# Minimum-Distance Based Construction of Multi-Kernel Polar Codes

## TL;DR

This paper introduces a new construction method for multi-kernel polar codes that maximizes minimum distance, leading to improved short-length code performance over traditional density evolution-based designs.

## Contribution

It presents a minimum-distance based construction and a greedy algorithm for multi-kernel polar codes, enhancing error-rate performance especially for short codes.

## Key findings

- Improved error-rate performance over Arikan polar codes
- Effective for short code lengths with less polarization impact
- Introduces minimum-distance profile and greedy design algorithm

## Abstract

In this paper, we propose a construction for multi-kernel polar codes based on the maximization of the minimum distance. Compared to the original construction based on density evolution, our new design shows particular advantages for short code lengths, where the polarization effect has less impact on the performance than the distances of the code. We introduce and compute the minimum-distance profile and provide a simple greedy algorithm for the code design. Compared to state-of-the-art punctured or shortened Arikan polar codes, multi-kernel polar codes with our new design show significantly improved error-rate performance.