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

It is shown that the asymptotic probability of error of a binary equiprobable hypothesis test for observed Poisson point processes with rates , 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.