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Error Control in Residue Number Systems

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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

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