Shortened Polarization Kernels
Abstract
A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick elimination of unsuitable shortening patterns. The proposed algorithm is applied to some kernels of sizes 16 and 32 to obtain shortened kernels of sizes from 9 to 31. These kernels are used in mixed-kernel polar codes of various lengths. Numerical results demonstrate the advantage of polar codes with shortened large kernels compared with shortened and punctured Arikan polar codes, and polar codes with small kernels.
Keywords
Cite
@article{arxiv.2110.07351,
title = {Shortened Polarization Kernels},
author = {Grigorii Trofimiuk},
journal= {arXiv preprint arXiv:2110.07351},
year = {2021}
}
Comments
Accepted to IEEE GLOBECOM 2021 Workshop on Channel Coding beyond 5G. arXiv admin note: text overlap with arXiv:2101.10269