### 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 | |

State | Published - Feb 20 2019 |

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 | Israel |

City | Eilat |

Period | 12/12/18 → 12/14/18 |

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'On Lossy Compression of Generalized Gaussian Sources'. Together they form a unique fingerprint.

## Cite this

*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