Optimum Discretization of Weak-Signal Observations under Constraints on the Quantization Rate

The paper investigates the problem of determining the optimum procedure of discretization of weak-signal observations in Gaussian noises under constraints on the rate of data quantization. The optimization is carried out with respect to the value of the asymptotical relative efficiency (ARE) of the likelihood-ratio criteria on the binary-symbol space and on the initial-data space. We find the conditions for the relationship between the powers of the determinate and stochastic components of the signal, in order that the single-digit discretization under the proper choice of the threshold be optimum.