A coding theorem for f-separable distortion measures

Yanina Shkel; Sergio Verdú

doi:10.3390/e20020111

A coding theorem for f-separable distortion measures

Yanina Shkel, Sergio Verdú

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English (US)
Article number	111
Journal	Entropy
Volume	20
Issue number	2
DOIs	https://doi.org/10.3390/e20020111
State	Published - Feb 1 2018

All Science Journal Classification (ASJC) codes

Information Systems
Electrical and Electronic Engineering
General Physics and Astronomy
Mathematical Physics
Physics and Astronomy (miscellaneous)

Keywords

F-separable distortion measure
Rate-distortion function
Subadditive distortion measure

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10.3390/e20020111

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abstract = "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.",

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AU - Verdú, Sergio

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N2 - 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.

AB - 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.

KW - F-separable distortion measure

KW - Rate-distortion function

KW - Subadditive distortion measure

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A coding theorem for f-separable distortion measures

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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