Efficient LDPC Decoding Algorithm Based On Continuous Variable Quantum Key Distribution

Today’s society has entered the information age, information reflects the value in circulation, but the circulation requires high efficiency and high quality. Classical cryptography plays a crucial role in information security, however, with the rapid development of modern computers, quantum computers come out. Quantum cryptography is a new discipline combining with quantum theory and classical cryptography, which is proved to be absolutely secure in the sense of information theory, Quantum Key Distribution (QKD) is an important branch of quantum cryptography. Currently, quantum key distribution protocol is divided into three protocols, they are discrete variable quantum key distribution (DV-QKD), continuous variable quantum key distribution (CV-QKD) and distributed phase reference (DPR-QKD).Reconciliation is an essential part of quantum key distribution, it can determine the presence of eavesdropping, correct a lot of communication in error, and achieve the key distilled by tightness enlarge. It is a protocol of correcting inconsistency in source and receiver which are transmitted by quantum channel, using classical communication technologies, so it belongs to the classical and quantum communication technology communication. Reconciliation is actually a channel coding problem, we choose a flexible check matrix, flexible rate low density parity check (LDPC) codes as error correcting codes of the whole system in this thesis.The main contents are as follows:In order to solve the problem of using conventional LDPC code encoding method for computer memory is difficult to bear by the increase of code length, we propose two efficient solutions:First, the reconciliation scheme differs from traditional parity bit decoding, it uses the syndrome decoding jointly produced by side information and the original data; Secondly, this solution forms a H matrix by sparse matrix storage, we use doubly cross-linked list only record the position of 1 to store H matrix of the LDPC, so can greatly save memory space, thus improving the timeliness and effectiveness of the coding.This thesis proposes a scheme that is discrete variables (i.e. single-photon) and Gaussian continuous variable QKD coordinated based on LDPC codes, continuous variable QKD is based on discrete variables. As for the problem of reconciliation of Gaussian quantum key distribution, Gaussian optimal continuous variables are quantified to achieve the maximum mutual information between Alice and Bob. On the basis of the sliced error correction (SEC) protocol and multi-level encoding/decoding multi-level (MLC/MSD) protocol, uses LDPC codes as each stream level’s error correction codes, and releases an inter-stage iterative update formula of the hard information to participate in MSD decoding algorithm.On a server with 2.4GHz CPU and 32G memory, for the discrete variables scheme, the best code length of this experiment is 105, whose BER is converged at 1.0dB, it only spends 4 seconds to decode one block, the code rate can reach to 24.85 kbits/s when the codeword is converged. For the Gaussian continuous variables scheme, simulation results show that the proposed algorithm can reconcile reliably 2×105 continuous quantum variables when SNR of the receiver is above 4.9 dB, with the reconciliation efficiency of 91.71%, the amount of the security key reaches 8.645 kbits/s.