POLYPARAMETRIC BLOCK CODING
Julia Milova
State University of Telecommunications, Educational-Scientific Institute of Telecommunications (Ukraine)
http://orcid.org/0000-0002-9977-2195
Yuri Melnik
melnik_yur@ukr.netState University of Telecommunications, Educational-Scientific Institute of Telecommunications (Ukraine)
https://orcid.org/0000-0002-5028-8749
Abstract
The principles of poly-parametric information coding have been considered. The methods for developing poly-parametric codes have been presented. It is shown that the protection of block codes from channel interference using check patterns can be developed by a mono- or poly-parametric method. A special type of block codes has been presented, the check patterns of which are formed on the basis of their neighbours, which are functionally related to the given code combination. Such codes have been called poly-parametric. Binary poly-parametric ring codes, the check patterns of which are designed to detect and correct channel errors, are developed using the properties of Galois fields and on the basis of the vector shift indicators of the codewords. To obtain digital poly-parametric block codes, the properties and features of the normalized natural sequence are used. It is shown that each codeword of a binary block code can be represented as a certain positive integer in the decimal number system, which is an element of the natural sequence. Its elements on an interval that equals the norm acquire a functional dependency.
Keywords:
codeword, vector shift indicators, natural sequence, poly-parametric codesReferences
Arora S., Barak B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge 2009.
DOI: https://doi.org/10.1017/CBO9780511804090
Google Scholar
Berlekamp E.: Algebraic coding theory. Mir, Moscow 1971.
DOI: https://doi.org/10.1007/978-3-7091-4325-4
Google Scholar
Blahut R. E.: Algebraic Codes for Data Transmission. Cambridge University Press, 2012.
Google Scholar
Bronshtein I. N., Semendyaev K. A.: Mathematics reference book for engineers and students of technical colleges. GITTL, Moscow 1957.
Google Scholar
Brouwer E., Shearer J. B., Sloane N. J. A., Smith W. D.: A new table of constant weight codes. IEEE Trans. Inform. Theory 36/1990, 1334–1380.
DOI: https://doi.org/10.1109/18.59932
Google Scholar
Carrasco R. A., Johnston M.: Non-binary error control coding for wireless communication and data storage. J. Wiley & Sons, 2008.
DOI: https://doi.org/10.1002/9780470740415
Google Scholar
Conway J. H., Sloane N. J. A.: Lexicographic codes: error-correcting codes from game theory. IEEE Trans. Inform. Theory 32/1986, 337–348.
DOI: https://doi.org/10.1109/TIT.1986.1057187
Google Scholar
Dikarev A. V.: Codes based on binary rings. Control systems, navigation and communication 1(29)/2014. 50–53.
Google Scholar
Etzion T.: Optimal constant weight codes over Zk. and generalized designs. Discrete Math. 169/1997, 55–82.
DOI: https://doi.org/10.1016/0012-365X(95)00333-R
Google Scholar
MacKay D., Neal R.: Near Shannon limit performance of low density parity check codes. IEEE Electronics Letters 32(18)/1996, 1645–1646.
DOI: https://doi.org/10.1049/el:19961141
Google Scholar
Milova J. A.: Parameters of total codes. Zvyazok 4/2018, 3–32.
Google Scholar
Milova Y.: Rationed natural row. Polyparametric coding. The European Journal of Technical and Natural Sciences 3/2020, 19–23 [http://doi.org/10.5604/20830157.1121333].
DOI: https://doi.org/10.5604/20830157.1121333
Google Scholar
Milova J. A. et al.: Total codes. Zvyazok 3/2018, 47–50.
Google Scholar
Robinson J. P., Bernstein A. J.: A class of binary recurrent codes with limited error propagation. EEE Transactions on Information Theory 13(1)/1967, 106–113 [http://doi.org/10.1109/TIT.1967.1053951].
DOI: https://doi.org/10.1109/TIT.1967.1053951
Google Scholar
Authors
Julia MilovaState University of Telecommunications, Educational-Scientific Institute of Telecommunications Ukraine
http://orcid.org/0000-0002-9977-2195
Authors
Yuri Melnikmelnik_yur@ukr.net
State University of Telecommunications, Educational-Scientific Institute of Telecommunications Ukraine
https://orcid.org/0000-0002-5028-8749
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