FACTORIAL CODING WITH ERROR CORRECTION

Abstract

Context. Factorial data coding allows combining operations of cryptographic protection, intentional alteration of data, and errorcorrecting coding which leads to the decrease of redundancy introduced by transmitter and to the increase of data rate and effective throughput. At the same time, the described methods of factorial coding do not correct errors, which limits their use. Objective of this work is to develop a method of factorial coding with data recovery that provides a comprehensive solution of cryptographic protection and error control coding and allows combining the functions of communication channel errors detecting and correcting. Method. The basic idea of the proposed coding method is to increase the distance between the allowed code words that represent permutations calculated for all information bits of a data block and represented in a binary form. The methods of distance increasing based on Euclidean and Hamming metrics are investigated. The basic properties of factorial code with error correction are defined for each of these methods. The estimate of probability characteristics is done on the condition of independence of communication channel errors and their binomial distribution. The receiver structures are developed. Decoding rules implemented in receiver are based on the maximum likelihood criteria and provide both forward error correction and error detection with further correction by retransmission of damaged data block. Results. The factorial error-correcting codes using Euclidean and Hamming metrics are implemented. The comparative analysis of the probability of an undetected error, the residual probability of erroneous reception, energy gain, and the relative transmission rate is done for these codes. It is shown that code characteristics are not invariant to the set of allowed code words, and the codes that use Hamming metric are the most efficient codes between the presented codes. Conclusions. The method of factorial coding data recovery by permutation has been further developed. Due to the combination of error correction and detection functions, it can increase the rate loss dynamic component and, consequently, the relative transmission rate, compared to error-detecting factorial coding by reducing its noise immunity. The experiments confirmed the effectiveness of the factorial error-correcting codes.