Asymptotic error probability of binary hypothesis testing for Poisson point-process observations (Corresp.)

Abstract

It is shown that the asymptotic probability of error of a binary equiprobable hypothesis test for observed Poisson point processes with rates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda_{i}(t)=b_{i}(t)+(\rho_{i}(t)+z)^{2}, i=0,1, z \rightarrow \infty</tex> , is equal to the error probability of optimum deterministic-signal detection in additive white Gaussian noise when the signals coincide with the square roots of the point-process rates. The implication of this result in the error rate analysis of optical digital communication systems is discussed.