Gaussian CEO Problem in the Case of Scalar Source and Vector Observations

Yasutada OOHAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.12   pp.2367-2375
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2367
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Shannon Theory
Keyword: 
multiterminal source coding,  rate distortion region,  CEO problem,  

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Summary: 
We consider the distributed source coding system of two correlated Gaussian Vector sources Yl=t(Yl1, Yl2),l=1,2 which are noisy observations of correlated Gaussian scalar source X0. We assume that for each (l,k)∈{1,2}, Ylk is an observation of the source X0, having the form Ylk=X0+Nlk, where Nlk is a Gaussian random variable independent of X0. We further assume that Nlk, (l,k)∈{1,2}2 are independent. In this system two correlated Gaussian observations are separately compressed by two 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 X0. The determination problem of the rate distortion region for this communication system can be regarded as an extension of the Gaussian CEO problem to the case of vector observations. For each vector observation we can obtain an estimation on X0 from this observation. Those estimations are sufficient statistics on X0. Using those sufficient statistics, we determine the rate distortion region by showing that it coincides with the rate distortion region of the CEO problem where the scalar observations of X0 are equal to the estimations computed from the vector observations. We further extend the result to the case of L terminal and general vector observations.