The Error Correction Of The Redundant Residue Number System With Gaussian Noise

Residue number system (RNS) is a concept of number theory which represents an integer as a set of its residues or remainders and usually utilizes Chinese Remainder Theorem (CRT) to reconstruct the integer from its multiple residues. Mainly, we consider the Redundant residue number system (RRNS) which all of the moduli have the same factor more than1, i.e., M>1. So, in order to estimate N, we must estimate the common solved, which can be calculated by rt and rc. We consider the RRNS with the Gaussian noise, and propose a sufficient condition for robustly reconstruct N in real domain. Under this condition, we obtain the performance of the system and obtain then the formulas when the number of the remainder are3and4. We obtain some useful conclusions about the error detection and correction both of single and multiple error of the RRNS. At last, we propose an algorithm to estimate N, that is, we choose some remainders which are close to the rc. We simulated the algorithm when the number of the remainders is7and the number of the redundance is3by using the Mento Carlo method. The simulation result tells us that the theory is correct and the above algorithm is practicable.