Multi-Kernel Polar Codes: Proof of Polarization and Error Exponents

TL;DR

This paper introduces multi-kernel polar codes, proves their polarization property, and analyzes their convergence rates, expanding the theoretical understanding of polar code constructions.

Contribution

It provides a new proof of polarization for multi-kernel polar codes and establishes conditions under which they polarize, along with their convergence rate analysis.

Findings

Multi-kernel polar codes polarize under certain conditions.

The convergence rate of multi-kernel codes relates to that of individual kernels.

A generalized proof of polarization for complex kernel constructions.

Abstract

In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient conditions for kernels to polarize. Finally, we derive the convergence rate of the multi-kernel construction and relate it to the convergence rate of each of the constituent kernels.