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Entropy

RC-LDPC-Polar Codes for Information Reconciliation in Continuous-Variable Quantum Key Distribution

Fei Hua, Kun Chen, Wei Deng, Jing Cheng, Banghong Guo, Huanwen Xie

Published Sep 29, 2025• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution faces significant challenges, including quantum channel instability, particularly fluctuations in the signal-to-noise ratio (SNR) and extremely low SNR scenarios. Furthermore, non-ideal polar codes, characterized by insufficient polarization in finite-length regimes, can lead to some sub-channels being neither completely noise-free nor fully noise-dominated. This phenomenon limits the error correction capability when such codes are applied to information reconciliation. To address these challenges, we propose a novel RC-LDPC-Polar code for the CV-QKD reconciliation algorithm. We combine the error resilience of LDPC codes with the efficiency advantages of polar coding. This scheme supports adaptive rate adjustment across varying SNR conditions. Our simulation experiments demonstrate that the RC-LDPC-Polar concatenated coding scheme achieves a lower error rate under varying SNR conditions. Meanwhile, the proposed scheme achieves a higher final key rate and a longer transmission distance.

DOI
10.3390/e27101025

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Continuous-variable quantum key distribution faces significant challenges, including quantum channel instability, particularly fluctuations in the signal-to-noise ratio (SNR) and extremely low SNR scenarios. Furthermore, non-ideal polar codes, characterized by insufficient polarization in finite-length regimes, can lead to some sub-channels being neither completely noise-free nor fully noise-dominated. This phenomenon limits the error correction capability when such codes are applied to information reconciliation. To address these challenges, we propose a novel RC-LDPC-Polar code for the CV-QKD reconciliation algorithm. We combine the error resilience of LDPC codes with the efficiency advantages of polar coding. This scheme supports adaptive rate adjustment across varying SNR conditions. Our simulation experiments demonstrate that the RC-LDPC-Polar concatenated coding scheme achieves a lower error rate under varying SNR conditions. Meanwhile, the proposed scheme achieves a higher final key rate and a longer transmission distance.
Abstract The error correction of information reconciliation affects the performance of the continuous-variable quantum key distribution (CV-QKD). Polar codes can be strictly proven to reach the Shannon-limit. However, due to the insufficient polarization of finite code-length, partial subchannels are neither completely noise-free nor completely noisy. In this paper, an intermediate channel low-density parity check code concatenated polar code (IC-LDPC Polar codes)-based reconciliation for CV-QKD is proposed for the above shortcomings. The experimental results show that the reconciliation efficiency of IC-LDPC Polar code can be over 98% when the signal-to-noise ratio is from −13.2 dB to −20.8 dB, the secret keys can be extracted, and the minimum frame error rate (FER) is 0.19. Therefore, the proposed scheme can improve the reconciliation efficiency and reduce the FER at a very low signal-to-noise ratio range, and it is more useful for a practical long-distance CV-QKD system.
Continuous-variable quantum key distribution (CV-QKD) systems face challenges in maintaining efficient reconciliation over long distances due to the time variant signal-to-noise ratio (SNR) imposed by channel quality fluctuations. Hence fixed-rate error-correction schemes using low-density parity-check (LDPC) or Polar codes lead to high block-error rates (BLER) and degraded secret key rates (SKR). To overcome this, we propose an incremental redundancy aided hybrid automatic repeat request (IR-HARQ) protocol using rate-compatible Polar and LDPC codes. Explicitly, by puncturing a mother code and progressively transmitting additional redundant bits, our method dynamically adapts the effective coding rate to the prevalent channel conditions, achieving 2–3 dB SNR gains per retransmission. This adaptive strategy avoids unnecessary redundancy in good channels and strengthens protection in poor channels, thereby improving reconciliation efficiency. Simulation results show that our IR-HARQ scheme significantly enhances the BLER, throughput, and secure transmission distance compared with single-transmission schemes. Moreover, our study highlights that Polar IR-HARQ achieves superior performance in short block-length and low-SNR scenarios, while LDPC IR-HARQ is more competitive for longer codes and higher SNR. These findings confirm IR-HARQ as an attractive and versatile reconciliation solution for real-world CV-QKD deployments.
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.
Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.
Information reconciliation significantly impacts the performance of the practical continuous-variable quantum key distribution (CV QKD) system. Fixed-rate error-correction codes limit the potential applications of the CV QKD because they lead to reduced reconciliation efficiency when the signal-to-noise ratio of the quantum channel changes, further deteriorating the system's performance. Therefore, we propose a rate-adaptive polar-coding-based reconciliation scheme for practical CV QKD systems with the time-variant quantum channel. Experimental results verify that the proposed scheme can successfully extract secret keys within the range of signal-to-noise ratios from $\ensuremath{-}0.5$ to $\ensuremath{-}4.5$ dB, and the minimum frame-error rate can be less than ${10}^{\ensuremath{-}3}$. Moreover, the proposed scheme can promote the application of the CV QKD system in a realistic environment.
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.