Continuous-variable quantum key distribution (QKD) utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. An essential ingredient of the QKD protocol is highly efficient information reconciliation. To achieve highly efficient reconciliation, error-correcting codes with a low channel coding rate are inevitable in the most common schemes of multilevel coding and multistage decoding (MLC-MSD) and multidimensional reconciliation. Multiedge-type (MET) low-density parity-check (LDPC) codes are well suited for highly efficient reconciliation at low rates. Here, we calculate the optimal channel coding rates in the MLC-MSD scheme for reverse reconciliation, introduce the concept of generalized extrinsic information transfer charts for MET-LDPC codes, which constitute a simple and fast asymptotic analysis tool, and present a set of MET-LDPC codes with asymptotic efficiency >97% for channel coding rates 0.1, 0.05, 0.02, and 0.01. We believe that our codes will find wide application in implementations of continuous-variable quantum key distribution based on Gaussian modulation.
Bibliographical noteFunding Information:
This project has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 820466 (CiViQ). The authors thank the Quantum Innovation Center Qubiz funded by the Innovation Fund Denmark for support. H.M., T.G., and U.L.A. acknowledge support from the Danish National Research Foundation, Center for Macroscopic Quantum States (bigQ, DNRF142), and from Innovation Fund Denmark (CryptQ, 0175-00018B).