{"id":2243,"date":"2021-01-18T19:34:10","date_gmt":"2021-01-18T17:34:10","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=2243"},"modified":"2021-02-16T14:23:25","modified_gmt":"2021-02-16T12:23:25","slug":"%d0%bc%d0%be%d0%b4%d0%b5%d0%bb%d1%96-%d1%81%d0%b8%d1%81%d1%82%d0%b5%d0%bc-%d0%b7%d0%b0%d0%b2%d0%b0%d0%b4%d0%be%d1%81%d1%82%d1%96%d0%b9%d0%ba%d0%be%d0%b3%d0%be-%d0%ba%d0%be%d0%b4%d1%83%d0%b2%d0%b0","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=2243","title":{"rendered":"\u041c\u043e\u0434\u0435\u043b\u0456 \u0441\u0438\u0441\u0442\u0435\u043c \u0437\u0430\u0432\u0430\u0434\u043e\u0441\u0442\u0456\u0439\u043a\u043e\u0433\u043e \u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u0443 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u044f"},"content":{"rendered":"

<\/p>\n

\u041c\u041e\u0414\u0415\u041b\u0406 \u0421\u0418\u0421\u0422\u0415\u041c \u0417\u0410\u0412\u0410\u0414\u041e\u0421\u0422\u0406\u0419\u041a\u041e\u0413\u041e \u041a\u041e\u0414\u0423\u0412\u0410\u041d\u041d\u042f \u0423 \u0422\u0415\u041b\u0415\u041a\u041e\u041c\u0423\u041d\u0406\u041a\u0410\u0426\u0406\u042f\u0425<\/p>\n

MODELS OF NOISELESS CODING SYSTEMS IN TELECOMMUNICATIONS<\/p>\n

 
\n<\/a>
\n\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 174-183. \u041d\u043e\u043c\u0435\u0440: \u21164, 2020 (287)<\/strong><\/p>\n

\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u042e.\u041c. \u0411\u041e\u0419\u041a\u041e, \u0406.\u0421. \u041f\u042f\u0422\u0406\u041d, \u0410.\u0412. \u0417\u0410\u0404\u0426\u042c
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435<\/p>\n

J. BOIKO, I. PYATIN, A. ZAIETS
\nKhmelnytskyi National University<\/p>\n

 
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2020-287-4-174-183<\/a><\/p>\n

 
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review : <\/strong>05.10.2020 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed : <\/strong>04.11.2020 \u0440.<\/p>\n

 
\n <\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0\u0412 \u0440\u043e\u0431\u043e\u0442\u0456 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u0441\u0438\u043d\u0442\u0435\u0437\u0443 \u0442\u0430 \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u043c\u043e\u0436\u043b\u0438\u0432\u043e\u0433\u043e \u0441\u0446\u0435\u043d\u0430\u0440\u0456\u044e \u0434\u0435\u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u043a\u043e\u0434\u0456\u0432 \u043d\u0438\u0437\u044c\u043a\u043e\u0457 \u0449\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043e\u043a \u043d\u0430 \u043f\u0430\u0440\u043d\u0456\u0441\u0442\u044c. \u0420\u043e\u0437\u0433\u043b\u044f\u043d\u0443\u0442\u0456 \u043f\u0440\u0438\u043d\u0446\u0438\u043f\u0438 \u0434\u0435\u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u043a\u043e\u0434\u0456\u0432 \u043d\u0438\u0437\u044c\u043a\u043e\u0457 \u0449\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043e\u043a \u043d\u0430 \u043f\u0430\u0440\u043d\u0456\u0441\u0442\u044c \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u0442\u0443\u0440\u0431\u043e-\u043f\u0456\u0434\u0445\u043e\u0434\u0443. \u0421\u0444\u043e\u0440\u043c\u043e\u0432\u0430\u043d\u043e \u0441\u0445\u0435\u043c\u0443 \u043f\u0435\u0440\u0435\u0434\u0430\u0432\u0430\u043b\u044c\u043d\u043e\u0457 \u0442\u0430 \u043f\u0440\u0438\u0439\u043c\u0430\u043b\u044c\u043d\u043e\u0457 \u0447\u0430\u0441\u0442\u0438\u043d\u0438 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u043e\u0433\u043e \u043a\u0430\u043d\u0430\u043b\u0443 \u0437 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f\u043c \u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f\u043c \u0437 \u043d\u0438\u0437\u044c\u043a\u043e\u044e \u0449\u0456\u043b\u044c\u043d\u0456\u0441\u0442\u044e \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043e\u043a \u043d\u0430 \u043f\u0430\u0440\u043d\u0456\u0441\u0442\u044c.<\/strong> \u041e\u043f\u0438\u0441\u0430\u043d\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0443\u0432\u0430\u043d\u043e\u0457 \u0441\u0445\u0435\u043c\u0438 \u0434\u0435\u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f. \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u0434\u0438\u043d\u0430\u043c\u0456\u043a\u0443 \u0440\u043e\u0431\u043e\u0442\u0438 \u0434\u0435\u043a\u043e\u0434\u0435\u0440\u0430 \u0442\u0430 \u0432\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043e \u0435\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u0447\u043d\u0443 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u0456\u0441\u0442\u044c \u0434\u0435\u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u0437\u0430 \u0440\u0456\u0437\u043d\u043e\u0457 \u043a\u0456\u043b\u044c\u043a\u043e\u0441\u0442\u0456 \u0456\u0442\u0435\u0440\u0430\u0446\u0456\u0439\u043d\u0438\u0445 \u0446\u0438\u043a\u043b\u0456\u0432. \u041d\u0430\u0432\u0435\u0434\u0435\u043d\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u043e\u0433\u043e \u043a\u0430\u043d\u0430\u043b\u0443 \u0437 \u043a\u043e\u0434\u0430\u043c\u0438 \u043d\u0438\u0437\u044c\u043a\u043e\u0457 \u0449\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043e\u043a \u043d\u0430 \u043f\u0430\u0440\u043d\u0456\u0441\u0442\u044c \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0443 \u0434\u0435\u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u00ab\u0441\u0443\u043c\u0430-\u0434\u043e\u0431\u0443\u0442\u043e\u043a\u00bb. \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u0430 \u0437\u0430\u0432\u0430\u0434\u043e\u0441\u0442\u0456\u0439\u043a\u0456\u0441\u0442\u044c \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u043e\u0433\u043e \u043a\u0430\u043d\u0430\u043b\u0443 \u0437 \u043a\u043e\u0434\u0430\u043c\u0438 \u043d\u0438\u0437\u044c\u043a\u043e\u0457 \u0449\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456 \u043f\u0435\u0440\u0435\u0432\u0456\u0440\u043e\u043a \u043d\u0430 \u043f\u0430\u0440\u043d\u0456\u0441\u0442\u044c \u043f\u0440\u0438 \u0437\u043c\u0456\u043d\u0456 \u043a\u043e\u0434\u043e\u0432\u043e\u0457 \u0448\u0432\u0438\u0434\u043a\u043e\u0441\u0442\u0456.<\/p>\n

