Binary Polarization Kernels From Code Decompositions

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

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general nonlinear. They provide a better polarization exponent than the previously known kernels of the same dimensions. In particular, nonlinear 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.

Original languageEnglish
Article number7055274
Pages (from-to)2227-2239
Number of pages13
JournalIEEE Transactions on Information Theory
Volume61
Issue number5
DOIs
StatePublished - 1 May 2015

Keywords

  • Polar codes
  • code decomposition
  • non-linear polar code kernels
  • rate of polarization

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