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Quantum Key Reconciliation for Satellite-Based Communications

Xiaoyu Ai, Robert Malaney, Soon Xin Ng

Published Dec 1, 2018• 4 citations
Publisher

Abstract

Quantum Key Distribution (QKD) has been regarded as a novel approach to establish a secure communication between two legitimate partners. With the recent success of space based experimental QKD systems, researchers are now focussing on implementing more practical and efficient QKD systems that meet the challenges faced in space-based implementations. One pressing problem is the need for efficient and easy to implement reconciliation schemes for practical QKD systems. Rate-adaptive schemes based on LDPC codes constitute an appealing implementation of the key reconciliation process since they cover the entire range of the channel parameter space with a limited set of pre-defined Mother codes. In this paper, we investigate in detail some rate- adaptive reconciliation schemes based on LDPC codes, illustrating how their performance compares to other set-ups in which fixed-rate non- adaptive LDPC codes optimised for different channel conditions are adopted. In particular, the impact rate-adaptive codes have on decoding complexity, and subsequently the overall secure key throughput, is quantified through full blown simulations of an entanglement-based version of the QKD protocol within the context of an entanglement source onboard a satellite. Our work highlights that even though rate adaptive schemes schemes for QKD reconciliation appear ideal for future space-based implementations of single- photon QKD, identification of ideal Mother codes for such schemes remains to be resolved.

DOI
10.1109/glocom.2018.8647658

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Quantum Key Distribution (QKD) has been regarded as a novel approach to establish a secure communication between two legitimate partners. With the recent success of space based experimental QKD systems, researchers are now focussing on implementing more practical and efficient QKD systems that meet the challenges faced in space-based implementations. One pressing problem is the need for efficient and easy to implement reconciliation schemes for practical QKD systems. Rate-adaptive schemes based on LDPC codes constitute an appealing implementation of the key reconciliation process since they cover the entire range of the channel parameter space with a limited set of pre-defined Mother codes. In this paper, we investigate in detail some rate- adaptive reconciliation schemes based on LDPC codes, illustrating how their performance compares to other set-ups in which fixed-rate non- adaptive LDPC codes optimised for different channel conditions are adopted. In particular, the impact rate-adaptive codes have on decoding complexity, and subsequently the overall secure key throughput, is quantified through full blown simulations of an entanglement-based version of the QKD protocol within the context of an entanglement source onboard a satellite. Our work highlights that even though rate adaptive schemes schemes for QKD reconciliation appear ideal for future space-based implementations of single- photon QKD, identification of ideal Mother codes for such schemes remains to be resolved.
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.
Quantum key distribution (QKD) relies on information reconciliation to determine transmission distance and secure key rate. Existing schemes (e.g., Cascade) demand costly multiround interaction, while binary LDPC-based methods suffer limited error correction capability. This work proposes a QKD reconciliation scheme using non-binary (NB) LDPC codes, combined with a rate-adaptive technique tailored to NB LDPC characteristics. Simulations show NB LDPC codes outperform binary counterparts in error correction performance and reconciliation efficiency-with gains increasing with finite field order, achieving 1.0661 over the finite field GF(128). The rate-adaptive technique extends fixed-rate code applicability, alleviating practical code construction and storage challenges.
In continuous-variable (CV) quantum key distribution (QKD), the reconciliation efficiency and frame error rate of the information reconciliation have a significant impact on the secret key rate. For a fixed-rate multiedge-type low-density parity-check (LDPC) code, the reconciliation efficiency and frame error rate will inevitably vary due to the fluctuations of the signal-to-noise ratio (SNR) of the CV QKD system, which degrades the performance of the system. We propose a high-efficiency rate-adaptive information reconciliation scheme by combining raptorlike (RL) LDPC codes with the addition of trusted noises. We establish the model of adding trusted noises and combine it with the RL LDPC codes to optimize the secret key rate under the time-varying channel. The simulation results show that our scheme can maintain a high reconciliation efficiency of more than 94.4% and a low frame error rate within 15% fluctuation range of the SNR. Furthermore, we implement the hardware acceleration of the proposed rate-adaptive scheme on a graphics processing unit and achieve a decoding throughput of 65.5 Mbits/s by optimizing the storage of the parity-check matrix. Our results are useful for the practical CV QKD under the realistic time-varying channel.
Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an easily implemented but efficiently rate-adaptive LDPC coding approach of reconciliation, different from the previously proposed puncturing- and shortening-based approach. We also give a measure for choosing the optimal LDPC parameter for our rate-adaptive approach according to error rates.
In this paper, a rate-adaptive method is proposed an alternative reconciliation protocol by employing the LDPC-accumulate codes to the practical implementation in the quantum key distribution (QKD). The proposed rate-adaptive reconciliation is adapted in the Slepian-Wolf scheme where specific low-density parity-check (LDPC) codes are constructed by accumulated syndrome encoding/decoding. Its objective is to skip the step of quantum bit error rate (QBER) estimation by the traditional key sampling that increases the final secret key length in practice. From the numerical results, the proposed method achieves a good performance in terms of the number of disclosed bits and reconciliation efficiency comparable to the conventional Winnow, Cascade, and fixed-rate compatible LDPC based protocols. Moreover, it can cover the possible cases of error rates in the QKD system. Therefore, method is suitable for the highspeed discrete-variable QKD applications.
A significant breakthrough in space-based quantum key distribution (QKD) inaugurated by the Micius satellite has brought us closer to the era of global QKD networks. An essential step in the post-processing QKD is key reconciliation (KR), which eliminates the mismatch in the raw keys between two legitimate users. However, the fluctuation in the quantum bit-error rate (QBER) caused by the free-space optical (FSO) turbulence channels poses various challenges for the KR design. This paper addresses the design of blind KR schemes for FSO-based low Earth orbit (LEO) satellite QKD systems, which allow operating without a prior QBER estimation. Specifically, we present a novel blind KR scheme with a protograph low-density parity check (LDPC) code extension. The proposed LDPC structure is constructed by gradually extending and exhaustively searching among all possible solutions. The proposed design is evaluated in terms of the final key rate performance over the QKD systems using a dual-threshold/direct detection (DT/DD) scheme. Simulation results confirm the effectiveness of our proposed design compared to the state-of-the-art design in different turbulence channel conditions.