Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number

The Residue Number System (RNS) is a number representation system used in applications that require high-speed arithmetic operations such as signal processing, digital filters, cryptography, and error correction codes. However, one of the problems with using RNS is determining the rank of a number r...

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Главные авторы:	Bezuglova, E. S., Безуглова, Е. С., Kulikova, A. L., Куликова, А. Л., Babenko, M. G., Бабенко, М. Г.
格式:	Статья
语言:	English
出版:	Springer Science and Business Media Deutschland GmbH 2024
主题:	Approximate method Residue number system (RNS) Calculation of the rank of a number Rank of a number
在线阅读:	https://dspace.ncfu.ru/handle/123456789/29178
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spelling	ir-123456789-291782024-10-30T12:41:14Z Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number Bezuglova, E. S. Безуглова, Е. С. Kulikova, A. L. Куликова, А. Л. Babenko, M. G. Бабенко, М. Г. Approximate method Residue number system (RNS) Calculation of the rank of a number Rank of a number The Residue Number System (RNS) is a number representation system used in applications that require high-speed arithmetic operations such as signal processing, digital filters, cryptography, and error correction codes. However, one of the problems with using RNS is determining the rank of a number represented in the system, which is a computationally difficult operation. This paper presents a method for detecting and correcting errors in arithmetic operations using the properties of the normalized rank of a number. The authors develop a lemma relating two functions of the rank of a number, which is used to efficiently calculate the normalized rank. The performance of error detection and correction algorithms largely depends on the efficiency of calculating the rank of a number in RNS. The paper also describes the development of methods for calculating the rank of a number using an approximate method, which shows the relationship between the rank of a number and the inversion of a prime number and is proved using mathematical equations. This article proposes a solution to this problem and is of great importance in improving the performance of RNS-based algorithms. 2024-10-30T12:39:37Z 2024-10-30T12:39:37Z 2024 Статья Bezuglova E., Kulikova A., Babenko M. Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number // Lecture Notes in Networks and Systems. - 2024. - 1044 LNNS. - pp. 105 - 114. - DOI: 10.1007/978-3-031-64010-0_11 https://dspace.ncfu.ru/handle/123456789/29178 en Lecture Notes in Networks and Systems application/pdf Springer Science and Business Media Deutschland GmbH
institution	СКФУ
collection	Репозиторий
language	English
topic	Approximate method Residue number system (RNS) Calculation of the rank of a number Rank of a number
spellingShingle	Approximate method Residue number system (RNS) Calculation of the rank of a number Rank of a number Bezuglova, E. S. Безуглова, Е. С. Kulikova, A. L. Куликова, А. Л. Babenko, M. G. Бабенко, М. Г. Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
description	The Residue Number System (RNS) is a number representation system used in applications that require high-speed arithmetic operations such as signal processing, digital filters, cryptography, and error correction codes. However, one of the problems with using RNS is determining the rank of a number represented in the system, which is a computationally difficult operation. This paper presents a method for detecting and correcting errors in arithmetic operations using the properties of the normalized rank of a number. The authors develop a lemma relating two functions of the rank of a number, which is used to efficiently calculate the normalized rank. The performance of error detection and correction algorithms largely depends on the efficiency of calculating the rank of a number in RNS. The paper also describes the development of methods for calculating the rank of a number using an approximate method, which shows the relationship between the rank of a number and the inversion of a prime number and is proved using mathematical equations. This article proposes a solution to this problem and is of great importance in improving the performance of RNS-based algorithms.
format	Статья
author	Bezuglova, E. S. Безуглова, Е. С. Kulikova, A. L. Куликова, А. Л. Babenko, M. G. Бабенко, М. Г.
author_facet	Bezuglova, E. S. Безуглова, Е. С. Kulikova, A. L. Куликова, А. Л. Babenko, M. G. Бабенко, М. Г.
author_sort	Bezuglova, E. S.
title	Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
title_short	Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
title_full	Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
title_fullStr	Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
title_full_unstemmed	Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number
title_sort	method for detecting and correcting errors in arithmetic operations based on rank of a number
publisher	Springer Science and Business Media Deutschland GmbH
publishDate	2024
url	https://dspace.ncfu.ru/handle/123456789/29178
work_keys_str_mv	AT bezuglovaes methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber AT bezuglovaes methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber AT kulikovaal methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber AT kulikovaal methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber AT babenkomg methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber AT babenkomg methodfordetectingandcorrectingerrorsinarithmeticoperationsbasedonrankofanumber
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Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a Number

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