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EPJ Quantum Technology

Block-metric-optimized rate-adaptive high-dimensional reconciliation for free-space CV-QKD

Nuerbiye Taiwaikuli, Ming Li, Yuxin Shen, Shengzhi Xu, Huimin Chen, Tianyi Wang, Milorad Cvijetić, Ziwen Pan

Published Oct 30, 2026• 0 citations
Publisher

Abstract

In free-space continuous-variable quantum key distribution (CV-QKD) systems, atmospheric turbulence induces time-varying fading, leading to random fluctuations in the signal-to-noise ratio (SNR). Consequently, rate-adaptive reconciliation becomes essential. This paper proposes a rate-adaptive high-dimensional reconciliation method based on Raptor-like LDPC codes. The proposed scheme achieves dynamic rate adaptation by leveraging a precomputed SNR threshold table. Furthermore, before adjusting the code length, the proposed method sorts high-dimensional vector blocks based on their norms, preferentially retaining blocks with higher signal power to bolster information reliability. Simulation results demonstrate that the proposed scheme outperforms the perforation and shortening (PS) method in terms of reconciliation efficiency and frame error rate, while maintaining decoding iterations below 100. Under random transmission rate samples, the optimized scheme achieves optimal secret key rate (SKR) performance and stability, validating its robustness and practicality in time-varying channels.

DOI
10.1140/epjqt/s40507-026-00590-z

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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.
In continuous-variable quantum key distribution (CV-QKD) systems, information reconciliation (IR) is a crucial step that significantly affects the secret key rate (SKR). The fixed-rate error-correcting codes used in IR are highly sensitive to changes in the signal-to-noise ratio (SNR) and cannot maintain a high reconciliation efficiency in practical CV-QKD systems. To address this issue, we first propose a rate-adaptive IR protocol, namely Threshold-based IR (TIR), which changes the code rate of low-density parity-check (LDPC) codes by selectively revealing bits with lower reliability and adjusting their log-likelihood ratios (LLRs). Then, we propose a rate-adaptive IR protocol, namely Sorting-based IR (SIR), which not only adjusts the code rate according to variations in SNR, but also enables the CV-QKD systems to achieve high reconciliation efficiency over a wide range of SNRs. Furthermore, we perform an analysis of the protocols in terms of code rate, reconciliation efficiency, and complexity. The simulation results demonstrate that the proposed protocols outperform other rate-adaptive IR protocols, achieving a reconciliation efficiency higher than 98.5% in the SNR range below -20 dB and maintaining a certain SKR in long-distance transmission.
In continuous-variable quantum key distribution (CV-QKD), the information reconciliation step plays a crucial role in ensuring the security and efficiency of the key exchange process. This paper investigates the use of heuristic and reinforcement learning-based methods to adaptively adjust the low-density parity check (LDPC) code rate in response to the time-varying channel signal-noise-ratio (SNR), with the goal of maximizing the final key rate. Leaving the SNR to fluctuate by ±1dB around a fixed value, we analyze the trade-off between the reconciliation efficiency and the frame error rate (FER). We propose a rate-adaptive reconciliation scheme that leverages reinforcement learning to select the optimal LDPC code rate, comparing its performance against traditional fixed-rate approaches. The results demonstrate that the proposed adaptive scheme significantly enhances the key rate and shows potential in applying for a wide range of SNR.
Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. We propose an efficient rate-adaptive reconciliation protocol suitable for practical CV-QKD systems with time-varying quantum channel. This protocol changes the code rate of multi-edge type low density parity check codes, by puncturing (increasing the code rate) and shortening (decreasing the code rate) techniques, to enlarge the correctable signal-to-noise ratios regime, thus improves the overall reconciliation efficiency comparing to the original fixed rate reconciliation protocol. We verify our rate-adaptive reconciliation protocol with three typical code rate, i.e., 0.1, 0.05 and 0.02, the reconciliation efficiency keep around 93.5%, 95.4% and 96.4% for different signal-to-noise ratios, which shows the potential of implementing high-performance CV-QKD systems using single code rate matrix.
Long block length rate-compatible low-density parity-compatible (LDPC) codes are designed to solve the problems of great variation of quantum channel noise and extremely low signal-to-noise ratio in continuous-variable quantum key distribution (CV-QKD). The existing rate-compatible methods for CV-QKD inevitably cost abundant hardware resources and waste secret key resources. In this paper, we propose a design rule of rate-compatible LDPC codes that can cover all potential SNRs with single check matrix. Based on this long block length LDPC code, we achieve high efficiency continuous-variable quantum key distribution information reconciliation with a reconciliation efficiency of 91.80% and we have higher hardware processing efficiency and lower frame error rate than other schemes. Our proposed LDPC code can obtain a high practical secret key rate and a long transmission distance in an extremely unstable channel.
Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use ofddd-dimensional reconciliation withd>8d > 8d>8to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.