Estimation of the probabilistic characteristics of the majority method for processing short segments of a pseudo-random sequence

Abstract

Simulation modeling of the processing method for pseudo-random sequence (PRS) short segments based on the majority tests gives the probability characteristics that are different from the results of a calculation using the Gaussian approximation. The simulation modeling shows that the probability of bit error decoding is changed discretely with the explicit minima and maxima for the length of the processed segment of the PRS. This is due to the fact that the decoder always uses a fixed test sequence, which is determined by the initial phase of the analyzer. Thus, the distribution of these checks determines the dependence of the bit error probability. On this basis, the paper conducts a theoretical study of the probability characteristics synchronization method based on the majority tests, taking into account the specifics of the PRS analyzer. The article formulates and solves the task of analyzing probabilistic characteristics of the majority method of processing short segments of the PRS, which required finding the probability of bit error of decoding. The analytical relations for the probability of bit error of decoding are obtained. The calculations and systematic analysis of the results are performed. It is shown that: with the increase in the length of the processed segment or the length of the valid section N the probability of error can be greater than the probability of destructive errors; the method based on the majority tests with a high probability of destructive errors has a significant advantage in the average code search time over the Ward’s method. Based on the obtained results a modification of the method that will provide the optimal choice of the length of the processed segment of PRS N will be offered in further studies.