Multiterminal detection with zero-rate data compression

The asymptotic performance of a multiterminal detection system comprising a central detector and two remote sensors that have access to discrete, spatially dependent, and temporally memoryless observations is discussed. It is assumed that prior to transmitting information to the central detector, each sensor compresses its observations at a rate which approaches zero as the sample size tends to infinity, and that, on the basis of the compressed data from both sensors, the central detector seeks to determine whether the true distribution of the observations belongs to a null class II or an alternative class Xi . Under the criterion that stipulates minimization of the type-II error rate subject to an upper bound epsilon on the type-I error rate, it is shown that, in the case of simple distribution classes ( mod Pi mod = mod Xi mod =1), the error exponent achievable by such a system has a simple characterization, is independent of the value of epsilon , and is insensitive to changes in compression rate as long as the asymptotic rate on one of the sensors is zero.<>