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Journal of Research of the National Institute of Standards and Technology

Polar Codes for Quantum Key Distribution

Anastase Nakassis

Published Dec 14, 2017• 7 citations
Publisher

Abstract

This paper addresses the performance of polar codes in the context of the quantum key distribution (QKD) protocol. It introduces the notion of an interactive polar decoder and studies its performance. The results demonstrate that the interactive decoder is efficient in the right environment and can be used to construct good classical polar codes efficiently.

DOI
10.6028/jres.122.042

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This paper addresses the performance of polar codes in the context of the quantum key distribution (QKD) protocol. It introduces the notion of an interactive polar decoder and studies its performance. The results demonstrate that the interactive decoder is efficient in the right environment and can be used to construct good classical polar codes efficiently.
Polar coding is the most recent encoding scheme in the quest for error correction codes that approaches the Shannon limit, has a simple structure, and admits fast decoders. As such, it is an interesting candidate for the quantum key distribution (QKD) protocol that normally operates at high bit error rates and requires codes that operate near the Shannon limit. This paper describes approaches that integrate Polar codes into the QKD environment and provides performance results of Polar code designs within the QKD protocol.
Information reconciliation is a critical process of any Quantum Key Distribution (QKD) protocol, where two legitimate parties agree on a secret key. Two parties attempt to eliminate the discrepancies between their correlated keys in the presence of an adversary, while revealing a minimum amount of information. In this paper, we propose a reconciliation protocol using polar codes with a soft-output decoder. We demonstrate that our method is better than a conventional protocol using polar codes in the view of reconciliation efficiency.
We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous variables quantum key distribution, their implementation on generic x86 Central Processing Units (CPUs) is practical. Thanks to recursive decoding, they exhibit excellent decoding speed, much higher than large, irregular Low Density Parity Check (LDPC) codes implemented on similar hardware, and competitive with implementations of the same codes on high-end Graphic Processing Units (GPUs).
Quantum Key Distribution (QKD) enables two parties to establish a common secret key that is information-theoretically secure by transmitting random bits that are encoded as qubits and sent over a quantum channel, followed by classical information processing steps known as information reconciliation and key extraction. Transmission of information over a quantum channel introduces errors that are generally considered to be due to the adversary's tempering with the quantum channel and needs to be corrected using classical communication over an (authenticated) public channel. Commonly used error-correcting codes in the context of QKD include cascade codes, low-density parity check (LDPC) codes, and more recently polar codes. In this work, we explore the applicability of designing of a polar code encoder based on a channel reliability sequence. We show that the reliability sequence can be derived and used to design an encoder independent of the choice of decoder. We then implement our design and evaluate its performance against previous implementations of polar code encoders for QKD as well as other typical error-correcting codes. A key advantage of our approach is the modular design which decouples the encoder and decoder design and allows independent optimization of each. Our work leads to more versatile polar code-based error reconciliation in QKD systems that would result in deployment in a broader range of scenarios.
Key reconciliation is important for practical Quantum key distribution (QKD) systems since it corrects the error bits in a key string by sacrificing some key bits. Therefore, its performance directly affects the secret key rate of a practical QKD system. Although key reconciliation scheme based on polar codes can achieve a high coding efficiency, the high frame error rate causes discarding key strings and decreases the secret key rate. In this paper, we fist analyze the limitation of successive cancellation decoding of polar codes, and then we propose an improved key reconciliation scheme using polar codes with successive cancellation list decoding and optimized coding structures, which can decrease the frame error probability, resulting in a higher secret key rate. Numerical results show that the proposed scheme can achieve a 12.8% higher secret key rate than the previous polar codes-based scheme with a code length of 216 bits and a quantum bit error rate of 2%. Besides, the proposed scheme is robust and it can extract secret key bits even when the quantum bit error rate reaches 10.2% with a code length of 220 bits and a coding efficiency of 90.6%.