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Short-block polar coding based CV-QKD reconciliation

Dingzhao Wang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) offers an attractive route to information-theoretic secure communications using coherent detection and largely off-the-shelf telecommunication components. However, practical deployment remains constrained by the efficiency and reliability of information reconciliation in the low signal-to-noise ratio (SNR) regime, finite block-length effects, and the need to operate robustly under time-varying channels. This thesis addresses these challenges by developing short-block polar-coded reconciliation schemes, an adaptive incremental-redundancy hybrid automatic repeat request (IR-HARQ) framework tailored to CV-QKD, and a simultaneous quantum and classical communication (SQCC) architecture with joint classical--quantum optimization. Firstly, this thesis investigates polar codes as a finite-length alternative to conventional LDPC-based reconciliation. By constructing and evaluating a series of progressively enhanced reconciliation architectures, it is shown that short-block polar codes can provide improved block-error-rate (BLER) performance and higher reconciliation efficiency in the operating regime relevant to practical CV-QKD systems. The study further analyzes implementation trade-offs, including computational load distribution between Alice and Bob and the impact of decoder choices, identifying list decoding with moderate list sizes as an effective performance--complexity compromise. Secondly, to address channel variability and the sensitivity of fixed-rate reconciliation at low SNR, an IR-HARQ reconciliation protocol is proposed. Instead of committing to a single code rate, the protocol progressively reveals additional redundancy across retransmissions, effectively lowering the coding rate only when needed. A reliability-driven frozen-bit scheduling strategy is developed to maximize the error-correction benefit per disclosed bit under finite-length constraints, while ensuring that the resulting leakage is properly accounted for in privacy amplification. The proposed IR-HARQ design significantly improves reconciliation robustness and extends the achievable secure distance compared with one-shot fixed-rate baselines. Thirdly, this thesis considers SQCC, where classical data transmission and CV-QKD share the same physical link. A power-allocation model is established through the power ratio between the quantum and classical components, and the resulting classical and quantum error behaviors are characterized. By incorporating successive interference cancellation and forward error correction on both components, the proposed SQCC designs enable simultaneous classical throughput and secure key generation with controllable trade-offs among reliability, excess noise, and secret key rate. Overall, the thesis demonstrates that short-block polar coding, when combined with adaptive IR-HARQ and SQCC-aware receiver processing, provides a coherent framework for improving the practicality of CV-QKD under finite-length and time-varying conditions, thereby supporting more resource-efficient and deployable quantum-secured communication systems.

