论文标题
通过WU列表解码，基于快速综合征的追逐二进制BCH代码解码
Fast syndrome-based Chase decoding of binary BCH codes through Wu list decoding
论文作者
论文摘要
我们提出了针对二进制BCH代码的新快速追逐解码算法。与作者（IEEETrans。IT，2022）相比，新算法与最新的快速追逐解码算法相比，降低了复杂性 - solomon（RS）代码，仅需要单个koetter迭代，仅需单个koetter迭代。与Kamiya（IEEE Trans。，2001）和Wu（IEEE Trans。，2012年）提出的快速追逐算法相比，在当前论文的整个算法中更新的多项式通常具有较低的程度。 为了实现复杂性的降低，我们建立在二进制案例中两个解决方案模块之间的新同构基础上，以及WU列表解码算法的软否决（SD）版本的退化情况。粗略地说，我们证明，当WU列表中的最大列表大小为$ 1 $时，对二进制BCH代码进行解码时，将$ 1 $的多重性分配给坐标的效果与在Chase DecDecting试验中翻转此坐标相同。 溶液模块同构还提供了一种从二进制字母中受益的系统方法，以降低有界距离硬性（HD）解码的复杂性。在此过程中，我们简要开发了WU列表的Groebner-Bases公式，用于二进制BCH代码的解码算法，该算法在文献中缺少。
We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed--Solomon (RS) codes by the authors (IEEE Trans. IT, 2022), by requiring only a single Koetter iteration per edge of the decoding tree. In comparison to the fast Chase algorithms presented by Kamiya (IEEE Trans. IT, 2001) and Wu (IEEE Trans. IT, 2012) for binary BCH codes, the polynomials updated throughout the algorithm of the current paper typically have a much lower degree. To achieve the complexity reduction, we build on a new isomorphism between two solution modules in the binary case, and on a degenerate case of the soft-decision (SD) version of the Wu list decoding algorithm. Roughly speaking, we prove that when the maximum list size is $1$ in Wu list decoding of binary BCH codes, assigning a multiplicity of $1$ to a coordinate has the same effect as flipping this coordinate in a Chase-decoding trial. The solution-module isomorphism also provides a systematic way to benefit from the binary alphabet for reducing the complexity in bounded-distance hard-decision (HD) decoding. Along the way, we briefly develop the Groebner-bases formulation of the Wu list decoding algorithm for binary BCH codes, which is missing in the literature.
