Indirect and Direct Gaussian Distributed Source Coding Problems

We consider the distributed source coding system of L correlated Gaussian sources Y l , l = 1, 2, ... , L, which are noisy observations of correlated Gaussian remote sources X k , k = 1,2, ..., K. We assume that Y L = t(Y 1 , Y 2 ,...,Y L ) is an observation of the source vector X K = t(X 1 , X 2 ,...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 60; no. 12; pp. 7506 - 7539
Main Author: Oohama, Yasutada
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Codes
Correlation analysis
Covariance matrices
Decoding
Distributed source coding
Estimating techniques
Estimation error
Gaussian CEO problem
Information processing
multiterminal source coding
Normal distribution
Random variables
rate distortion region
Rate-distortion
remote sources
Source coding
Vectors
Gaussian CEO problem
rate distortion region
remote sources
multiterminal source coding
Distributed source coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We consider the distributed source coding system of L correlated Gaussian sources Y l , l = 1, 2, ... , L, which are noisy observations of correlated Gaussian remote sources X k , k = 1,2, ..., K. We assume that Y L = t(Y 1 , Y 2 ,...,Y L ) is an observation of the source vector X K = t(X 1 , X 2 , . . . , X K ), having the form Y L = AX K +N L , where A is a L×K matrix and N L = t(N 1 , N 2 , ... , N L ) is a vector of L-independent Gaussian random variables also independent of X K . In this system, L correlated Gaussian observations are separately compressed by L encoders and sent to the information processing center. We study the remote source coding problem, where the decoder at the center attempts to reconstruct the remote source X K . We consider three distortion criteria based on the covariance matrix of the estimation error on X K . For each of those three criteria, we derive explicit inner and outer bounds of the rate distortion region. Next, in the case of K = L and A = I L , we study the multiterminal source coding problem, where the decoder wishes to reconstruct the observation Y L = X L + N L . To investigate this problem, we shall establish a result that provides a strong connection between the remote source coding problem and multiterminal source coding problem. Using this result, we derive several new partial solutions to the multiterminal source coding problem.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2361332