Paper Info
Title
The Exponential Distribution in Rate Distortion Theory: The Case of Compression with Independent Encodings
Abstract
In this paper, we consider the rate-distortion problem where a source X is encoded into k parallel descriptions Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , . . ., Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> , such that the error signals X - Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , 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 Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , . . ., Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> . 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.
Year
DOI
Venue
2020
10.1109/DCC47342.2020.00040
2020 Data Compression Conference (DCC)
Keywords
DocType
ISSN
error signals,parallel descriptions,rate distortion theory,exponential distribution,source estimate,absolute error criterion,optimal decoder,rate-distortion problem,independent encodings
Conference
1068-0314
ISBN
Citations 
PageRank 
978-1-7281-6458-8
0
0.34
References 
Authors
3
3
Name
Order
Citations
PageRank
Uri Erez11209112.39
Jan Østergaard220128.38
Zamir, R.31496141.87