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 (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 (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 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.
The performance of the information reconciliation phase is crucial for quantum key distribution (QKD). Reverse reconciliation (RR) is typically preferred over direct reconciliation (DR) because it yields higher secure key rates. However, a significant challenge in continuous-variable (CV) QKD with discrete modulations (such as QAM) is that Alice lacks soft information about the symbol decisions made by Bob. This limitation restricts error correction to hard-decoding methods, with low reconciliation efficiency. This work introduces a reverse reconciliation softening (RRS) procedure designed for CV-QKD scenarios employing discrete modulations. This procedure generates a soft metric that Bob can share with Alice over a public channel, enabling her to perform soft-decoding error correction without disclosing any information to a potential eavesdropper. After detailing the RRS procedure, we investigate how the mutual information between Alice's and Bob's variables changes when the additional metric is shared. We show numerically that RRS improves the mutual information with respect to RR with hard decoding, practically achieving the same mutual information as DR with soft decoding. Finally, we test the proposed RRS for PAM-4 signalling with a rate 1/2 binary LDPC code and bit-wise decoding through numerical simulations, obtaining more than 1dB SNR improvement compared to hard-decoding RR.
In continuous-variable quantum key distribution, information reconciliation is required to extract a shared secret key from correlated random variables obtained through the quantum channel. Reverse reconciliation (RR) is generally preferred, since the eavesdropper has less information about Bob’s measurements than about Alice’s transmitted symbols. When discrete modulation formats are employed, however, soft information is available only at Bob’s side, while Alice has access only to hard information (her transmitted sequence). This forces her to rely on hard-decision decoding to recover Bob’s key. In this work, we introduce a novel RR technique for PAM (and QAM) in which Bob discloses a carefully designed soft metric to help Alice recover Bob’s key, while leaking no additional information about the key to an eavesdropper. We assess the performance of the proposed technique in terms of the achievable secret key rate (SKR) and its bounds, showing that the achievable SKR closely approaches the upper bound, with a significant gain over hard-decision RR. Finally, we implement the scheme at the coded level using binary LDPC codes with belief-propagation decoding, assess its bit-error rate through numerical simulations, compare the observed gain with theoretical predictions from the achievable SKR, and discuss the residual gap.