Remainder Theorem

Abstract — This work presents some results on multiple error detection and correction based on the Redundant Residue Number System (RRNS). RRNS is often used in parallel processing environments because of its ability to increase the robustness of information passing between the processors. The proposed multiple error correction scheme utilizes the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. An extension of the scheme further reduces the computational complexity without compromising its error correcting capability. Proofs and examples are provided for the coding technique which be implemented using Cadence virtuoso tool of 180nm CMOS process. Index Terms—Arithmetic codes, error correction coding, maximum likelihood decoding, redundant number systems, residue codes