一种(41,21,9)平方剩余码的快速代数译码算法  

A Fast Algebraic Decoding of the (41, 21, 9) Quadratic Residue Code

作　　者：吴怡[1] 罗春兰 张新球 林潇[1] 徐哲鑫[1] WU Yi;LUO Chunlan;ZHANG Xinqiu;LIN Xiao;XU Zhexin(Fujian Provincial Engineering Technology Research Center of Photoelectric Sensing Application,Fujian Normal University,Fuzhou 350007,Chin)

机构地区：[1]福建师范大学福建省光电传感应用工程技术研究中心,福州350007

出　　处：《电子与信息学报》2018年第8期1949-1955,共7页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61571128;61701118)~~

摘　　要：为了降低译码时的计算复杂度以及减少译码时间,该文通过对牛顿恒等式进行推导得到了(41,21,9)QR码不需要计算未知校验子就可求得错误位置多项式系数的代数译码算法,同时也针对改善部分客观地给出了计算复杂度的理论分析。此外,为了进一步降低译码时间,提出判定接收码字中出现不同错误个数的更简化的判断条件。仿真结果表明该文提出算法在不降低Lin算法所达到的译码性能的前提下,降低了译码时间。In order to reduce the computational complexity of computing unknown syndromes for the coefficients of the error-locator polynomial and reduce the decoding time when one is decoding, this paper proposed an algebraic decoding algorithm of （41, 21, 9） QR code without calculating the unknown syndromes by solving the Newtonian identity. Simultaneously, an objective theoretical analysis of the computational complexity is given for the part of improvement. Besides, this paper also puts forward the simplifying conditions to determine the number of errors in the received word, which in order to further reducing the decoding time. Simulation results show that the proposed algorithm reduces the decoding time with maintaining the same decoding performance of Lin＇s algorithm.

关 键 词：平方剩余码 代数译码 牛顿恒等式 未知校验子 错误位置多项式 

分 类 号：TN911.22[电子电信—通信与信息系统]