A Closed-Form Robust Chinese Remainder Theorem and Its Performance Analysis

Abstract

Chinese remainder theorem (CRT) reconstructs an integer from its multiple remainders that is well-known not robust in the sense that a small error in a remainder may cause a large error in the reconstruction. A robust CRT has been recently proposed when all the moduli have a common factor and the robust CRT is a searching based algorithm and no closed-from is given. In this paper, a closed-form robust CRT is proposed and a necessary and sufficient condition on the remainder errors for the closed-form robust CRT to hold is obtained. Furthermore, its performance analysis is given. It is shown that the reason for the robustness is from the remainder differential process in both searching based and our proposed closed-form robust CRT algorithms, which does no exist in the traditional CRT. We also propose an improved version of the closed-form robust CRT. Finally, we compare the performances of the traditional CRT, the searching based robust CRT and our proposed closed-form robust CRT (and its improved version) algorithms in terms of both theoretical analysis and numerical simulations. The results demonstrate that the proposed closed-form robust CRT (its improved version has the best performance) has the same performance but much simpler form than the searching based robust CRT.