On the Weight Spectrum of Pre-Transformed Polar Codes
Abstract
Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels with efficient encoding and decoding algorithms. But the weight spectrum of Polar codes is relatively poor compared to RM codes, which degrades their ML performance. Pre-transformation with an upper-triangular matrix (including cyclic redundancy check (CRC), parity-check (PC) and polarization-adjusted convolutional (PAC) codes), improves weight spectrum while retaining polarization. In this paper, the weight spectrum of upper-triangular pre-transformed Polar Codes is mathematically analyzed. In particular, we focus on calculating the number of low-weight codewords due to their impact on error-correction performance. Simulation results verify the accuracy of the analysis.
Keywords
Cite
@article{arxiv.2102.12625,
title = {On the Weight Spectrum of Pre-Transformed Polar Codes},
author = {Yuan Li and Huazi Zhang and Rong Li and Jun Wang and Guiying Yan and Zhiming Ma},
journal= {arXiv preprint arXiv:2102.12625},
year = {2021}
}