Binary Polarization Kernels from Code Decompositions
Information Theory
2015-03-09 v2 math.IT
Abstract
In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general non-linear. They provide a better polarization exponent than the previously known kernels of the same dimensions. In particular, non-linear kernels of dimensions 14, 15, and 16 are constructed and are shown to have optimal asymptotic error-correction performance. The optimality is proved by showing that the exponents of these kernels achieve a new upper bound that is developed in this paper.
Keywords
Cite
@article{arxiv.1410.8433,
title = {Binary Polarization Kernels from Code Decompositions},
author = {Noam Presman and Ofer Shapira and Simon Litsyn and Tuvi Etzion and Alexander Vardy},
journal= {arXiv preprint arXiv:1410.8433},
year = {2015}
}
Comments
The paper was accepted for publication in the Transactions on Information Theory. It can be considered as an extended version of "Binary Polar Code Kernels from Code Decompositions" arXiv:1101.0764