一种(71,36,11) QR码的快速代数译码算法

在平方剩余(quadratic residue,QR)码的译码过程中,当接收码字中出现的错误个数较多时,未知校正子的计算非常困难,计算量与复杂度都很高,因此增加了解码过程所需要的时间.鉴于此,在(71,36,11)QR码的错误模式权重为4时,通过对牛顿恒等式的数学推导,在不需要计算未知校正子的情况下,导出了其错误位置多项式的系数,简化了(71,36,11)QR码中出现4个错误时的判断条件,并对所有可纠错的错误图案进行了穷举验证.仿真结果表明,提出的算法在解4个错与5个错时,分别提高了56.12％与18.19％的解码效率,验证了算法的正确性与有效性.

A fast algebraic decoding algorithm of the (71,36,11) quadratic residue code

In the decoding process of quadratic residue (QR) codes, it is difficult to calculate unknown syndromes when multiple errors occurred in the receive word since the high computation and complexity are required,thus increasing the decoding time.In view of this,we directly determine the coefficients of the error-locator polynomial by solving Newton identities without computing the unknown syndromes in the four-error case for the (71, 36, 11) QR code. Moreover, this paper also simplifies the condition that indicates the occurrence of four errors for the (71, 36, 11) QR code and an exhaustive verification of all correctable error patterns was conducted. Simulation results show that in the four-error and five-error case, the decoding efficiency was increased by 56.12% and 18.19% respectively when using the new proposed decoding algorithm. Therefore verify the correctness and effectiveness of the algorithm.