Hypothesis testing via a comparator
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE International Symposium on Information Theory Proceedings (ISIT), 2012
Institute of Electrical and Electronics Engineers (IEEE)
Polyanskiy, Yury. Hypothesis Testing via a Comparator. In Pp. 2206–2210. IEEE, 2012.
Author's final manuscript