Efficient Implementations of the Chinese Remainder Theorem for Sign Detection and Residue Decoding
IEEE Transactions on Computers
Residue number system arithmetic: modern applications in digital signal processing
Residue number system arithmetic: modern applications in digital signal processing
An Algorithm for Scaling and Single Residue Error Correction in Residue Number Systems
IEEE Transactions on Computers
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Low-Cost On-Line Test for Digital Filters
VTS '99 Proceedings of the 1999 17TH IEEE VLSI Test Symposium
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Previously proposed error detection algorithms for the residue number system require a complete recombination. A weighted approximation via the Chinese remainder theorem is shown to be sufficient to detect 100% of single errors. This makes real-time single-error diagnosis possible, which involves up to N+2 iterations of detection (N is the number of nonredundant channels). One approach uses a scaled range of L+1+log/sub 2/ (N+1) bits for detection in contrast with full decoding of approximately=L(N+1) bits, where L is the number of bits in the largest modulus. A second method forms a redundant residue number representation of the overflow multiplier A(x), although A(x) does not need to be carried through processing operations. This permits real-time single-error diagnosis and correction with a parallel array of approximately=(N+2)/sup 2/ tables.