混合核极化码的陪集码谱

On the Coset Weight Spectrum of Multi-Kernel Polar Codes

极化码是信道编码领域的一项重大进展,通过高效的编码和解码算法实现了二进制输入离散记忆无失真信道(B-DMC)的对称容量。在极化码中,零陪集和一陪集之间的最小汉明距离以及重量谱与在第i个阶段的SCL解码中的路径度量惩罚密切相关。本文提出了一种概率方法,构造一个新的生成矩阵,这个生成矩阵是上三角的,并且上三角元素随机,一次来生成遍历全部陪集的一个码本,以此为基础,计算出了针对二阶核、三阶核和多核的陪集码谱的概率表达式。

Polar codes are a significant advancement in the field of channel coding, achieving the symmetric capacity of binary-input discrete memoryless channels (B-DMC) through efficient encoding and decoding algorithms. In polar codes, the minimum Hamming distance between the zero and one cosets, as well as the weight spectrum, are closely related to the path metric in SCL decoding at the i-th stage. This study first demonstrates the relationship between the coset weight spectrum and the error probability of decoding, highlighting the importance of computing the coset weight spectrum.