Binary Polarization Kernels from Code Decompositions

Noam Presman; Ofer Shapira; Simon Litsyn; Tuvi Etzion; Alexander Vardy

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arXiv · 1410.8433

Binary Polarization Kernels from Code Decompositions

Noam Presman·Ofer Shapira·Simon Litsyn·Tuvi Etzion·Alexander Vardy

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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.

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Noam Presman, Ofer Shapira, Simon Litsyn, Tuvi Etzion, Alexander Vardy. 2014-10-30. Binary Polarization Kernels from Code Decompositions. https://arxiv.org/abs/1410.8433

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