Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Space Optics (ICSO)

Study on application of polar codes to information reconciliation in free-space quantum key distribution

Yuma Yamashita, Hiroyuki Endo, Shingo Fujita, Eiji Okamoto, Hideki Takenaka, Morio Toyoshima

Published Jun 11, 2021• 0 citations
Publisher

Abstract

Quantum key distribution (QKD) is a technology to securely share keys against any attack physically permitted, with the principle of quantum mechanics. In recent years, the satellite QKD, which employs artificial satellites as trusted mobile nodes, has been attracting attention in order to overcome the bottleneck of transmission distance. However, in the satellite QKD, quality degradation due to atmospheric effects is expected, as in ordinary satellite laser communications. Therefore, it is desirable to apply an error-correcting code (ECC) that has high error-correcting performance even under the atmospheric-induced effects to the error-correcting process of the satellite QKD. Therefore, in this paper, we examined the application of polar codes, which is known as an ECC with high error correction capability. First, in order to optimize the error correction efficiency, we propose a method to adaptively obtain an appropriate code rate for the received signal strength that changes momentarily due to atmospheric effects. Then, we compare the throughput performances with polar codes to it with low-density parity-check (LDPC) codes, with the numerical simulation assuming Bennett-Brassard 1984 protocol (BB84).

DOI
10.1117/12.2599964

Related papers

A reconciliation protocol with delayed error correction for quantum key distribution

Shengmei Zhao, Peng Jia Shi, Hong XIAO

A delayed error-correction (EC) reconciliation protocol for quantum key distribution (QKD) is proposed in the paper, where the error correction operation is operated after the messages have been transmitted. There are two advantages of the proposed protocol. First, it is possible for the two nodes without a direct quantum link to share secret keys, when the two nodes are separately connected to a common trusted relay in the QKD network. Besides, the reconciliation protocol with the delayed EC also simplifies the whole reconciliation process. It corrects both errors caused by communications during QKD process and that inherent in message bits. The key generation rate of the delayed EC protocol is presented. Finally, the bit error rate of the proposed protocol is analyzed when using polar codes as the error correction codes. The results show that the performance of the delayed EC reconciliation protocol with polar codes were better than those using low-density parity check code.

Scientia Sinica Technologica•Aug 1, 2015•0 citations

One-way information reconciliation schemes of quantum key distribution

Li Yang, Hua Dong, Li Zhao

With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.

Cybersecurity•May 22, 2019•10 citations

Flexible polar encoding for information reconciliation in QKD

Snehasis Addy, Sabyasachi Dutta, Somnath Panja +3 more

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.

arXiv:2312.03100•Nov 30, 2023•0 citations

An Analysis of Error Reconciliation Protocols for use in Quantum Key Distribution

James Samuel Johnson

Abstract : Quantum Key Distribution (QKD) is a method for transmitting a cryptographic key between a sender and receiver in a theoretically unconditionally secure way. Unfortunately, the present state of technology prohibits the flawless quantum transmission required to make QKD a reality. For this reason, error reconciliation protocols have been developed which preserve security while allowing a sender and receiver to reconcile the errors in their respective keys. The most famous of these protocols is Brassard and Salvail's Cascade, which is effective, but suffers from a high communication complexity and therefore results in low throughput. Another popular option is Buttler's Winnow protocol, which reduces the communication complexity over Cascade, but has the added detriment of introducing errors, and has been shown to be less effective than Cascade. Finally, Gallager's Low Density Parity Check (LDPC) codes have recently been shown to reconcile errors at rates higher than those of Cascade and Winnow with a large reduction in communication, but with greater computational complexity. This research seeks to evaluate the effectiveness of these LDPC codes in a QKD setting, while comparing real-world parameters such as runtime, throughput and communication complexity empirically with the well-known Cascade and Winnow algorithms. Additionally, the effects of inaccurate error estimation, non-uniform error distribution and varying key length on all three protocols are evaluated for identical input key strings. Analyses are performed on the results in order to characterize the performance of all three protocols and determine the strengths and weaknesses of each.

•Feb 1, 2012•8 citations

Key Reconciliation with RC-LDPC/Error Estimation for Satellite-based FSO/QKD Systems

Cuong T. Nguyen, Hoang D. Le, Anshul Jaiswal +2 more

Satellite-based free-space optics (FSO) quantum key distribution (QKD) systems have recently attracted significant research interest due to their potential to enable globally secured applications. However, the inherent uncertainty of FSO channels, caused by weather conditions and satellite mobility, induces severe fluctuations in quantum bit-error rate (QBER) between legitimate users. This makes designing an efficient key reconciliation, an essential step in the QKD post-processing, particularly challenging. In this work, we propose a key reconciliation scheme that combines protograph rate-compatible (RC) low-density parity-check (LDPC) codes with a syndrome-based error estimation method. The proposed error estimation method reduces the number of communication rounds without requiring additional information disclosure. Furthermore, to our best knowledge, an analytical framework is first developed to evaluate end-to-end secret-key throughput (SKT), accounting for the impact of imperfect error estimation and dynamic FSO channel conditions. Numerical results demonstrate that the proposed scheme consistently outperforms conventional blind reconciliation under diverse FSO channel conditions and provide practical guidelines for system parameter selection. Finally, we validate the proposed framework through a case study that incorporates data from a Starlink low-Earth orbit (LEO) satellite and moving ground vehicles.

arXiv:2609.25646•IEEE Transactions on Vehicular Technology•Jan 1, 2026•0 citations

Application of Adaptive Polar Code based CV-QKD Scheme for LEO Satellite Systems

Qiang Wang, Thara Son, Meixiang Zhang +1 more

The information reconciliation protocol plays a crucial role in achieving a high secret key rate in continuous variable quantum key distribution (CV-QKD) systems. It is closely intertwined with a forward error correction scheme. In systems that operate under dynamic channel conditions, such as low earth orbit (LEO) satellite systems, the utilization of an adaptive reconciliation protocol becomes essential to ensure efficiency. This necessity calls for an efficient rate-adaptive forward error correction scheme, encompassing a single encoder and decoder. This paper provides a comprehensive review of adaptive information reconciliation schemes utilizing polar codes. It also explores their application to LEO satellite systems.

