Factorial coding with data recovery

Introduction. Methods of coding that provide a comprehensive solution of cryptographic protection, protection against intentional alteration of data, and data protection against communication channel errors can improve the efficiency of information processing tools by reducing included redundancy and used computing resources. The development of such methods is a topical area of current research. The purpose of this study is to develop and analyze the method of factorial coding with data recovery that realizes functions of communication channel error detection and cryptographic protection of information, and to assess its properties in data transmission systems with decision feedback. The main material. Factorial code with data recovery by permutation is a non-systematic code that provides a replacement of information sequence into permutation of the numbers computed by all information bits. In the article, the main properties of the proposed code are defined. The transmission reliability, cryptographic strength and strength against intentional alteration of data are evaluated. Dependences of undetected error probability assessments, energy gain and code rate from information vector length at the encoder input are studied. A comparative analysis of known factorial codes is done. Recommendations for the use of factorial coding are given. Conclusions. The performed work extends the scientific and technical base of factorial methods and means of data coding. The proposed factorial code with data recovery: provides protection against unauthorized reading, provides protection against channel errors, does not provide protection against intentional alteration of data, has higher detection ability for small data block length on encoder input as compared with a full factorial code, has the property of self-synchronization, and excludes collisions