A Coding Theorem for f-Separable Distortion Measures

A Coding Theorem for f-Separable Distortion Measures

In this work we relax the usual separability assumption made in rate-distortion literature and propose f -separable distortion measures, which are well suited to model non-linear penalties. The main insight behind f -separable distortion measures is to define an n-letter distortion measure...

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Main Authors: Yanina Shkel, Sergio Verdú
Format: Article
Language:English
Published: MDPI AG 2018-02-01
Series:Entropy
Subjects:
rate-distortion function
f-separable distortion measure
subadditive distortion measure
Online Access:http://www.mdpi.com/1099-4300/20/2/111
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spelling doaj-7e6367b0ba2d4aa5b7e7679a2960fda52020-11-24T23:15:41ZengMDPI AGEntropy1099-43002018-02-0120211110.3390/e20020111e20020111A Coding Theorem for f-Separable Distortion MeasuresYanina Shkel0Sergio Verdú1Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USADepartment of Electrical Engineering, Princeton University, Princeton, NJ 08544, USAIn this work we relax the usual separability assumption made in rate-distortion literature and propose f -separable distortion measures, which are well suited to model non-linear penalties. The main insight behind f -separable distortion measures is to define an n-letter distortion measure to be an f -mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with f -separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions. Finally, we discuss connections between f -separable distortion measures, and the subadditive distortion measure previously proposed in literature.http://www.mdpi.com/1099-4300/20/2/111rate-distortion functionf-separable distortion measuresubadditive distortion measure
collection DOAJ
language English
format Article
sources DOAJ
author Yanina Shkel
Sergio Verdú
spellingShingle Yanina Shkel
Sergio Verdú
A Coding Theorem for f-Separable Distortion Measures
Entropy
rate-distortion function
f-separable distortion measure
subadditive distortion measure
author_facet Yanina Shkel
Sergio Verdú
author_sort Yanina Shkel
title A Coding Theorem for f-Separable Distortion Measures
title_short A Coding Theorem for f-Separable Distortion Measures
title_full A Coding Theorem for f-Separable Distortion Measures
title_fullStr A Coding Theorem for f-Separable Distortion Measures
title_full_unstemmed A Coding Theorem for f-Separable Distortion Measures
title_sort coding theorem for f-separable distortion measures
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2018-02-01
description In this work we relax the usual separability assumption made in rate-distortion literature and propose f -separable distortion measures, which are well suited to model non-linear penalties. The main insight behind f -separable distortion measures is to define an n-letter distortion measure to be an f -mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with f -separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions. Finally, we discuss connections between f -separable distortion measures, and the subadditive distortion measure previously proposed in literature.
topic rate-distortion function
f-separable distortion measure
subadditive distortion measure
url http://www.mdpi.com/1099-4300/20/2/111
work_keys_str_mv AT yaninashkel acodingtheoremforfseparabledistortionmeasures
AT sergioverdu acodingtheoremforfseparabledistortionmeasures
AT yaninashkel codingtheoremforfseparabledistortionmeasures
AT sergioverdu codingtheoremforfseparabledistortionmeasures
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