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UDK 004.021 Алгоритмы
Purpose: To investigate the dependence of the maximum power of codes on the number of digits and the minimum code distance; to find an approach to determine the optimal rules for constructing the check vector of a separable code from the point of view of ensuring minimal redundancy with a given reliability of message transmission. Methods: Computer simulation has been used to conduct experimental studies. For theoretical studies, the method of analytical review, graph theory, and coding theory have been applied. Results: Theoretical and experimental studies have obtained certain specific cases of power distribution for code alphabets with a given Hamming distance for various constant lengths, generated using the previously described algorithm. A method for doubling the power of arbitrary binary codes is proposed and described, as well as a method for obtaining codes with the least redundancy of powers M=2f, where f is a natural number for a predetermined minimum code distance by recursively using the method proposed in the article. Practical significance: An algorithm has been developed for doubling the power of the code alphabet while maintaining the required reliability of data transmission. A technique for analyzing the resulting matrices of code vectors is obtained in order to determine the rules for calculating check bits without using cyclic algorithms.
Anti-jamming coding, least redundant codes, code alphabet, code word, Hamming distance, separable codes
1. Hamming R. W. Error detecting and error correcting codes / R. W. Hamming // The Bell system technical journal. - 1950. - Vol. 29. - Iss. 2. - DOI:https://doi.org/10.1002/j.1538-7305.1950.tb00463.x.
2. Pronin G. Yu. Algoritm generacii uslovno optimal'nyh kodov / G. Yu. Pronin, E. A. Volkov, Yu. V. Ivanov i dr. // Transport: problemy, idei, perspektivy. - 2022. - № 2. - S. 96-98.
3. Manoj S. G. Diagonal Hamming Based Multi-Bit Error Detection and Correction Technique for Memories / S. G. Manoj, A. K. Mohan, N. L. Sri Ganesh et al. // International Conference on Communication and Signal Processing. - July 28-30, 2020. - DOI:https://doi.org/10.1109/ICCSP48568.2020.9182249.
4. Van W. J. Effectiveness of Hamming Single Error Correction Codes Under Harsh Electromagnetic Disturbances / W. J. Van, J. Lannoo, J. Vankeirsbilck et al. // International Symposium on Electromagnetic Compatibility. - August 27-30, 2018. - DOI:https://doi.org/10.1109/EMCEurope.2018.8485176.
5. Tshagharyan G. Experimental Study on Hamming and Hsiao Codes in the Context of Embedded Applications / G. Tshagharyan, G. Hatutyunyan, S. Shoukourian et al. // Proceedings of 15th IEEE East-West Design & Test Symposium (EWDTS’2017), Novi Sad, Serbia, September 29 - October 2, 2017.
6. Musayelyan R. Hamming Distance Based Data Correction Combined With Low Power XOR Circuit / R. Musayelyan // Proceedings of 19th IEEE East-West Design & Test Symposium (EWDTS’2021), Batumi, Georgia, September 10-13, 2021.
7. Sridevi N. Implementation of Error Correction Techniques in Memory Applications / N. Sridevi, K. Jamal, K. Mannem // 5th International Conference on Computing Methodologies and Communication. - April 8-10, 2021. - DOI:https://doi.org/10.1109/ICCMC51019.2021.9418432.
8. Tolentino L. K. S. Overhead Interspersing of Redundancy Bits Reduction Algorithm by Enhanced Error Detection Correction Code / L. K. S. Tolentino, I. C. Valenzuela, R. O. Serfa Juan // Journal of Engineering Science & Technology Review. - 2019. - T. 12. - Iss. 2.
9. Shahariar Parvez A. H. M. Design and implementation of hamming encoder and decoder over FPGA / A. H. M. Shahariar Parvez et al. // International Conference on Computer Networks and Communication Technologies: ICCNCT 2018. - Springer Singapore, 2019. - Pp. 1005-1022.
10. Panem C. Polynomials in Error Detection and Correction in Data Communication System / C. Panem, V. Gad, R. Gad // Coding Theory. - 2019. - P. 29.