\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043a\u043e\u0434\u0438 LDPC, \u043a\u043e\u0434\u0435\u0440, \u0434\u0435\u043a\u043e\u0434\u0435\u0440, \u043c\u043e\u0434\u0443\u043b\u044f\u0442\u043e\u0440, \u0437\u0430\u0432\u0430\u0434\u043e\u0441\u0442\u0456\u0439\u043a\u0435 \u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f.<\/p>\n

 <\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

\u00a0 \u00a0 \u00a0The paper presents the results of the synthesis and analysis of a possible scenario for decoding low-density parity-check codes. The principles of decoding low-density parity-check codes based on the turbo approach are considered. The modern communication theory is based on a scientific task, the essence of which is based on the synthesis of a model of information transfer from an information source to a receiver based on its spatial or temporal dislocation. We will design the decoder based on the \u201cturbo\u201d approach on the basis that the modulation and code will be processed in the receiving device separately. A diagram of the transmitting and receiving parts of the telecommunication channel is formed using coding with a low density of parity checks. The mathematical models of the investigated decoding scheme are described. The dynamics of the decoder’s operation is investigated and the energy efficiency of decoding for a different number of iteration cycles is determined. The mathematical model of the proposed decoder scheme is presented on the basis of such a statistical parameter as the message distribution function (the average mutual information between the total number of transmitted bits of the codeword and the general message in the decoder, which refers to a specific bit). The modelling process is a fundamental and central step in the analysis and design of advanced communications systems. The decoding process of the decoder for low density parity codes was represented as an iterative exchange of message sets between the variable node detector and the check node detector. In particular, every time when the target task for the design of a telecommunication system is to obtain high system performance close to the theoretical (final) boundaries, the quality of the model has a direct impact on the final result. It is possible to quantify the result obtained using information-theoretical tools. The results of modelling a telecommunication channel with low-density parity-check codes based on the “Sum-Product” decoding algorithm are presented. The noise immunity of a telecommunication channel with codes of low density of parity checks when changing the code rate is investigated.
\nKeywords:<\/strong> LDPC codes, encoder, decoder, modulator, noiseless coding.<\/p>\n

