Issue No.09 - September (1974 vol.23)
F. Barsi , Istituto di Elaborazione dell'Informazione, Consiglio Nazionale delle Ricerche
The arithmetic error detecting and correcting capabilities of product (AN) codes in residue number systems (RNS) are described. The redundancy necessary and sufficient to allow single residue digit error detection or correction is determined, under the hypothesis that the error affects either an arbitrary legitimate number or a number in overflow. It is shown that single-bit errors are also correctable, provided that the residue digits are conveniently encoded. Two different approaches to this problem are discussed. Simple procedures for error detection and correction are presented, and it is shown that the additive overflow detection is a by-product of such procedures. Proofs and examples are given.
Arithmetic error codes, error correction, error detection, product codes, residue arithmetic, residue number systems.
F. Barsi, P. Maestrini, "Error Detection and Correction by Product Codes in Residue Number Systems", IEEE Transactions on Computers, vol.23, no. 9, pp. 915-924, September 1974, doi:10.1109/T-C.1974.224055