Riabukha O. Syndrome decoding techniques in corrective positional and timing codes

The object - the process of detecting and correcting errors using corrective timer signal structures (TSS) with basic information elements smaller than Nyquist that ensure efficient use of channels, but independently in the channel is not transferred. Subject of research - methods and algorithm of forming sets corresponding to TSS syndromes that meet the requirements of reliability and transmission speed within the parameters of noise in the channel. Methods - systems theory, probability theory (for the determination of the likelihood of errors and evaluation), noise-immune coding theory (for development, analysis, characterization and efficiency coding methods), stochastic processes and mathematical statistics (for processing experimental data) and mathematical simulation (modeling processes for transmission in communication systems. Theoretical and practical results: the model of distortion flows in the telephone network channel, allowing us to determine the properties of corrective code; the statistical parameters of signal distortions in the real city telephone network channels, allowing ability to determine the optimal corrective code; synthesized algorithm formation timer signal designs with syndromes correction displacement significant recovery moments (SRM), thus increasing the power of the set corrective TSS at a given time interval, set the connection coefficients of quality and values syndromes; Algorithms transformation quality communications in "good" model ranges in the channels in Hilbert rate followed the transformation speed increase in transmission quality throughout the range lines; The algorithm improves the quality of transmission by 4-5 orders of unilateral system that provides increased data transfer rate of more than 2.5 times comparing to the corrective positional block codes; improved algorithms improve transfer rates at least twice in systems with feedback systems compared with adaptive positional codes; the results obtained and reflected in the materials research and implemented in the educational process at the Department of Information Security and Data transmission of Odessa National Academy of Telecommunications, named after A.S. Popov, as evidenced by the relevant implementing acts. The results are suitable for engineering design of radio and telecommunications systems, as confirmed by the acts of implementation.