DOI
10.5258/soton/01/t024

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Continuous-variable quantum key distribution (CV-QKD) offers an attractive route to information-theoretic secure communications using coherent detection and largely off-the-shelf telecommunication components. However, practical deployment remains constrained by the efficiency and reliability of information reconciliation in the low signal-to-noise ratio (SNR) regime, finite block-length effects, and the need to operate robustly under time-varying channels. This thesis addresses these challenges by developing short-block polar-coded reconciliation schemes, an adaptive incremental-redundancy hybrid automatic repeat request (IR-HARQ) framework tailored to CV-QKD, and a simultaneous quantum and classical communication (SQCC) architecture with joint classical--quantum optimization. Firstly, this thesis investigates polar codes as a finite-length alternative to conventional LDPC-based reconciliation. By constructing and evaluating a series of progressively enhanced reconciliation architectures, it is shown that short-block polar codes can provide improved block-error-rate (BLER) performance and higher reconciliation efficiency in the operating regime relevant to practical CV-QKD systems. The study further analyzes implementation trade-offs, including computational load distribution between Alice and Bob and the impact of decoder choices, identifying list decoding with moderate list sizes as an effective performance--complexity compromise. Secondly, to address channel variability and the sensitivity of fixed-rate reconciliation at low SNR, an IR-HARQ reconciliation protocol is proposed. Instead of committing to a single code rate, the protocol progressively reveals additional redundancy across retransmissions, effectively lowering the coding rate only when needed. A reliability-driven frozen-bit scheduling strategy is developed to maximize the error-correction benefit per disclosed bit under finite-length constraints, while ensuring that the resulting leakage is properly accounted for in privacy amplification. The proposed IR-HARQ design significantly improves reconciliation robustness and extends the achievable secure distance compared with one-shot fixed-rate baselines. Thirdly, this thesis considers SQCC, where classical data transmission and CV-QKD share the same physical link. A power-allocation model is established through the power ratio between the quantum and classical components, and the resulting classical and quantum error behaviors are characterized. By incorporating successive interference cancellation and forward error correction on both components, the proposed SQCC designs enable simultaneous classical throughput and secure key generation with controllable trade-offs among reliability, excess noise, and secret key rate. Overall, the thesis demonstrates that short-block polar coding, when combined with adaptive IR-HARQ and SQCC-aware receiver processing, provides a coherent framework for improving the practicality of CV-QKD under finite-length and time-varying conditions, thereby supporting more resource-efficient and deployable quantum-secured communication systems.
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.
Continuous-variable quantum key distribution (CV-QKD) is a promising technique of supporting quantum-safe wireless networks in the emerging 6G era, mapping quantum information onto the amplitude or phase of electromagnetic waves. However, conventional CV-QKD reconciliation methods often assume ideal classical side-information channels, which is an unrealistic scenario in practical deployments. To address this critical challenge, we propose a novel protection scheme integrating Polar and low-density parity-check (LDPC) codes. Specifically, Polar codes safeguard quantum transmissions due to their superior performance for short block lengths, while LDPC codes robustly protect the classical side information exchanged over auxiliary classical channels. We further enhance the CV-QKD performance by harnessing a soft-decision Polar decoding method combined with protocols specifically tailored for reverse reconciliation (RR) and direct reconciliation (DR). In the RR scheme, conceived decoding complexity is strategically distributed: Polar decoding is performed by Alice, and LDPC decoding by Bob, hence significantly reducing the computational demands compared to traditional schemes where both decoding processes are invoked at a single node. Simulation results validate the effectiveness of our approach, demonstrating that Polar codes consistently outperform LDPC codes in quantum transmission scenarios having short block lengths under 512 bits. These findings emphasize the strong potential of Polar coding-assisted CV-QKD in achieving secure and efficient quantum-safe control information transmissions, paving the way for practical implementation in next-generation wireless networks.
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.
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.
Reconciliation is an essential procedure for continuous-variable quantum key distribution (CV-QKD). As the most commonly used reconciliation protocol in short-distance CV-QKD, the slice error correction (SEC) allows a system to distill more than 1 bit from each pulse. However, the quantization efficiency is greatly affected by the noisy channel with a low signal-to-noise ratio (SNR), which usually limits the secure distance to about 30 km. In this paper, an improved SEC protocol, named Rotated-SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for the quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. The experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99%, and maintain at around 96% even at the relatively low SNRs (0.5,1), which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with a block length of 16 Mb, the RSEC achieved a reconciliation efficiency of above 95%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieved a secret key rate of 7.83×10-3 bits/pulse at a distance of 33.93 km (the corresponding SNR value is 1). These results indicate that the proposed protocol significantly improves the performance of SEC and is a competitive reconciliation scheme for the CV-QKD system.
Reconciliation is an essential procedure for continuous-variable quantum key distribution (CV-QKD). As the most commonly used reconciliation protocol in short-distance CV-QKD, the slice error correction (SEC) allows a system to distill more than 1 bit from each pulse. However, its quantization efficiency is greatly affected by the noisy channel with a low signal-to-noise ratio (SNR), which usually limits the secure distance to about 30 km. In this paper, an improved SEC protocol, named Rotation-based SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. Experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99\%, and maintains at around 96\% even at the relatively low SNRs (0.5,1)(0.5,1)(0.5,1), which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with block length of 16 Mb, the RSEC can achieve a reconciliation efficiency of above 95\%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieve a secret key rate of 7.83×10−37.83\times10^{-3}7.83×10−3 bits/pulse at a distance of 33.93 km (the corresponding SNR value is 1). These results indicate that the proposed protocol significantly improves the performance of SEC and is a competitive reconciliation scheme for the CV-QKD system.