Algebraic Decoding Algorithm For Quadratic Residue Codes With Code Lengths Of 41, 47 And 71

Error control in a digital transmission system,which ensures reliable reproduction of data,is a major issue in current digital communication systems.This paper focuses on fast algebraic decoding algorithm for Quadratic Residue(QR)codes.In the process of algebraic decoding,the algorithm checks the number of errors in the received codeword,then the corresponding error location polynomial is solved for different errors,finally the purpose of correcting the error is achieved.Therefore,improving the decision condition effectiveness and reducing the calculation of the error position polynomial can greatly reduce the decoding time of the QR code.This paper studies three kinds of QR codes with code lengths of 41,47 and 71,and presents corresponding fast algebraic decoding algorithms.Firstly,we introduced fast algebraic decoding algorithm of(41,21,9)QR code which without calculating the relevant unknown syndrome and simplifying the proposed decision condition.The simulation demonstrated that the algorithm costs 75% of decoding time than Lin-41 algorithm.Meanwhile,the decoding performance did not change.Secondly,this paper simplifies the condition where(47,24,11)QR code is used to determine whether there are 4 errors in the accepted codeword during decoding,and proposes a method to solve the related unknown syndrome quickly.The simulation results show that the algorithm not only improves the decoding performance but also reduces the decoding time.Finally,this paper simplifies the decoding process of(71,36,11)QR code when there are 4 errors in the received codewordm,which reduces the calculation of decision condition.Simulation results show that the algorithm in this paper reduces the execution time of decision condition by about 53.9% at the time of decoding,and achieves same decoding performance as the Lin-71 et al.This paper provides a feasible way to improve the decoding efficiency of QR code,in order to obtain more research results of QR code and a greater breakthrough in practical applications.