A Method for Reliable Permutation Transmission in Short-Packet Communication Systems

Abstract

The paper describes the research, development, and implementation of a method for permutation transmission over communication channels with a bit error probability close to 0.5. The developed method can be used for communication systems with non-separable factorial coding, in particular, to implement a three-pass cryptographic protocol based on permutations. The method uses circular shifts of the carrier permutation to represent each transmitted permutation symbol. The carrier permutation has the maximum value of the minimum Hamming distance from the binary representation of permutation to all its circular shifts. The majority and correlation processing of the fragments received from the communication channel makes it possible to implement a reliable permutation transmission under high-intensity channel noise. A mathematical model for permutation transmitting has been developed. Analytical expressions for calculating the probability of a permutation being received correctly and incorrectly are presented. An algorithm that applies the proposed method has been developed and implemented. The results of the constructed simulation software model of the data transmission system confirm the effectiveness of the developed method in comparison with the traditional DSSS method for the bit error probability equal to 0.495.