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An Algorithm for Scaling and Single Residue Error Correction in Residue Number Systems
August 1990 (vol. 39 no. 8)
pp. 1053-1064

An algorithm for scaling and single residue digit error correction is proposed. This algorithm is fully based on mixed radix conversion (MRC). The redundant digits of MRC can be used to establish a lookup table to correct single residue digit errors. By using this algorithm the error correction and scaling operation can be unified in one hardware, thereby reducing the complexity of these implementations. The scaling error e/sub s/ is analyzed and found to be limited to the interval of -1>e/sub s/>1. Since scaling is often required in the computations of digital signal processing (DSP), which is the main application of RNS, and error-correction circuit with scaling (ECCS) will by very efficient in the fault-tolerant systems for the DSP applications. Two examples for the application of the proposed ECCS are given.

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Index Terms:
residue number systems; single residue digit error correction; mixed radix conversion; redundant digits; lookup table; scaling error; digital signal processing; RNS; error-correction circuit with scaling; fault-tolerant systems; digital arithmetic; digital signal processing chips; error correction; fault tolerant computing; number theory.
C.-C. Su, H.-Y. Lo, "An Algorithm for Scaling and Single Residue Error Correction in Residue Number Systems," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1053-1064, Aug. 1990, doi:10.1109/12.57044
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