A Frame Synchronization Method Based on Tuples of Pairwise Distinct Elements

Abstract

The further development of the frame synchronization method is presented, which uses as a synchronization word the permutation of the elements of the set of integers of the segment [0; M  1], was further developed. It is proposed to use a tuple of M-η pairwise distinct elements of the set of integers of the segment [0; M 1] as a syncword. The elements of this set are encoded with a fixed-length binary code and the minimum binary Hamming distance between the syncword and all its circular shifts is the maximum. The paper established that the maximum value of the minimum Hamming distance for tuples of 15 pairwise distinct elements of the set of integers for M = 16 is equal to 30. A comparative assessment of the frame synchronization effectiveness was performed based on tuples of 15 elements, as well as on permutations of length 16 and 8. A computer simulation model of the frame synchronization system in a binary symmetric communication channel was built. Synchronization indicators were determined with parameters calculated for bit error probability 0,4 and 0,495, as well as requirements for a min-imum probability of correct synchronization of 0,9997 and a maximum probability of false synchronization of 3E-4. The effectiveness of using tuples of pairwise distinct elements in frame synchronization systems has been confirmed. The efficiency indicator depends on com-munication channel bit error probability.