POLYPARAMETRIC BLOCK CODING
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.
codeword; vector shift indicators; natural sequence; poly-parametric codes
Arora S., Barak B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge 2009.
Berlekamp E.: Algebraic coding theory. Mir, Moscow 1971.
Blahut R. E.: Algebraic Codes for Data Transmission. Cambridge University Press, 2012.
Bronshtein I. N., Semendyaev K. A.: Mathematics reference book for engineers and students of technical colleges. GITTL, Moscow 1957.
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.
Carrasco R. A., Johnston M.: Non-binary error control coding for wireless communication and data storage. J. Wiley & Sons, 2008.
Conway J. H., Sloane N. J. A.: Lexicographic codes: error-correcting codes from game theory. IEEE Trans. Inform. Theory 32/1986, 337–348.
Dikarev A. V.: Codes based on binary rings. Control systems, navigation and communication 1(29)/2014. 50–53.
Etzion T.: Optimal constant weight codes over Zk. and generalized designs. Discrete Math. 169/1997, 55–82.
MacKay D., Neal R.: Near Shannon limit performance of low density parity check codes. IEEE Electronics Letters 32(18)/1996, 1645–1646.
Milova J. A.: Parameters of total codes. Zvyazok 4/2018, 3–32.
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].
Milova J. A. et al.: Total codes. Zvyazok 3/2018, 47–50.
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].
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.