A closed-form robust chinese remainder theorem and its performance analysis

Authors:
Wenjie Wang;Xiang-Gen Xia
Affiliations:
School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, China;Department of Electrical and Computer Engineering, University of Delaware, Newark, DE and Institute of Information and Communication, Chonbuk National University, Jeonju, Korea
Venue:
IEEE Transactions on Signal Processing
Year:
2010

Citing 7
Cited 0

Chinese remainder theorem: applications in computing, coding, cryptography

Chinese remainder theorem: applications in computing, coding, cryptography
Number Theory in Digital Signal Processing

Number Theory in Digital Signal Processing
"Soft-decision" decoding of Chinese remainder codes

FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Noisy Chinese remaindering in the Lee norm

Journal of Complexity - Special issue on coding and cryptography
Multi-frequency Phase Unwrapping from Noisy Data: Adaptive Local Maximum Likelihood Approach

SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
A robust Chinese remainder theorem with its applications in frequency estimation from undersampled waveforms

IEEE Transactions on Signal Processing
Chinese remaindering with errors

IEEE Transactions on Information Theory

Quantified Score

Hi-index	35.68

Visualization

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.