International Conference on Information and Communication Technology Convergence (ICTC)•Oct 11, 2023•1 citation
Quantum key distribution (QKD) is a technology to securely share keys against any attack physically permitted, with the principle of quantum mechanics. In recent years, the satellite QKD, which employs artificial satellites as trusted mobile nodes, has been attracting attention in order to overcome the bottleneck of transmission distance. However, in the satellite QKD, quality degradation due to atmospheric effects is expected, as in ordinary satellite laser communications. Therefore, it is desirable to apply an error-correcting code (ECC) that has high error-correcting performance even under the atmospheric-induced effects to the error-correcting process of the satellite QKD. Therefore, in this paper, we examined the application of polar codes, which is known as an ECC with high error correction capability. First, in order to optimize the error correction efficiency, we propose a method to adaptively obtain an appropriate code rate for the received signal strength that changes momentarily due to atmospheric effects. Then, we compare the throughput performances with polar codes to it with low-density parity-check (LDPC) codes, with the numerical simulation assuming Bennett-Brassard 1984 protocol (BB84).
A delayed error-correction (EC) reconciliation protocol for quantum key distribution (QKD) is proposed in the paper, where the error correction operation is operated after the messages have been transmitted. There are two advantages of the proposed protocol. First, it is possible for the two nodes without a direct quantum link to share secret keys, when the two nodes are separately connected to a common trusted relay in the QKD network. Besides, the reconciliation protocol with the delayed EC also simplifies the whole reconciliation process. It corrects both errors caused by communications during QKD process and that inherent in message bits. The key generation rate of the delayed EC protocol is presented. Finally, the bit error rate of the proposed protocol is analyzed when using polar codes as the error correction codes. The results show that the performance of the delayed EC reconciliation protocol with polar codes were better than those using low-density parity check code.
With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.
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.
Abstract : Quantum Key Distribution (QKD) is a method for transmitting a cryptographic key between a sender and receiver in a theoretically unconditionally secure way. Unfortunately, the present state of technology prohibits the flawless quantum transmission required to make QKD a reality. For this reason, error reconciliation protocols have been developed which preserve security while allowing a sender and receiver to reconcile the errors in their respective keys. The most famous of these protocols is Brassard and Salvail's Cascade, which is effective, but suffers from a high communication complexity and therefore results in low throughput. Another popular option is Buttler's Winnow protocol, which reduces the communication complexity over Cascade, but has the added detriment of introducing errors, and has been shown to be less effective than Cascade. Finally, Gallager's Low Density Parity Check (LDPC) codes have recently been shown to reconcile errors at rates higher than those of Cascade and Winnow with a large reduction in communication, but with greater computational complexity. This research seeks to evaluate the effectiveness of these LDPC codes in a QKD setting, while comparing real-world parameters such as runtime, throughput and communication complexity empirically with the well-known Cascade and Winnow algorithms. Additionally, the effects of inaccurate error estimation, non-uniform error distribution and varying key length on all three protocols are evaluated for identical input key strings. Analyses are performed on the results in order to characterize the performance of all three protocols and determine the strengths and weaknesses of each.
Satellite-based free-space optics (FSO) quantum key distribution (QKD) systems have recently attracted significant research interest due to their potential to enable globally secured applications. However, the inherent uncertainty of FSO channels, caused by weather conditions and satellite mobility, induces severe fluctuations in quantum bit-error rate (QBER) between legitimate users. This makes designing an efficient key reconciliation, an essential step in the QKD post-processing, particularly challenging. In this work, we propose a key reconciliation scheme that combines protograph rate-compatible (RC) low-density parity-check (LDPC) codes with a syndrome-based error estimation method. The proposed error estimation method reduces the number of communication rounds without requiring additional information disclosure. Furthermore, to our best knowledge, an analytical framework is first developed to evaluate end-to-end secret-key throughput (SKT), accounting for the impact of imperfect error estimation and dynamic FSO channel conditions. Numerical results demonstrate that the proposed scheme consistently outperforms conventional blind reconciliation under diverse FSO channel conditions and provide practical guidelines for system parameter selection. Finally, we validate the proposed framework through a case study that incorporates data from a Starlink low-Earth orbit (LEO) satellite and moving ground vehicles.
The information reconciliation protocol plays a crucial role in achieving a high secret key rate in continuous variable quantum key distribution (CV-QKD) systems. It is closely intertwined with a forward error correction scheme. In systems that operate under dynamic channel conditions, such as low earth orbit (LEO) satellite systems, the utilization of an adaptive reconciliation protocol becomes essential to ensure efficiency. This necessity calls for an efficient rate-adaptive forward error correction scheme, encompassing a single encoder and decoder. This paper provides a comprehensive review of adaptive information reconciliation schemes utilizing polar codes. It also explores their application to LEO satellite systems.