UDC
004.624 004.021

POWER DISTRIBUTION OF CODES WITH THE LOWEST ALPHABET REDUNDANCY DEPENDING ON THE NUMBER OF BITS AND CODE DISTANCE Power Distribution of Codes with the Lowest Alphabet Redundancy Depending on the Number of Bits and Code Distance

Published in Proceedings of Petersburg Transport University · Pages 365–375 · Rubric: HIGH TECHNOLOGIES FOR TRANSPORT
DOI: https://doi.org/10.20295/1815-588X-2023-2-365-375
Received: 20.06.2023 Accepted: 20.06.2023 Published: 20.06.2023
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
Text References
Text (PDF)
Read Download

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.