Abstract.
This paper introduces an alternate approach to error control in residue number systems which utilizes sets of moduli that include pairs with non-trivial common factors. Necessary and sufficient conditions for achieving a specified capacity for error detection or correction are derived by considering the minimum Hamming distance of an associated linear code. Effective error-control procedures are developed based on a syndrome matrix whose entries are obtained directly from the residue digits. The potential of a priori bounds on the magnitude of measurement errors to increase the efficiency of the control process is analyzed.
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Received: January 12, 2001; revised version: June 25, 2002
Keywords: Residue number systems, Error correction, Error detection, Computational errors, Instrumentation errors, Transmission noise, Coding theory.
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Miller, D., Rutter, E. Error Control in Residue Number Systems. AAECC 13, 301–312 (2002). https://doi.org/10.1007/s00200-002-0103-3
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DOI: https://doi.org/10.1007/s00200-002-0103-3