A Method to Reduce the Complexity of Computing the Complete Weight Distribution of Polar Codes
Information Theory
2024-10-24 v1 math.IT
Abstract
The code spectrum of polar codes is crucial to the performance of polar codes. Based on the lower-triangular affine group (LTA) of decreasing monomial codes and the one-variable descendance (ovd) relation, we define a new subgroup of LTA which can find more cosets with the same weight distribution. Using this algebraic structure, we further reduce the complexity by proofing the group action on a coset set is transitive. Our method is an enhanced version of previous research, and the complexity of most cases can be reduced exceeding several times.
Keywords
Cite
@article{arxiv.2410.17872,
title = {A Method to Reduce the Complexity of Computing the Complete Weight Distribution of Polar Codes},
author = {Zhichao Liu and Zhiming Ma and Guiying Yan},
journal= {arXiv preprint arXiv:2410.17872},
year = {2024}
}
Comments
9 pages, 3 tables