Source Coding in Networks with Covariance Distortion Constraints

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Abstract

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.
Original languageEnglish
JournalI E E E Transactions on Signal Processing
Volume64
Issue number22
Pages (from-to)5943-5958
Number of pages16
ISSN1053-587X
DOIs
Publication statusPublished - Nov 2016

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Covariance matrix
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@article{866437af5ae4401594463c0bd92e99dd,
title = "Source Coding in Networks with Covariance Distortion Constraints",
abstract = "We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.",
author = "Adel Zahedi and Jan {\O}stergaard and Jensen, {S{\o}ren Holdt} and Patrick Naylor and S{\o}ren Bech",
year = "2016",
month = "11",
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language = "English",
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journal = "I E E E Transactions on Signal Processing",
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Source Coding in Networks with Covariance Distortion Constraints. / Zahedi, Adel; Østergaard, Jan; Jensen, Søren Holdt; Naylor, Patrick; Bech, Søren.

In: I E E E Transactions on Signal Processing, Vol. 64, No. 22, 11.2016, p. 5943-5958.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Source Coding in Networks with Covariance Distortion Constraints

AU - Zahedi, Adel

AU - Østergaard, Jan

AU - Jensen, Søren Holdt

AU - Naylor, Patrick

AU - Bech, Søren

PY - 2016/11

Y1 - 2016/11

N2 - We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.

AB - We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup.

U2 - 10.1109/TSP.2016.2603973

DO - 10.1109/TSP.2016.2603973

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JO - I E E E Transactions on Signal Processing

JF - I E E E Transactions on Signal Processing

SN - 1053-587X

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