Construction and Decoding Algorithms for for Polar Codes based on $2\times2$ Non-Binary Kernels

TL;DR

This paper explores the design and decoding of non-binary polar codes using $2\times2$ kernels over GF(q), introducing efficient algorithms that achieve near-optimal performance with reduced complexity.

Contribution

It proposes a method to select non-binary kernels for polar codes based on polarization effects and extends decoding algorithms to non-binary codes, including a low-complexity SCL decoder.

Findings

Decoders perform close to traditional SCL with lower complexity

Kernel selection via Monte-Carlo maximizes polarization effect

Extended BP and SC algorithms for non-binary polar codes

Abstract

Polar codes based on $2\times2$ non-binary kernels are discussed in this work. The kernel over $\text{GF}(q)$ is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive cancellation (SC) based decoding algorithms are extended to non-binary codes. Additionally, a successive cancellation list (SCL) decoding with a pruned tree is proposed. Simulation results show that the proposed decoder performs very close to a conventional SCL decoder with significantly lower complexity.