Comparative analysis of recurrent algorithms for estimating the parameters
of Markov models of memory communication channels
P. A. Budko1, M. Y. Konyshev2, Y. A. Konysheva3, M. D. Artamonov4
1Information Telecommunication Technologies Public Joint Stock Company.
2FSUE "NTC "Orion".
3MIREA - Russian Technological University.
4Autonomous Non-commercial Organization "Digital Audit".
DOI 10.24412/2410-9916-2026-3-120-134
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XML JATSAbstract
Purpose. The need to improve the reliability of information exchange in telecommunication systems operated in an environment with non-gaussian noise. Real data transmission channels are subject to pulse noise. They often contain error grouping, which is not considered by standard decoding algorithms designed for channels with additive white gaussian noise, which reduces their accuracy. The aim of the work is to develop and compare the analysis of two recurrent algorithms for estimating the parameters of binary Markov processes of arbitrary order. Methods. To solve the problem of developing algorithms for estimating the parameters of Markov models is based on using the previously obtained system of equations linking multidimensional probability distributions to derive recurrent formulas for estimating the probability distribution of the elements of the "four", four interrelated elements of the probability distribution. The comparison of the proposed algorithms was carried out by the method of simulation modeling using metrics: average absolute error, standard deviation, calculation time, number of arithmetic operations. Novelty. The novelty elements of the presented solution are the derivation of recurrent formulas for calculating probabilistic characteristics based on boundary relations of multidimensional distributions, as well as the development of an optimized algorithm that eliminates repeated calculations due to the recurrent calculation of elements through one basic parameter of the previous level. Results. The result is the development of a recurrent algorithm for estimating the probabilistic characteristics of binary sequences, and the justification for its high accuracy and speed. Practical relevance. The practical implementation of the proposed method is possible as part of the algorithmic support of adaptive receivers and decoding devices of telecommunication systems. Its integration will ensure a given level of noise immunity in real memory channels without changing correction codes and without increasing signal processing time.
Key words
non-Gaussian noise, memory channel, Markov chain, probability estimation, error packets, transmission reliability, recurrent algorithm, comparative analysis.
Reference for citation
Budko P. A., Konyshev M. Y., Konysheva Y. A., Artamonov M. D. Comparative analysis of recurrent algorithms for estimating the parameters of Markov models of memory communication channels. Systems of Control, Communication and Security, 2026, no. 3, pp. 120-134. DOI: 10.24412/2410-9916-2026-3-120-134 (in Russian).
References
1. Gridchin D. N. A Simulation Model of a Discrete Communication Channel with Error Packaging and Noise Resistant Coding. Information systems and technologies, 2019, vol. 112, no. 2, pp. 35-40 (in Russian).
2. Tsifrovaya obrabotka signalov i eyo primenenie – DSPA-2019 [Digital Signal Processing and its Applications – DSPA-2019]. Doklady 21 Mezhdunarodnoy konferentsii [Proceedings of the 21st International Conference]. Moscow, Moscow Scientific and Technical Society of Radio Engineering, Electronics and Communications named after A.S. Popov, 2019, 584 p. (in Russian).
3. Veresova A. M., Ovchinnikov A. A. Usage of Low-Density Parity-Check Codes in Channels with Memory with Different Number of Error Bursts. Naukoemkie tekhnologii, 2021, vol. 22, no. 8, pp. 41--49. doi:10.18127/j19998465-202108-07 (in Russian).
4. Isaeva M. N., Ovchinnikov A. A. Evaluation of the correcting ability of low-density codes for multiple error bursts. Obrabotka, peredacha i zashchita informatsii v komp'yuternykh sistemakh 22: Sbornik dokladov Vtoroy Mezhdunarodnoy nauchnoy konferentsii [Processing, Transmission and Protection of Information in Computer Systems 22: Proceedings of the 2nd International Scientific Conference]. Saint Petersburg, Saint Petersburg State University of Aerospace Instrumentation, 2022, pp. 242--245. doi: 10.31799/978-5-8088-1701-2-2022-2-242-245 (in Russian).
