Context. To improve the noise immunity of communication and data transmission systems, error-correcting coding is widely used. The most common because of their effectiveness are block coding methods. Under conditions of partial a priori uncertainty of the type and parameters of encoding, before decoding the digital sequence, a preliminary analysis is carried out to determine them. In block coding, to determine the period of a digital sequence caused by the addition of a sync sequence to it, and which can determine the type and parameters of coding, a common approach is to use their correlation properties.
Objective. The object of the research is the presentation of periodicity search algorithms in digital sequences with block errorcorrecting coding under conditions of partial a priori uncertainty of the type and parameters of the error-correcting code.
Method. The article presents two periodicity search algorithms in digital sequences with block coding and describes the principle of their operation. The basis of one algorithm is the calculation of the autocorrelation function, the basis of the other is calculation of the cross-correlation function. It is shown that the length of the digital sequence should be twice as long as the maximum possible period. The operation of both algorithms is illustrated by examples.
Results. Based on the proposed algorithms, special software has been developed. The results of determining the period of digital sequences with block error-correcting coding at different values of the period confirmed the efficiency of the proposed algorithms. Both proposed algorithms give approximately the same result. Experimental dependences of the calculation time of auto- and crosscorrelation functions from the length of the digital sequence and the maximum possible period are established. The period search algorithm in a digital sequence, that use the cross-correlation function of its components, is more efficient due to fewer calculations.
Conclusions. For the first time, two periodicity search algorithms in digital sequences with block error-correcting based on the determination of their correlation functions are obtained. The application of the developed algorithms in practice allows, under partial a priori uncertainty of the type and parameters of the error-correcting code, to determine the period of digital sequences in real time even at large values of the period, and based on it, to identify the type and parameters of block error-correcting codes.
Contribution of wave aberrations represented by Zernike polynomials to the cross-correlation function between distorted and actual speckle patterns
