Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions With Maximum Exponents

@article{Lin2015LinearAN,
  title={Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions With Maximum Exponents},
  author={Hsien-Ping Lin and Shu Lin and Khaled A. S. Abdel-Ghaffar},
  journal={IEEE Transactions on Information Theory},
  year={2015},
  volume={61},
  pages={5253-5270}
}
Polar codes are constructed based on kernels with polarizing properties. The performance of a polar code is characterized asymptotically in terms of the exponent of its kernel. The pioneering work of Arıkan on polar codes is based on a linear kernel of dimension two and exponent 0.5. In this paper, constructions of linear and nonlinear binary kernels of dimensions up to 16 are presented. The kernels are obtained using computer search or by shortening longer kernels obtained by computer search… CONTINUE READING
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