

PY - 2019/2/20

Y1 - 2019/2/20

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.

UR - http://www.scopus.com/inward/record.url?scp=85063135752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063135752&partnerID=8YFLogxK

U2 - 10.1109/ICSEE.2018.8646192

DO - 10.1109/ICSEE.2018.8646192

M3 - Conference contribution

AN - SCOPUS:85063135752

T3 - 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018

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

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE International Conference on the Science of Electrical Engineering in Israel, ICSEE 2018

Y2 - 12 December 2018 through 14 December 2018

ER -