Comparative evaluation of factorial codes
Abstract
In the work, the mechanism of generation of decoding errors, their connection with error statistics and algorithms of decision making in the process of decoding by factorial codes are investigated in detail. To perform a comparative estimation of the stability of various factorial codes to the influence of the error flow, experimental-calculation models for full factorial code (FFC), factorial code with data recovery (FCDR), FCDR with additional verification bits (FCDRd) and factorial cascading code (FCC) were created. The reliability of the data transmission, the speed of the code and the value of the energy gain for proposed codes were evaluated with the same values of the length of the information block and the probability of a bit error in the communication channel in the binomial distribution of errors at the decoder input. An analysis of the mechanism of generation of decoding errors is performed. On the basis of the obtained results, recommendations were made for the use of each of the factorial codes when solving the problems of ensuring the control of the integrity of information and cryptographic protection
Keywords
factorial code; full factorial code; factorial code with data recovery; reliability of data transmission; energy gain; integrity control of information; cryptographic protection
References
- Faure, E. V., Shvydkyi, V. V., Shcherba, A. I. (2017) Information integrity control based on factorial number system. Journal of Baku Engineering University. Mathematics and Computer Science, No. 1, vol. 2.
- Faure, E. V., Shvydkyi, V. V, Shcherba, V. A. (2016) Combined factorial coding and its properties. Radioelektronika, informatyka, upravlinnya, No. 3, pp. 80-86.
- Faure, E. V. (2016) Factorial coding with data recovery. Visnyk Cherkaskogo derzhavnogo tehnologichnogo universitetu. Seria: Tehnichni nauky, No. 2, pp. 33-39.
- Faure, E. V. (2016) The method of increasing the efficiency of factorial coding with data recovery. Visnyk Cherkaskogo derzhavnogo tehnologichnogo universitetu. Seria: Tehnichni nauky, No. 3, pp. 57-61.
- Kharin, O. O. (2017) Estimation of properties of cascade code, which combines factorial and equilibrium codes. Visnyk Cherkaskogo derzhavnogo tehnologichnogo universitetu. Seria: Tehnichni nauky, No. 2, pp. 86-90.
- Knut, D. E. (2002) The art of computer programming. Vol. 1. Fundamental algorithms. Moscow: Vil’yams, 720 p.
- Knut, D. E. (2007) The art of computer programming. Vol. 2. Seminumerical algorithms. Moscow: Vil’yams, 832 p.
- Proakis, J. G. (2001) Digital сommunications. Boston: McGraw-Hill.
- Faure, E. V., Kharin, O. O., Shvydkyi, V. V., Shcherba, A. I. (2017) The mode of factorial coding with data recovery. Cherkasy State Technological University, assignee. UA Patent 117004, printed June 12.
- Faure, E. V., Shvydkyi, V. V., Shcherba, A. I. (2016) The mode of staffing formation.