Algorithms and simulation model for the synchronisation subsystem of the noise-resilient communication system based on permutations

In modern data transmission systems, one of the key tasks is to ensure the reliability of communication in conditions of noise. This is especially relevant for channels with high bit error rate, in particular, for radio communication channels with intense natural or artificial noise, which limits the use of traditional error correction methods. The purpose of this work was to develop algorithms for communication using code words of non-separable factorial code, which implies the representation of code words in the form of permutations using simplex binary symmetric communication channel with high bit error probability. To build these algorithms, the method of frame synchronisation of non-separable factorial code, which uses majority and correlation processing of fragments received from communication channel, was taken as a basis. Methods and algorithms for noise-resilient transmission of permutations in communication channels with high bit error probability were investigated. A general scheme of the protocol for organisation of simplex communication was developed. An algorithm for detecting false synchronisations under conditions of high noise level in communication channel was proposed. The effectiveness of the protocol for synchronisation of code words of factorial code was studied, advantages of the used approach were identified and presented. A simulation model of the communication system using a simplex binary symmetric communication channel and the possibility of setting the bit error value in it was developed. The structure of the simulation model and the algorithms of its component blocks were presented. Synchronisation parameters were calculated for bit error probability of 0.4, simulation results based on 10,000 tests were presented, which made it possible to experimentally determine synchronisation algorithm parameters. Simulation modelling was performed and the accuracy of determining the boundaries of synchronisation blocks was estimated based on bit error probability in the range from 0.1 to 0.4. An approach was proposed to reduce the error when determining the boundaries of permutations. The obtained results indicate the effectiveness of the proposed solutions, the consistency of theoretical and practical indicators of the synchronisation subsystem, as well as the possibility of using the developed algorithms to implement a three-pass cryptographic protocol based on permutations