论文标题
二进制循环代码的衍生后代和上升者和衍生物解码
Derivative Descendants and Ascendants of Binary Cyclic Codes, and Derivative Decoding
论文作者
论文摘要
本文分别定义了来自Mattson-Solomon多项式衍生物的延伸循环代码的环状和最小衍生后代（DDS）。首先，它表明环状DDS是相同的扩展循环代码。它使我们能够根据其循环DDS对扩展的循环代码执行软性解码。然后，证明最小的DDS是等效的代码。它还使我们能够根据具有排列的最小DDS执行软性决定解码。仿真结果表明，我们提出的衍生化解码可以接近某些扩展循环代码的最大似然解码，包括一些扩展的BCH代码。
This paper defines cyclic and minimal derivative descendants (DDs) of an extended cyclic code from the derivative of the Mattson-Solomon polynomials, respectively. First, it demonstrates that the cyclic DDs are the same extended cyclic code. It allows us to perform soft-decision decoding for extended cyclic codes based on their cyclic DDs. Then, it proves that the minimal DDs are equivalent codes. It also allows us to perform soft-decision decoding based on the minimal DDs with permutations. Simulation results show that our proposed derivative decoding can be close to the maximum likelihood decoding for certain extended cyclic codes, including some extended BCH codes.