5. Lobach S. V. Rekurrentnoe otsenivanie parametrov ARMA-modeley vremennykh ryadov s vybrosami [Recurrent Estimation of ARMA Model Parameters for Time Series with Outliers]. Problemy prognozirovaniya i gosudarstvennogo regulirovaniya sotsial'no-ekonomicheskogo razvitiya: Materialy XVIII Mezhdunarodnoy nauchnoy konferentsii: v 3 tomakh [Problems of Forecasting and State Regulation of Socio-Economic Development: Proceedings of the XVIII International Scientific Conference: in 3 volumes]. Minsk, Research Economic Institute of the Ministry of Economy of the Republic of Belarus, 2017, pp. 197--199 (in Russian).
6. Sandler I. L. Recurrent Estimation of Parameters Being Multidimensional in Terms of Input and Output of Various Orders of Linear Dynamic Systems in the Presence of Autocorrelated Noises in Input and Output Signals. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki, 2016, vol. 40, no. 4, pp. 14--27. doi: 10.21685/2072-3040-2016-4-2 (in Russian).
7. Sandler I. L. Recursive Algorithm for Estimating the Parameters of Multidimensional Discrete Linear Dynamic Systems of Different Orders with Errors on the Input. Tambov University Reports. Series: Natural and Technical Sciences, 2018, vol. 23, no. 124, pp. 707--716. doi: 10.20310/1810-0198-2018-23-124-707-716 (in Russian).
8. Chernyshev K. R. Сonstructing and simulating recursive algorithms of the generalized stichastic approximation. Desyataya vserossiyskaya nauchno-prakticheskaya konferentsiya po imitatsionnomu modelirovaniyu i ego primeneniyu v nauke i promyshlennosti «Imitatsionnoe modelirovanie. Teoriya i praktika» (IMMOD-2021): Trudy konferentsii (elektronnoe izdanie) [Tenth All-Russian Scientific and Practical Conference on Simulation Modeling and its Applications in Science and Industry "Simulation Modeling. Theory and Practice" (IMMOD-2021): Proceedings of the Conference (electronic edition)]. Saint Petersburg, JSC "Center for Shipbuilding and Ship Repair Technology", 2021, pp. 471--476 (in Russian).
9. Semenova D. V., Lukyanova N. A. Rekurrentnoye Postroyeniye Raspredeleniy Veroyatnostey Konechnykh Sluchaynykh Mnozhestv [Recursive Construction of Probability Distributions of Finite Random Sets]. Siberian Federal University, Institute of Mathematics and Fundamental Informatics. Krasnoyarsk: Siberian Federal University, 2018. 134 p. (in Russian).
10. Veresova A. M. Reducing the Complexity of Error Bursts Decoding Using Block-Permutation Codes Based on the Method of Determining the Location of the Burst. T-Comm, vol. 18, no. 10, pр. 12-19. doi:10.36724/2072-8735-2024-18-10-12-19 (in Russian).
11. Kvashennikov V. V., Bugakov I. A., Kuzin A. V. Estimation of Probabilities of Reception Noiseproof Code in Channels with Independent and Grouped Errors. Izvestiya Instituta inzhenernoy fiziki, 2020, vol. 58, no. 4, pp. 11--16 (in Russian).
12. Konyshev M. Yu., Dvilyanskiy A. A., Barabashov A. Yu., Petrov K. E. Binary Vectors of Errors Source of Markov Discrete Communication Channel with Memory Probability Distributions Formation with the Error Vectors Probability Grouping Method Application. Promyshlennye ASU i kontrollery, 2018, no. 3, pp. 42--52 (in Russian).
13. Frenkel' S. L., Zakharov V. N., Basok B. M. A Probabilistic Model for Estimation of Software Robustness to Short-Term Hardware Failures. Informatika i ee primeneniya, 2017, vol. 11, no. 1, pp. 46--57. doi: 10.14357/19922264170104 (in Russian).
