A model for processing messages from multiple sources encoded in the block coupling mode

Purpose of research. The article considers a model for processing messages received by the receiver from several sources. For a class of distributed systems with restrictions on the size of transmitted messages and the size of their identification fields, it is relevant to use block coupling encoding, which, with the identifier size unchanged, implies a significantly lower probability of identifier collisions. A negative consequence of this is the need to identify the source not for a single message, but for a sequence of messages associated with the source. As a result, the receiver can consider the same message at any given time as a potential message from several sources, forcing it to be stored in various banks of intermediate calculation results. The aim of the work is to reduce the probability of error in determining the source of messages by taking into account the results of parallel processing in independent structures.
Methods. An approach to improving the reliability of message processing is considered. It consists in the parallel formation of dynamic structures storing messages that can be associated with the corresponding source. When deciding whether a message belongs to one of the sources under consideration, information about such a message is deleted from all structures in which it was contained, since for such structures this message is extraneous.
Results. A mathematical model of parallel message processing in independent structures has been created. The probabilities of errors are calculated based on the use of the method without using joint message processing and using. The dependences of error occurrence on the intensity and length of messages are graphically plotted. Error probability values were obtained for the two compared data processing options.
Conclusion. The article shows how using the results of message processing in independent structures associated with the corresponding source of a distributed system can affect the reliability and complexity of the process of determining the sources of messages encoded in the block coupling mode.

1. O'Brien D., Rajbhandari S., Chun H. Transmitter and receiver technologies for optical wireless. Philos. Trans. A Math. Phys. Eng. Sci. 2020;(378):20190182. https://doi.org/10.1098/rsta.2019.0182

2. Tanygin M.O., Akhmad A.A., Kazakova O.V. A model for placing data in the internal memory of a computer implementing a data encoding scheme in the block coupling mode. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta = Proceedings of the Southwest State University. 2023;27(1):73–91. (In Russ.) https://doi.org/10.21869/2223-1560-2023-27-1-73-91

3. Bakulina M.P. Effective method of block coding of two-level images. Programmnye produkty i sistemy = Software Products and Systems. 2017;30(2):282–285. (In Russ.) https://doi.org/10.15827/0236-235X.030.2.282-285

4. Time accounting vulnerabilities in symmetric decryption in CBC mode using padding. Available at: https://learn.microsoft.com/ru-ru/dotnet/standard/security/vulnerabilities-cbc-mode (accessed 04.12.2024)

5. Wolfowitz J. The coding of messages subject to chance errors. Available at: https://projecteuclid.org/journalArticle/Download?urlId=10.1215%2Fijm%2F1255380682 (accessed 10.12.2024).

6. Tanygin M.O., Alshaya H.Yu., Kuleshova E.A. A method for monitoring the integrity of information of transmitted blocks. Radioelektronika, informatika, upravlenie = Radio Electronics, Computer Science, Management. 2020;1:181–189. (In Russ.)

7. Zhanfang Zhao, Sung-Kook Han, In-Mi So. Architecture of Knowledge Graph Construction Techniques. International Journal of Pure and Applied Mathematics. 2018;118(19):1869–1883. (In Russ.)

8. Plugatarev A.V. A model for determining the source of messages based on statistical analysis of metadata in an open communication channel. Prikaspiiskii zhurnal: upravlenie i vysokie tekhnologii = Caspian Journal: Management and High Technologies. 2022;(4):30–37. (In Russ.)

9. Tanygin M.O. Chesnokova A.A. Akhmad A.A.A Reduction in resource costs for processing message authentication codes by limiting the number of processed messages. Prikaspiiskii zhurnal: upravlenie i vysokie tekhnologii = Caspian Journal: Management and High Technologies. 2022;(4):22–29. (In Russ.)

10. Tanygin M.O., Alshaia H.Ya., Altukhova V.A., Marukhlenko A.L. Establishing a trusted data exchange channel between the source and receiver of information using a modified one-time role method. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Upravlenie, vychislitel'naya tekhnika, informatika. Meditsinskoe priborostroenie = Proceedings of the Southwest State University. Series: Control, Computer Engineering, Information Science. Medical Instruments Engineering. 2018;8(4):63–71. (In Russ.)

11. Kai Luo, Athanassios Manikas. Joint Transmitter – Receiver Optimization in Multitarget MIMO Radar. IEEE Transactions on Signal Processing. 2017;65:6292–6302. https://doi.org/10.1109/TSP.2017.2726993

12. Bidokhti Sh. S., Wigger M., Timo R. Noisy Broadcast Networks With Receiver Caching. IEEE Transactions on Information Theory. 2018;64:6996–7016. https://doi.org/10.1109/TIT.2018.2835507

13. Vasilkov Y.V., Timoshenko A.V., Sovetov V.A., Kirmel A.S. Methodology for assessing the functional characteristics of radio monitoring systems with limited data on reliability parameters. Trudy MAI = Proceedings of MAI. 2019;(108):1–23. (In Russ.) https://doi.org/10.34759/trd-2019-108-16

14. Tanygin M.O., Kuleshova E.A., Mitrofanov A.V., Gladilina E.Yu. Increasing the speed of error detection in the formation of data block chains based on the analysis of the number of hash matches. Prikaspiiskii zhurnal: upravlenie i vysokie tekhnologii = Caspian Journal: Management and High Technologies. 2022;1:85-93. (In Russ.) https://doi.org/10.54398/2074-1707_2022_1_85

15. Greefrath G., Siller H.-S., Vorhölter K., Kaiser G. Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching. ZDM – Mathematics Education. 2022;54:865–879.

16. Tung-Huang Feng, Wei Teng Li, Min-Shiang Hwang. A false data report filtering scheme in wireless sensor networks: A Survey. International Journal of Network Security. 2015;17(3):141.

17. Tanygin M.O., Alshaia H.Ya., Mitrofanov A.V. The complexity of the algorithm for determining the data source. Trudy MAI = Proceedings of MAY. 2021;(117):1–21. https://doi.org/10.34759/trd-2021-117-12

18. Gargiulo F., Caen A., Lambiotte R., Carletti T. The classical origin of modern mathematics. EPJ Data Science. 2016;(5):26. https://doi.org/10.1140/epjds/s13688-016-0088-y

19. Tanygin M.O. Investigation of the probability of occurrence of one type of error in the system for determining the source of information packages. Izvestiya vuzov. Priborostroenie = Journal of Instrument Engineering. 2020;63(9):777–785. (In Russ.) https://doi.org/10.17586/0021-3454-2020-63-9-777-7

20. Spyros G. Tzafestas. Information I: Communication, Transmission, and Information Theory. Energy, Information, Feedback, Adaptation, and Self-organization. Cham: Springer; 2018. P. 157–217.