论文标题
基于球体约束的枚举方法，分析极性代码的最小重量分布
Sphere Constraint based Enumeration Methods to Analyze the Minimum Weight Distribution of Polar Codes
论文作者
论文摘要
在本文中，根据代码字的距离属性，列举了极地代码和串联极性代码的最小重量分布（MWD）。我们首先提出了一种基于球体约束的枚举方法（SCEM），以分析具有中等复杂性的极地代码的MWD。 SCEM利用所有具有相同锤子重量的代码字均分布在球形外壳上的距离属性。然后，基于SCEM和Plotkin的极地代码的构建，提出了基于球体的递归枚举方法（SCREM），以递归以较低的复杂性来递归计算MWD。最后，我们提出了一个平价检查SCEM（PC-SCEM），以通过引入外部代码的奇偶校验检查方程来分析串联极性代码的MWD。此外，由于代码字的距离属性，提出的三种方法可以准确地列举属于MWD的所有代码字。枚举结果表明，SCREM可以枚举具有高达$ 2^{14} $的极性代码的MWD，并且PC-SCEM可用于优化CRC偏置的串联代码。
In this paper, the minimum weight distributions (MWDs) of polar codes and concatenated polar codes are exactly enumerated according to the distance property of codewords. We first propose a sphere constraint based enumeration method (SCEM) to analyze the MWD of polar codes with moderate complexity. The SCEM exploits the distance property that all the codewords with the identical Hamming weight are distributed on a spherical shell. Then, based on the SCEM and the Plotkin's construction of polar codes, a sphere constraint based recursive enumeration method (SCREM) is proposed to recursively calculate the MWD with a lower complexity. Finally, we propose a parity-check SCEM (PC-SCEM) to analyze the MWD of concatenated polar codes by introducing the parity-check equations of outer codes. Moreover, due to the distance property of codewords, the proposed three methods can exactly enumerate all the codewords belonging to the MWD. The enumeration results show that the SCREM can enumerate the MWD of polar codes with code length up to $2^{14}$ and the PC-SCEM can be used to optimize CRC-polar concatenated codes.
