Abstract In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol gives a reconciliation efficiency higher than 98.1% in the SNR below −20 dB and maintains a certain SKR in long-distance transmission.
Abstract In continuous-variable quantum key distribution systems, reconciliation is a crucial step that significantly affects the secret key rate (SKR). The rateless protocol based on Raptor codes can achieve high reconciliation efficiency at low signal-to-noise ratios (SNRs). However, the high complexity of low-density parity-check (LDPC) codes used for the precoding in Raptor codes limits the speed of reconciliation. In this paper, we propose an adaptive reconciliation protocol by modifying Raptor codes. The length of random binary sequences is increased because we remove the LDPC precoding that adds redundancy. The modified Raptor codes reduce the complexity of encoding with better performance. The proposed protocol gives a reconciliation efficiency higher than 98.1% in the SNR below −20 dB and maintains a certain SKR in long-distance transmission.
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 (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.
Discrete modulation continuous-variable quantum key distribution protocols are compatible with modern coherent optical communication technologies and devices. As a key part of the protocol, the performance of information reconciliation directly affects the secret key rate and transmission distance. Herein, we propose a reconciliation scheme for hard-decision strategy--based discrete modulation continuous-variable quantum key distribution protocol with eight-phase shift keying by combining slice reconciliation and raptor-like low-density parity-check (RL-LDPC) codes. We design the optimal binary sequence encoding of the discretized values of the receiver and sender, which reduce both the number of levels of error correction and the reconciliation complexity. In order to reduce the frame error rate, both the degree distribution and the size of the base matrix of RL-LDPC code is optimized. Simulation results show that the proposed scheme can reach reconciliation efficiencies of 92.05% and 93% with frame error rates of 6.2% and 11.7% at the signal-to-noise ratio of 0.15, respectively. At these points, the key rates can reach 0.0193 and 0.0195 bits/pulse, respectively.
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.
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.
Information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CVQKD) 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.