Hypothesis testing via a comparator
This paper investigates the best achievable performance by a hypothesis test satisfying a structural constraint: two functions are computed at two different terminals and the detector consists of a simple comparator verifying whether the functions agree. Such tests arise as part of study of fundamen...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2013
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| Online Access: | http://hdl.handle.net/1721.1/78925 https://orcid.org/0000-0002-2109-0979 |
| _version_ | 1826190045151756288 |
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| author | Polyanskiy, Yury |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Polyanskiy, Yury |
| author_sort | Polyanskiy, Yury |
| collection | MIT |
| description | This paper investigates the best achievable performance by a hypothesis test satisfying a structural constraint: two functions are computed at two different terminals and the detector consists of a simple comparator verifying whether the functions agree. Such tests arise as part of study of fundamental limits of channel coding, but are also useful in other contexts. A simple expression for the Stein exponent is found and applied to showing a strong converse in the problem of multi-terminal hypothesis testing with rate constraints. Connections to the Gács-Körner common information and to spectral properties of conditional expectation operator are identified. Further tightening of results hinges on finding λ-blocks of minimal weight. Application of Delsarte's linear programming method to this problem is described. |
| first_indexed | 2024-09-23T08:34:10Z |
| format | Article |
| id | mit-1721.1/78925 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:34:10Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/789252022-09-23T12:57:37Z Hypothesis testing via a comparator Polyanskiy, Yury Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Polyanskiy, Yury This paper investigates the best achievable performance by a hypothesis test satisfying a structural constraint: two functions are computed at two different terminals and the detector consists of a simple comparator verifying whether the functions agree. Such tests arise as part of study of fundamental limits of channel coding, but are also useful in other contexts. A simple expression for the Stein exponent is found and applied to showing a strong converse in the problem of multi-terminal hypothesis testing with rate constraints. Connections to the Gács-Körner common information and to spectral properties of conditional expectation operator are identified. Further tightening of results hinges on finding λ-blocks of minimal weight. Application of Delsarte's linear programming method to this problem is described. Center for Science of Information (Grant Agreement CCF-09-39370) 2013-05-17T19:08:31Z 2013-05-17T19:08:31Z 2012-07 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-2578-3 978-1-4673-2580-6 2157-8095 http://hdl.handle.net/1721.1/78925 Polyanskiy, Yury. Hypothesis Testing via a Comparator. In Pp. 2206–2210. IEEE, 2012. https://orcid.org/0000-0002-2109-0979 en_US http://dx.doi.org/10.1109/ISIT.2012.6283845 IEEE International Symposium on Information Theory Proceedings (ISIT), 2012 Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Polyanskiy via Amy Stout |
| spellingShingle | Polyanskiy, Yury Hypothesis testing via a comparator |
| title | Hypothesis testing via a comparator |
| title_full | Hypothesis testing via a comparator |
| title_fullStr | Hypothesis testing via a comparator |
| title_full_unstemmed | Hypothesis testing via a comparator |
| title_short | Hypothesis testing via a comparator |
| title_sort | hypothesis testing via a comparator |
| url | http://hdl.handle.net/1721.1/78925 https://orcid.org/0000-0002-2109-0979 |
| work_keys_str_mv | AT polyanskiyyury hypothesistestingviaacomparator |