Evaluation of properties of signal-code structures synthesized on the basis of lattice theory for inseparable factorial codes

One of the main functions of computer systems and networks is to ensure the security of information circulating in the system. At the same time, an equally important function is to protect information from the effects of interference in the communication channel. The use of factorial codes is one approach to combining noise-tolerant encryption and cryptographic protection. But these codes are vulnerable to even errors, which lead to the transformation of one permutation from the allowed set to another permutation belonging to the same set. Therefore, the issue of improving the reliability of data transmission in systems with factorial coding is relevant. The purpose of the study is to evaluate the method of forming a signal-code structure, which ensures the achievement of the required value of transmission reliability and allows to maximize the code speed by forming a subset of permutations based on lattice theory. The relative transmission rate and the probability of undetected error as a result of the use of synthesized signal-code constructs in systems with integral factorial coding are subject to evaluation. To evaluate the efficiency of the synthesized signal-code constructions, the methods of factorial coding with data recovery by permutation and factorial coding with data recovery by permutation with error correction have been used. In order to determine the probability of undetected error, a software model has been developed that simulates a data transmission environment with independent bit errors. The results of the software model have made it possible to establish the dependence of the probability of undetected error in systems with integral factorial coding on the probability of bit error in channels with independent bit errors. A comparative analysis of the relative transmission rate and the probability of undetected error in systems with factorial coding with data recovery by permutation and factorial coding with data recovery by permutation with error correction is also performed. The results obtained in this paper have made it possible to determine the main advantages and disadvantages of the method of forming signal-code structures based on the lattice theory, as well as to determine the scope of this method

factorial code; relative transmission rate; bit error probability; noise-tolerant encoding; cryptographic protection