Distributed Binary Detection With Lossy Data Compression

Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations, this receiver is required to first identify the legitimacy of...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 63; no. 8; pp. 5207 - 5227
Main Authors: Katz, Gil, Piantanida, Pablo, Debbah, Merouane
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
asymptotic performance
central detector
Computer Science
Data compression
Decoding
discrete spatially dependent observations
Distortion
distributed detection
Error analysis
Error detection
error exponent
Error probability
error statistics
Hypotheses
Information Theory
lossy source coding
Mathematics
multiterminal detection
multiterminal source coding
Networking and Internet Architecture
Receivers
Reconstruction
side information
signal detection
Source coding
Statistics
Testing
type-I error rate
type-II error rate
signal detection
asymptotic performance
multiterminal source coding
Data compression
type-II error rate
lossy source coding
distributed detection error exponent
multiterminal detection
central detector
side infomation
discrete spatially dependent observations
error statistics
type-I error rate
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations, this receiver is required to first identify the legitimacy of its sender by declaring the joint distribution of the process, and then depending on such authentication, it generates adequate reconstruction of the observations, satisfying an average per-letter distortion. The performance of this setup is investigated through the corresponding rate-error-distortion region, describing the tradeoff between: the communication rate, the error exponent induced by the detection, and the distortion incurred by the source reconstruction. In the special case of testing against independence, where the alternative hypothesis implies that the sources are independent, the optimal rate-error-distortion region is characterized. An application example to binary symmetric sources is given subsequently and the explicit expression for the rate-error-distortion region is provided as well. The case of "general hypotheses" is also investigated. A new achievable rate-error-distortion region is derived based on the use of non-asymptotic binning, improving the quality of communicated descriptions. Further improvement of performance in the general case is shown to be possible when the requirement of source reconstruction is relaxed, which stands in contrast to the case of general hypotheses.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2688348