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arXiv · 2410.19242

On the Weight Spectrum of Rate-Compatible Polar Codes

Zicheng Ye·Yuan Li·Zhichao Liu·Huazi Zhang·Jun Wang·Guiying Yan·Zhiming Ma
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Abstract

The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes remains elusive. In this paper, we address this gap by presenting the theoretical results for enumerating the number of minimum-weight codewords for quasi-uniform punctured, Wang-Liu shortened, and bit-reversal shortened decreasing polar codes. Additionally, we propose efficient algorithms for computing the average spectrum of random upper-triangular pre-transformed shortened and punctured polar codes. Notably, our algorithms operate with polynomial complexity relative to the code length. Simulation results affirm that our findings yield a precise estimation of the performance of rate-compatible polar codes.

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Zicheng Ye, Yuan Li, Zhichao Liu, Huazi Zhang, Jun Wang, Guiying Yan, Zhiming Ma. 2024-10-25. On the Weight Spectrum of Rate-Compatible Polar Codes. https://arxiv.org/abs/2410.19242

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