Polar Codes and Their Quantum-Domain Counterparts

TL;DR

This paper surveys the development and implementation of polar codes, including their quantum counterparts, highlighting their capacity-achieving properties, decoding methods, and significance in modern communication systems like 5G.

Contribution

It provides a comprehensive overview of polar codes and introduces quantum polar codes, emphasizing their theoretical foundations and recent advancements.

Findings

Polar codes achieve Shannon capacity with low complexity.

Quantum polar codes extend classical concepts to quantum information.

Polar codes are integral to 5G communication standards.

Abstract

Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce competition to both the turbo as well as the Low Density Parity Check (LDPC) codes, making its way into the 5G New Radio (NR). Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the polar encoder, decoders as well as the code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndrome-based quantum polar codes.