14. Veresova A. M., Ovchinnikov A. A. About using matched metrics in channels with memory for Gilbert codes. Volnovaya elektronika i infokommunikatsionnye sistemy: Sbornik statey XXIII mezhdunarodnoy nauchnoy konferentsii [Wave Electronics and Infocommunication Systems: Collection of Articles of the XXIII International Scientific Conference]. Saint Petersburg, Saint Petersburg State University of Aerospace Instrumentation, 2020, pp. 176--182 (in Russian).
15. Isaeva M. N., Ovchinnikov A. A. About using of decoding by information sets when correcting error bursts. Radiotekhnicheskie, opticheskie i biotekhnicheskie sistemy. Ustroystva i metody obrabotki informatsii: Sbornik dokladov. Chetvertaya Vserossiyskaya nauchnaya konferentsiya [Radio Engineering, Optical and Biotechnical Systems. Devices and Methods of Information Processing: Proceedings. Fourth All-Russian Scientific Conference]. Saint Petersburg, Saint Petersburg State University of Aerospace Instrumentation, 2023, pp. 188--191 (in Russian).
16. Kuleshov V. V., Leshchinskiy A. V., Chayka S. V. Otsenka sposobov zashchity ot paketov oshibok v tsifrovykh kanalakh svyazi [Evaluation of Methods for Protection Against Error Bursts in Digital Communication Channels]. REDS: Telekommunikatsionnye ustroystva i sistemy, 2013, vol. 3, no. 3, pp. 230--232 (in Russian).
17. Veresova A. M., Ovchinnikov A. A. About one algorithm for correcting bursts using block-permutation LDPC codes. Volnovaya elektronika i infokommunikatsionnye sistemy: Sbornik statey XXII Mezhdunarodnoy nauchnoy konferentsii: v 2-chastyakh [Wave Electronics and Infocommunication Systems: Collection of Articles of the XXII International Scientific Conference: in 2 parts]. Saint Petersburg, Saint Petersburg State University of Aerospace Instrumentation, 2019, pp. 154--159 (in Russian).
18. Ovchinnikov A. A., Veresova A. M. Comparison of the Probability of Reed -- Solomon and LDPC Codes Decoding Error in the Gilbert -- Elliott Channel. Volnovaya elektronika i infokommunikatsionnye sistemy: Sbornik statey XXV Mezhdunarodnoy nauchnoy konferentsii. V 3 chastyakh [Wave Electronics and Infocommunication Systems: Collection of Articles of the XXV International Scientific Conference. In 3 parts]. Saint Petersburg, Saint Petersburg State University of Aerospace Instrumentation, 2022, pp. 71--75 (in Russian).
19. Karpov S. S., Ryabinin Yu. E., Finko O. A. Ensuring the Integrity of Data Transmitted over the Communication Channels of Virtual Private Networks. Voprosy kiberbezopasnosti, 2021, vol. 44, no. 4, pp. 81--97. doi: 10.21681/2311-3456-2021-4-81-97 (in Russian).
20. Akimov E. M., Struev D. A., Gavrikov N. S., Gluskin V. A. Sposob povysheniya dostovernosti priema soobshcheniy v diskretnykh kanalakh svyazi s peremezheniem i gruppirovaniem oshibok na osnove otsenok simvolov kodirovannogo soobshcheniya [A Method for Improving the Reliability of Message Reception in Discrete Communication Channels with Interleaving and Error Bursting Based on Estimates of Encoded Message Symbols]. Tekhnologii informatsionnogo obshchestva: Sbornik trudov XVII Mezhdunarodnoy otraslevoy nauchno-tekhnicheskoy konferentsii [Technologies of the Information Society: Proceedings of the XVII International Industry Scientific and Technical Conference]. Moscow, LLC "Publishing House Media Publisher", 2023, pp. 62--64 (in Russian).
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