Hypothesis testing via a comparator and hypercontractivity
نویسنده
چکیده
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 checking if the functions agree. Such tests arise as part of study of fundamental limits of channel coding, and hypothesis testing with communication (rate) constraints. A simple expression for the Stein exponent is found. Connections to the Gács-Körner common information and to hypercontractivity properties of the conditional expectation operator are identified. In the case of zero Stein exponent, a non-vanishing lower bound on probability of error is established by pairing estimates of Ahslwede-Gács and Mossel et al.
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