On the Optimality of Binning for Distributed Hypothesis Testing

We study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 58; no. 10; pp. 6282 - 6303
Main Authors: Rahman, M. S., Wagner, A. B.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Binning
Coding
Coding, codes
Compressed
Detectors
distributed hypothesis testing
Encoding
Entropy
Error probability
Errors
Exact sciences and technology
Exponents
Gaussian many-help-one hypothesis testing against independence
Gel'fand and Pinsker hypothesis testing against independence
Hypothesis testing
Information theory
Information, signal and communications theory
Optimization
outer bound
Probability distribution
Quantize-Bin-Test scheme
Random variables
rate-exponent region
Signal and communications theory
Source coding
Telecommunications and information theory
test against conditional independence
Testing
Vectors
Error probability
Source coding
Quantize-Bin-Test scheme
Measurement sensor
Distributed source signal
Hypothesis test
Binning
test against conditional independence
outer bound
Gaussian many-help-one hypothesis testing against independence
distributed hypothesis testing
rate-exponent region
Gel'fand and Pinsker hypothesis testing against independence
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value. For related problems in distributed source coding, schemes based on random binning perform well and are often optimal. For distributed hypothesis testing, however, the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process. We show that despite this complication, binning is optimal for a class of problems in which the goal is to "test against conditional independence." We then use this optimality result to give an outer bound for a more general class of instances of the problem.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2206793