 <\/p>\n

References<\/strong><\/p>\n

    \n
  1. \u0406. Pyatin, J. Boiko, Investigation of energy efficiency of channel coding of user data by LDPC codes for 5G communication systems \/\/ Herald of Khmelnytskyi National University. \u2013 2020. \u2013 \u2116 3. \u2013 S. 174\u2013185.<\/li>\n
  2. Bae, A. Abotabl, H. Lin, K. Song, and J. Lee, \u201cAn overview of channel coding for 5G NR cellular communications,\u201d\u00a0APSIPA Trans. on Signal and Inform. Proces.,\u00a08, E17, June 2019. URL: https:\/\/doi.org\/10.1017\/ATSIP.2019.10.<\/li>\n
  3. T.B. Nguyen, Tan, T. Nguyen and H. Lee, \u201cEfficient QC-LDPC Encoder for 5G New Radio,\u201d\u00a0Electronics,\u00a08, 668, June 2019. URL: https:\/\/doi.org\/10.3390\/electronics8060668.<\/li>\n
  4. Boiko, I. Kovtun and S. Petrashchuk, “Productivity of telecommunication systems with modified signal-code constructions,” 2017 IEEE 4th Inter. Scientific-Practical Conf. Problems of Infocom. Science and Technology (PIC S&T), Kharkov, 2017, pp. 173\u2013178. URL: https:\/\/doi.org\/10.1109\/INFOCOMMST.2017.8246374.<\/li>\n
  5. Boiko, I. Pyatin, O. Eromenko and M. Stepanov, \u201cMethod of the adaptive decoding of self-orthogonal codes in telecommunication,\u201d Indones. Journal of Electrical Engineering and Computer Science, vol. 19, no. 3, pp. 1287\u20131296, Sept. 2020. URL: http:\/\/doi.org\/10.11591\/ijeecs.v19.i3.pp1287-1296.<\/li>\n
  6. Fang, G. Bi, Y. L. Guan and F. C. M. Lau, “A Survey on Protograph LDPC Codes and Their Applications,” in\u00a0IEEE Communic. Surveys & Tutorials, vol. 17, no. 4, pp. 1989\u20132016, Fourthquarter 2015. URL: https:\/\/doi.org\/10.1109\/COMST.2015.2436705.<\/li>\n
  7. Boiko, O. Eromenko, “Signal Processing in Telecommunications with Forward Correction of Errors,” Indonesian Journal of Electrical Engineering and Computer Science, vol.11, no. 3, pp. 868\u2013877, Sept. 2018. DOI:\u00a0http:\/\/doi.org\/10.11591\/ijeecs.v11.i3.pp868-877.<\/li>\n
  8. Boiko J.\u041c. Teoretychni aspekty pidvyshchennia zavadostiikosti y efektyvnosti obrobky syhnaliv v radiotekhnichnykh prystroiakh ta zasobakh telekomunikatsiinykh system za naiavnosti zavad \/ J.\u041c. Boiko, V.\u0410. Druzhin\u0456n, S.V. Tolyupa. \u2013 Kyiv : Lohos, 2018. \u2013 227 s.<\/li>\n
  9. Boiko J.\u041c. Research into effectiveness of channel coding algorithms in protected telecommunication information transmission systems \/ J.\u041c. Boiko, D.A. Makarishkin, O.I. Pasichnyk \/\/ Zviazok : zahalnohaluz. nauk.-vyrob. zhurn. \u2013 Kyiv, 2016. \u2013 \u2116 5. \u2013 S. 56\u201367.<\/li>\n
  10. Liveris, Z. Xiong and C. N. Georghiades “Compression of binary sources with side information at the decoder using LDPC codes,” IEEE communications letters, vol. 6, no. 10, pp. 440\u2013442, 2002.<\/li>\n
  11. Myung, Y. Kyeongcheol, and K. Jaeyoel. “Quasi-cyclic LDPC codes for fast encoding.”\u00a0IEEE Transactions on Information Theory, vol.\u00a051, no. 8, pp. 2894\u20132901, 2005.<\/li>\n
  12. E. Hocevar, “A reduced complexity decoder architecture via layered decoding of LDPC codes.”\u00a0IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004. IEEE, 2004.<\/li>\n
  13. Yang, W. E. Ryan, Y. Li, “Design of efficiently encodable moderate-length high-rate irregular LDPC codes,” IEEE Transactions on Communications, vol. 52, no. 4. pp. 564\u2013571, 2004.<\/li>\n
  14. Boiko, I. Pyatin and O. Eromenko, “Farrow Interpolator Features in QPSK Telecommunication Devices.”\u00a02020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET). IEEE, 2020. DOI:\u00a010.1109\/TCSET49122.2020.235410.<\/li>\n
  15. Boiko J.M. Improvements encoding energy benefit in protected telecommunication data transmission channels \/ J.M. Boiko, A.I. Eromenko \/\/ Communications. \u2013 2014. \u2013 Vol. 2, \u0406ss. 1 (July). \u2013 P. 7\u201314. DOI:\u00a010.11648\/j.com.20140201.12.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[23],"tags":[],"_links":{"self":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/2243"}],"collection":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2243"}],"version-history":[{"count":3,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/2243\/revisions"}],"predecessor-version":[{"id":3793,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=\/wp\/v2\/posts\/2243\/revisions\/3793"}],"wp:attachment":[{"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/journals.khnu.km.ua\/vestnik\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}