Multi-Kernel Construction of Polar Codes

TL;DR

This paper introduces a multi-kernel approach to construct binary polar codes with flexible lengths, achieving improved error performance and maintaining low encoding complexity, thus broadening practical applications.

Contribution

It presents a novel multi-kernel construction method for polar codes that allows for arbitrary block lengths and better error performance without increasing complexity.

Findings

Outperforms existing puncturing-based polar codes in error rate

Enables construction of polar codes with non-power-of-two lengths

Maintains low encoding complexity similar to original polar codes

Abstract

We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms stateof the-art constructions using puncturing methods.