A Search Method for Large Polarization Kernels

TL;DR

This paper introduces a novel search method for large polarization kernels that improves lower bounds on the maximum rate of polarization and enables low complexity processing, enhancing the performance of polar codes.

Contribution

The paper presents a new search algorithm combining depth-first search and search space reduction, significantly advancing kernel design for polar codes.

Findings

Improved lower bounds on polarization rates for kernels of size 17 to 27.

Designed kernels compatible with low complexity recursive trellis algorithms.

Numerical results show superior performance over shortened polar codes and small kernels.

Abstract

A new search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing depth-first search combined with some methods which reduce the search space. Using the proposed method, we improved almost all existing lower bounds on the maximum rate of polarization for kernels of size from 17 to 27. We also obtained kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results demonstrate the advantage of polar codes with the proposed kernels compared with shortened polar codes and polar codes with small kernels.