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Journal of Bioengineering, Technologies and Health

A Comprehensive Survey on LDPC Code Design for CV-QKD

Mauro Q. Nooblath Neto, Guilherme Vergne de Oliveira, Micael Andrade Dias, Nelson Alves Ferreira Neto, Francisco Revson Fernandes Pereira, Valéria Loureiro da Silva

Published Jul 8, 2026• 0 citations
Publisher

Abstract

Continuous-Variable Quantum Key Distribution (CV-QKD) represents a promising technology for secure communication, but its practical implementation heavily relies on highly efficient information reconciliation (IR) to extract a secret key from correlated quantum data shared over noisy channels. Low-density parity-check codes (LDPC) have emerged as the state-of-the-art solution for this task due to their capacity-approaching performance. However, designing LDPC codes that perform reliably in the very low signal-to-noise ratio (SNR) regime of CV-QKD, while preserving practical implementation complexity, remains a major challenge. This work presents a comprehensive survey of LDPC code design methodologies for CV-QKD, with particular emphasis on three key structural classes: Quasi-Cyclic (QC-LDPC), Multi-Edge Type (MET-LDPC), and their hybrid form (QC-MET-LDPC).

DOI
10.34178/jbth.v9i5.619

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Continuous-Variable Quantum Key Distribution (CV-QKD) represents a promising technology for secure communication, but its practical implementation heavily relies on highly efficient information reconciliation (IR) to extract a secret key from correlated quantum data shared over noisy channels. Low-density parity-check codes (LDPC) have emerged as the state-of-the-art solution for this task due to their capacity-approaching performance. However, designing LDPC codes that perform reliably in the very low signal-to-noise ratio (SNR) regime of CV-QKD, while preserving practical implementation complexity, remains a major challenge. This work presents a comprehensive survey of LDPC code design methodologies for CV-QKD, with particular emphasis on three key structural classes: Quasi-Cyclic (QC-LDPC), Multi-Edge Type (MET-LDPC), and their hybrid form (QC-MET-LDPC).
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.
Abstract In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.
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.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.
Due to the rapid development of quantum computing technology, encryption systems based on computational complexity are facing serious threats. Based on the fundamental theorem of quantum mechanics, continuous-variable quantum key distribution (CVQKD) has the property of physical absolute security and can effectively overcome the dependence of the current encryption system on the computational complexity. In this paper, we construct the spatially coupled (SC)-low-density parity-check (LDPC) codes and quasi-cyclic (QC)-LDPC codes by adopting the parity-check matrices of LDPC codes in the Advanced Television Systems Committee (ATSC) 3.0 standard as base matrices and introduce these codes for information reconciliation in the CVQKD system in order to improve the performance of reconciliation efficiency, and then make further improvements to final secret key rate and transmission distance. Simulation results show that the proposed LDPC codes can achieve reconciliation efficiency of higher than 0.96. Moreover, we can obtain a high final secret key rate and a long transmission distance through using our proposed LDPC codes for information reconciliation.
Abstract The speed at which two remote parties can exchange secret keys in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of key reconciliation. Multi-dimensional reconciliation using multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths has been shown to improve error-correction performance and extend the maximum reconciliation distance. We introduce a quasi-cyclic code construction for multi-edge codes that is highly suitable for hardware-accelerated decoding on a graphics processing unit (GPU). When combined with an 8-dimensional reconciliation scheme, our LDPC decoder achieves an information throughput of 7.16 Kbit/s on a single NVIDIA GeForce GTX 1080 GPU, at a maximum distance of 142 km with a secret key rate of 6.64 × 10−8 bits/pulse for a rate 0.02 code with block length of 106 bits. The LDPC codes presented in this work can be used to extend the previous maximum CV-QKD distance of 100 km to 142 km, while delivering up to 3.50× higher information throughput over the tight upper bound on secret key rate for a lossy channel.