This paper introduces an efficient algorithm based on the Parity-Consistent Decomposition (PCD) method to determine the WD of pre-transformed polar codes. First, to address the bit dependencies introduced by the pre-transformation matrix, we propose an iterative algorithm to construct an \emph{Expanded Information Set}. By expanding the information bits within this set into 0s and 1s, we eliminate the correlations among information bits, thereby enabling the recursive calculation of the Hamming weight distribution using the \emph{PCD method}. Second, to further reduce computational complexity, we establish the theory of equivalence classes for pre-transformed polar codes. Codes within the same equivalence class share an identical weight distribution but correspond to different \emph{Expanded Information Set} sizes. By selecting the pre-transformation matrix that minimizes the \emph{Expanded Information Set} size within an equivalence class, we optimize the computation process. Numerical results demonstrate that the proposed method significantly reduces computational complexity compared to existing deterministic algorithms.

翻译：本文提出了一种基于奇偶一致性分解(PCD)的高效算法，用于确定预变换极化码的重量分布。首先，为处理预变换矩阵引入的比特依赖关系，我们提出了一种迭代算法来构建扩展信息集。通过将该集合中的信息比特扩展为0和1，我们消除了信息比特间的相关性，从而能够使用PCD方法递归计算汉明重量分布。其次，为进一步降低计算复杂度，我们建立了预变换极化码的等价类理论。同一等价类中的码字具有相同的重量分布，但对应不同的扩展信息集规模。通过选择等价类中最小化扩展信息集规模的预变换矩阵，我们优化了计算过程。数值结果表明，与现有确定性算法相比，所提方法显著降低了计算复杂度。