The exponential distribution in rate distortion theory: The case of compression with independent encodings

Uri Erez, Jan Ostergaard, Ram Zamir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper, we consider the rate-distortion problem where a source X is encoded into k parallel descriptions Y1,..., Yk, such that the error signals X - Yi, i = 1,..., k, are mutually independent given X. We show that if X is one-sided exponentially distributed, the optimal decoder (estimator) under the one-sided absolute error criterion, is simply given by the maximum of the outputs Y1,..., Yk. We provide a closed-form expression for the rate and distortion for any k number of parallel descriptions and for any coding rate. We furthermore show that as the coding rate per description becomes asymptotically small, encoding into k parallel descriptions and using the maximum output as the source estimate, is rate-distortion optimal.

Original languageEnglish
Title of host publicationProceedings - DCC 2020
Subtitle of host publicationData Compression Conference
EditorsAli Bilgin, Michael W. Marcellin, Joan Serra-Sagrista, James A. Storer
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Electronic)9781728164571
StatePublished - Mar 2020
Event2020 Data Compression Conference, DCC 2020 - Snowbird, United States
Duration: 24 Mar 202027 Mar 2020

Publication series

NameData Compression Conference Proceedings
ISSN (Print)1068-0314


Conference2020 Data Compression Conference, DCC 2020
Country/TerritoryUnited States

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