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Science China Information Sciences

Effective rate-adaptive reconciliation for CV-QKD using QC-MET-LDPC codes

Kun Zhang, Jia Hou, Xueqin Jiang, Jisheng Dai, Peng Huang, Guihua Zeng

Published Jul 4, 2025• 3 citations
Publisher
DOI
10.1007/s11432-024-4480-x

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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).
Abstract Non‐binary (NB) low‐density parity‐check (LDPC) codes over high‐order finite fields offer error‐correction performance closer to the Shannon limit while directly processing NB symbols, making them well‐suited for continuous‐variable quantum key distribution (CV‐QKD), which inherently involves high‐dimensional data. However, current CV‐QKD implementations have not been deeply researched in this area and still rely on binary error‐correcting codes, limiting the full exploitation of continuous‐variable information. Furthermore, the high sensitivity of CV‐QKD to signal‐to‐noise ratio (SNR) fluctuations renders fixed‐rate codes inadequate for practical channel variations. To address these issues, in this work an information reconciliation protocol is proposed based on rate‐adaptive NB LDPC codes. It not only leverages the advantages of using LDPC codes over NB fields, but also exploits their ability to directly correct NB symbols by incorporating rate‐adaptive techniques at both the symbol‐wise and bit‐wise granularity. Simulation results indicate that under identical conditions, reconciliation efficiency increases with field order, reaching 98.90% over Galois Field(GF)(64). In addition, both symbol‐wise and bit‐wise rate‐adaptive techniques extend the applicability of fixed‐rate NB LDPC codes, with the bit‐wise scheme consistently yielding higher secure‐key rates across all fields. Together, these techniques significantly enhance the efficiency and adaptability of CV‐QKD information reconciliation.
The information reconciliation (IR) stage is a critical component of post-processing in continuous-variable quantum key distribution (CV-QKD), which is essential to ensure high secret key rates and long transmission distances. Currently, improving reconciliation efficiency is a key research focus in the CV-QKD field. Additionally, the low-density parity-check (LDPC) decoding speed in IR is a post-processing bottleneck in high-speed CV-QKD. In this paper, we propose a construction scheme for spatially coupled (SC) LDPC codes in CV-QKD systems and maintain a constant code rate when extending the code length as required. Furthermore, we investigate the relationship between the syndrome variation pattern (SVP) and the frame error rate. Adaptively adjusting the number of decoding iterations according to the distinct convergence behaviors of the SVP, the convergence-based early termination (C-ET) scheme is proposed, which can reduce invalid iterations. The simulation results show that the proposed construction scheme for SC-LDPC codes can improve the reconciliation efficiency to 97% and achieve a flexible code length. The C-ET scheme achieves a 292% improvement in information throughput compared to the original ET scheme when the reconciliation efficiency reaches 97%. Moreover, the C-ET scheme also achieves a reduction in decoding latency compared to the existing syndrome-based early termination scheme. These advances provide a substantial step toward improving reconciliation efficiency and breaking the post-processing bottleneck in CV-QKD systems.