A Novel Exploitation of Errors in Redundant Residue Number System Architecture

Abstract

Residue Number System (RNS) is an unweighted number system that symbolizes big integers with smaller numbers. It can perform operations in particular addition and multiplication in parallel. Because of this property, RNS is extensively used in communication, Finite Impulse Response (FIR), cryptography and signal processing devices. The transfer of data in digital channels is very important for some critical applications where accuracy is very important. In this study, we proposed a novel algorithm that is premised on the Hamming Distance (HD) and one of the reverse conversion methods, which is, the Chinese Remainder Theorem (CRT) and) as a joint technique for the detection and correction of multiple bit errors in RNS. The proposed algorithm provides a more efficient technique that improves on the hardware size and increases the processing speed with fewer iterations when compared with other stateof-the-art schemes. The work analyses the area and delay of the hardware architecture and compared with other similar schemes. The results indicated the effectiveness of our proposed scheme in terms of the area and delay specifications.

Error-Correction Coding Using Polynomial Residue Number System

“…However, according to the provided information, an error occurred in the code combination of PRNS and the residue is d * i (z) = d i (z). Therefore, the code combination D * i (z) contains an error on the i-th base of the code of polynomial residue number system and Condition (33) is valid for it.…”

“…Therefore, redundant arithmetical codes of RNS have found wide application in the construction of fault-tolerant DSP systems, as the usage of redundant arithmetical codes of RNS allows for the operability of the computing device to be maintained by detecting and correcting errors that occur during data processing. For example, the works [30][31][32][33] consider the issues with building a fault-tolerant special processor operating in codes of RNS. The issues with increasing the fault tolerance of digital filters functioning in codes of RNS are considered in [34][35][36][37].…”