Weight Structure of Low/High-Rate Polar Codes and Its Applications
CoRR(2024)
摘要
The structure of a linear block code is pivotal in defining fundamental
properties, particularly weight distribution, and code design. In this study,
we characterize the Type II structure of polar codewords with weights less than
twice the minimum weight w_min, utilizing the lower triangular affine (LTA)
transform. We present a closed-form formula for their enumeration. Leveraging
this structure and additionally characterizing the structure of weight
2w_min, we ascertain the complete weight distribution of low-rate and,
through the utilization of dual codes properties, high-rate polar codes,
subcodes of Reed–Muller (RM) codes, and RMxPolar codes. Furthermore, we
introduce a partial order based on the weight distribution and briefly explore
its properties and applications in code construction and analysis.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要