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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.E98A
No.12
pp.23672375 Publication Date: 2015/12/01 Online ISSN: 17451337
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 Y_{l}=^{t}(Y_{l1}, Y_{l2}),l=1,2 which are noisy observations of correlated Gaussian scalar source X_{0}. We assume that for each (l,k)∈{1,2}, Y_{lk} is an observation of the source X_{0}, having the form Y_{lk}=X_{0}+N_{lk}, where N_{lk} is a Gaussian random variable independent of X_{0}. We further assume that N_{lk}, (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 X_{0}. 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 X_{0} from this observation. Those estimations are sufficient statistics on X_{0}. 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 X_{0} 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.

