Binary Polarization Kernels from Code Decompositions

TL;DR

This paper introduces new binary polarization kernels derived from code decompositions, including non-linear kernels of dimensions 14 to 16, which achieve optimal error-correction performance and surpass previous kernels in polarization exponent.

Contribution

The paper presents a novel method of designing binary polarization kernels using code decompositions, achieving optimal asymptotic error-correction performance with non-linear kernels.

Findings

Non-linear kernels of dimensions 14, 15, and 16 constructed.

These kernels achieve a new upper bound on polarization exponents.

Kernels demonstrate improved polarization exponents over known kernels.

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.