Convolutional Polar Kernels

TL;DR

This paper introduces convolutional polar kernels based on convolutional polar codes, providing a polynomial-time algorithm to compute their scaling exponents and polarization rates for kernels up to size 1024.

Contribution

It presents a new family of polarizing kernels and an efficient algorithm for analyzing their polarization properties, advancing the understanding of convolutional polar codes.

Findings

Scaling exponent and polarization rate computed for kernels up to size 1024.

Polynomial-complexity algorithm for weight spectrum analysis.

Convolutional polar kernels exhibit favorable polarization characteristics.

Abstract

A family of polarizing kernels is presented together with polynomial-complexity algorithm for computing scaling exponent. The proposed convolutional polar kernels are based on convolutional polar codes, also known as b-MERA codes. For these kernels, a polynomial-complexity algorithm is proposed to find weight spectrum of unrecoverable erasure patterns, needed for computing scaling exponent. As a result, we obtain scaling exponent and polarization rate for convolutional polar kernels of size up to 1024.