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...
Сохранить в:
| Главные авторы: | , , , , , |
|---|---|
| 格式: | Статья |
| 语言: | English |
| 出版: |
Springer Science and Business Media Deutschland GmbH
2024
|
| 主题: | |
| 在线阅读: | https://dspace.ncfu.ru/handle/123456789/29178 |
| 标签: |
添加标签
没有标签, 成为第一个标记此记录!
|
| 总结: | 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. |
|---|