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RS码在通信领域有着广泛的应用,其中最重要的是关键方程的求解。传统欧几里德算法是利用多项式长除法来求解关键方程,它需要多项式次数的判断,并且必须通过迭代运算才能求出商式和余式,造成硬件电路复杂,译码速度下降。通过矩阵论的相关知识,提出一种改进型欧几里德算法。它不需要进行多项式次数的判断和迭代运算就能快速地计算出商式和余式,能够降低译码的复杂度,提高译码速度。在VCS软件中通过FPGA仿真,仿真结果表明该算法能够实现正确译码的效果。
RS code has a wide range of applications in the field of communications, of which the most important is the solution of the key equation. The traditional Euclidean algorithm uses the polynomial long division method to solve the key equation. It needs the judgment of the polynomial number, and must be solved by iteration to find the quotient and the remainder, resulting in the complexity of the hardware circuit and the declining of the decoding speed. Based on the knowledge of matrix theory, an improved Euclidean algorithm is proposed. It can quickly calculate the quotient and remainder without the need of polynomial judgment and iterative operation, which can reduce the complexity of decoding and improve the decoding speed. In the VCS software by FPGA simulation, simulation results show that the algorithm can achieve the correct decoding effect.