Reconciliation Of A Quantum-Distributed Gaussian Key Based On LDPC Codes

QKD(Quantum Key Distribution) has been considered one of the rapid development area of cryptographic communication field in two decades. Contrast with the classical key distribution which the security of the distributed key is based on math problems and computational complexity, QKD uses basic quantum principle such as "The Uncertainty Principle","The Quantum No-cloning Theorem"and other physical properties to provide absolute security. Depends on the information carrier QKD could be divided into Discrete variable Quantum Key Distribution (DQKD) and continuous variable Quantum Key Distribution(CVQKD). DQKD is developed earlier and it uses single-photon as the information carrier, CVQKD which uses coherent state light source and the homodyne detector has a better performance than DQKD because the lower efficiency of light source and detection. So far, CVQKD has become one of the research hotspots in quantum communication field.Data reconciliation is one important step in quantum key distribution process, after the quantum channel data transmission, Alice and Bob need to remove the errors introduced by the eavesdropper or channel noise through a data reconciliation agreement, in essence, an error correction process. At the same time Data reconciliation could be seen as an asymmetrically distributed source coding process, by compression one source and combine the other one for a joint decoding to obtain a common sequence. So the coding process need a channel code to compress source sequence. LDPC for its flexibility of parity check matrix construction, fast decoding and adjustable code rate could be a good component codes of the data reconciliation.We firstly viewing the essence of the reverse data reconciliation in QKD a source coding/decoding process which is a Slepian-Wolf model in information theory. This paper uses the Sliced Error Correction (SEC), Multi-Level Coding (MLC) and Multi-Stage Decoding scheme (MSD) for this special case of CVQKD to establish a Reverse Reconciliation model, the optimal quantization interval of continuous variables is showed, and gives extrinsic and intrinsic, hard and soft information concept. Export a level information iterative decoding formula of MSD, coding rate at all levels was given by experiment results. This algorithm experimentally determined the minimum SNR requirements, experimental results show that the efficiency of the reconciliation reached92.3%.