Asymptotically optimal criteria for testing parametric hypothesis on the distribution of a random vector. I

We construct asymptotically optimal criteria for testing two simple hypotheses on the scalar parameter of discrete noise in a combined semicontinuos communication channel for the triangular scheme. Probabilistic characteristics of these criteria are obtained (in particular, asymptotics of the minimal sample size for given error probabilities of two kinds). It is shown that the minimal sample size depends essentially on the channel parameters.