Exponential-type error probabilities for multiterminal hypothesis testing

Multiterminal hypothesis testing is considered, subject to the exponential-type constraint α_n⩽exp(-nr) on the error probability of the first kind. The problem is to determine the minimum β*_n of the error probability of the second kind under the given constraint at limited rates R₁ and R₂ for observing the respective pairs of variables. Good lower bounds on the power exponent for β*_n are presented by invoking basic properties of r-divergent sequences. In particular, the one-bit and the zero-rate compression cases are considered. The power exponent for the former and a lower bound for the latter are established