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Error correction in redundant residue number systems
1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972In this paper, two error-correcting algorithms for redundant residue number systems are presented, one for single residue-error correction and the other for burst residue-error correction. Neither algorithm requires table look-up and hence their implementations need a memory space which is much smaller than that required by existing methods ...
Stephen S. Yau, Yu-Cheng Liu
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On the simulation of residue number systems
ICASSP '81. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005It is sometimes difficult to simulate on general purpose computers the performance of digital systems that use residue number systems. This paper demonstrates a new technique that makes effective use of a Fast Fourier Transform (FFT) to simulate the basic arithmetic operations required by such number systems. An algorithm for performing such operations
G. Robert Redinbo, William J. Hunnebeck
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Integer division in residue number systems
IEEE Transactions on Computers, 1995Summary: This contribution to the ongoing discussion of division algorithms for Residue Number Systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a
Markus A. Hitz, Erich L. Kaltofen
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Error Control in Residue Number Systems
Applicable Algebra in Engineering, Communication and Computing, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David F. Miller, Edgar A. Rutter
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Symmetric Cryptoalgorithms in the Residue Number System
Cybernetics and Systems Analysis, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kasianchuk, M. M. +2 more
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Residue Number System Asymmetric Cryptoalgorithms
Cybernetics and Systems Analysis, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nykolaychuk, Ya. M. +3 more
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On residue number system decoding
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986The use of a residue number system (RNS) in digital systems and especially filter designs is facilitated by efficient algorithms for the conversion from RNS to binary numbers. The conversion is generally based on the Chinese remainder theorem or the mixed radix conversion.
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Single Residue Error Correction in Residue Number Systems
IEEE Transactions on Computers, 1983Summary: We present a new method to correct single errors in an \(n\)-residue number system through the use of \(r\) redundant moduli. The method requires \(\lceil 2n/r\rceil + 2\) recombinations of \(n\) residues in the worst case. This is of lower complexity than any other known method.
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Integer division in residue number system
ICECS 2001. 8th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.01EX483), 2002Division, sign detection and number comparison are the more difficult operations in residue number systems (RNS). These shortcomings limited most RNS implementations to additions, subtractions and multiplications. In this paper, a high level description of a RNS division algorithm is proposed.
Badreddine Rejeb +2 more
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IEEE Transactions on Electronic Computers, 1959
A novel number system called the residue number system is developed from the linear congruence viewpoint. The residue number system is of particular interest because the arithmetic operations of addition, subtraction and multiplication may be executed in the same period of time without the need for carry.
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A novel number system called the residue number system is developed from the linear congruence viewpoint. The residue number system is of particular interest because the arithmetic operations of addition, subtraction and multiplication may be executed in the same period of time without the need for carry.
openaire +1 more source