Power Distribution of Codes with the Lowest Alphabet Redundancy Depending on the Number of Bits and Code Distance-Reference-Cited by-同舟云学术

Power Distribution of Codes with the Lowest Alphabet Redundancy Depending on the Number of Bits and Code Distance

Published:2023-06-20 Issue:2 Volume:20 Page:365-375
ISSN:1815-588X
Container-title:Proceedings of Petersburg Transport University
language:en
Short-container-title:

Author:

Blyudov Anton¹,Pivovarov Dmitry¹,Pronin Georgiy¹

Affiliation:

1. Emperor Alexander I St. Petersburg State Transport University

Abstract

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.

Publisher

Petersburg State Transport University

Subject

General Medicine

Reference10 articles.

1. Hamming R. W. Error detecting and error correcting codes / R. W. Hamming // The Bell system technical journal. — 1950. — Vol. 29. — Iss. 2. — DOI: 10.1002/j.1538-7305.1950.tb00463.x., Hamming R. W. Error detecting and error correcting codes / R. W. Hamming // The Bell system technical journal. — 1950. — Vol. 29. — Iss. 2. — DOI: 10.1002/j.1538-7305.1950.tb00463.x.

2. Пронин Г. Ю. Алгоритм генерации условно оптимальных кодов / Г. Ю. Пронин, Е. А. Волков, Ю. В. Иванов и др. // Транспорт: проблемы, идеи, перспективы. — 2022. — № 2. — С. 96–98., 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: 10.1109/ICCSP48568.2020.9182249., 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: 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: 10.1109/EMCEurope.2018.8485176., 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: 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., 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.