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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| Vydáno v: | IEEE transactions on information theory Ročník 58; číslo 10; s. 6282 - 6303 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York, NY
IEEE
01.10.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Author | Wagner, A. B. Rahman, M. S. |
| Author_xml | – sequence: 1 givenname: M. S. surname: Rahman fullname: Rahman, M. S. email: mr534@cornell.edu organization: Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY, USA – sequence: 2 givenname: A. B. surname: Wagner fullname: Wagner, A. B. email: wagner@cornell.edu organization: Sch. of Electr. & Comput. Eng., Cornell Univ., Ithaca, NY, USA |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | On the Optimality of Binning for Distributed Hypothesis Testing |
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