Using CUDA technology to form ensembles of pseudo-random sequences and calculating their correlation functions

The proposed work explores the possibility of using CUDA technology (parallel calculations by means of a video processor) to form pseudo-random sequences and calculate their autocorrelation and cross-corelations functions. The main principles of CUDA technology, limitations of technology applied to the video processor, and the composition of the software development kit for Nvidia are discussed. Experiments on the formation of Gold's pseudo-random sequences with the help of CUDA technology, as well as the calculation of the correlation functions of pseudo-random de Bruijn sequences by means of a video processor were performed. The received gain in speed of formation of pseudo-random sequences and calculation of correlation functions by means of technology CUDA in comparison with calculation with application of the central processor is investigated. When calculating the correlation functions of the ensemble of sequences, various calculation algorithms were used, including elementwise comparison of sequences and calculation using a fast Fourier transform. During the study of the time of formation of pseudo-random Gold's sequences of different lengths, an estimate of the obtained gain in the formation time of the sequence ensemble for different lengths of Gold's sequences is given. The article describes the algorithm for the formation of Gold's ensemble of sequences using CUDA technology. The numerical results of the experiment are indicated and the corresponding graphs are given. For Gold's sequences of length 8191, the gain in the formation using CUDA technology was 390%. In the course of studying the time for calculating the correlation function for pseudo-random de Bruijn sequences of different length and size of the ensemble, using different algorithms, when implemented on the computer's central processing unit and using CUDA technology, the results are shown in the table. The elapsed time is compared depending on the applied algorithm for calculating the correlation function, performing calculations on the computer central processor or using CUDA technology, and also depending on the length of the pseudo-random sequences and the size of the ensemble sequence being processed. Graphs of the calculation time for various experimental conditions are given. When calculating the correlation functions of an ensemble of de Bruijn sequences of length 8192 in an amount of 1000 pieces, the gain from the processing speed of 14% has the FFT algorithm realized with the help of CUDA technology.