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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.
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.
In this work, the main trends in research and publication activity in digital transformation in the world and Ukraine are analyzed using meta- and bibliometric analysis. For this purpose, bibliometric data on scientific publications on the topic of digital transformations in the Google Scholar and Scopus databases were selected, which were additionally analyzed using the VOSviewer software package. Based on filtering the results obtained, an array was formed that included 366 scientific publications for 2019–2023 in Ukrainian in the Google Scholar database and 3,703 scientific publications in English for 2020–2023 in the Scopus database. Dynamic time analysis revealed a significant surge of scientific interest in the topic of digital transformations in recent years, while structural analysis revealed the multi-industry structure of existing research. The creation of bibliographic maps of keywords and publication maps allowed us to form an idea of the main thematic areas of research in the context of digital transformations and their opinion leaders. The data obtained became the basis for formulating recommendations for further areas of research in digital transformation, in particular, on the development of a unified roadmap for the digital transformation of education at different educational qualification levels and for various specialties. This will contribute to the formation of a single systemic approach to the digital transformation of Ukraine as a guarantee for the state’s sustainable development, well-being, strengthening of national security, speeding up the pace of European integration processes, as well as promoting national interests at the international level.
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