Research On Information Reconciliation Algorithm For Continuous Variable Quantum Key Distribution

With the flourishing of science and technology,information security has gradually attracted great attention.Quantum Key Distribution(QKD)is based on several basic quantum mechanical properties such as the inability of exact replication of unknown quantum states,superposition and entanglement of quantum states to make up for the shortcomings of traditional cryptography that cannot achieve unconditional secure key distribution,and therefore has received much attention and research from scholars.The quantum key distribution has received a lot of attention from scholars and has been studied.Currently,there are two protocols for generating symmetric keys through quantum channels,namely,Discrete Variable Quantum Key Distribution(DV-QKD)and Continuous Variable Quantum Key Distribution(CV-QKD).Both DV-QKD and CV-QKD protocols involve the following four processes:(1)quantum transmission over a private quantum channel,(2)filtering the measured quantum state according to the measurement basis,(3)reconciliation over a presumed noise-free public channel,and(4)privacy amplification through a hash function.In CV-QKD,the purpose of information reconciliation is to correct the asymmetric key due to eavesdropping party interference and quantum channel noise.The reconciliation efficiency and Frame Error Rate(FER)of the error correction code used in the whole process are two parameters that determine the final key rate and the maximum transmission distance of the quantum key distribution system.The most widely used is the Multi-Edge Type Low-Density Parity-Check(MET-LDPC)code.By designing the check matrix and optimizing the decoding algorithm,the information reconciliation with MET-LDPC code can achieve high reconciliation efficiency and system throughput with very low signal-to-noise ratio.However,MET-LDPC codes need to design extremely complex check matrices for different SNR ranges in order to adapt to fluctuating quantum channels,and the performance can be drastically reduced with small changes in SNR.In this paper,to address this problem,we investigated the information reconciliation algorithm of CV-QKD,and improve the information reconciliation algorithm of error correction codes with no fixed code rate to avoid the drawbacks of MET-LDPC,and the main work of this paper is as follows:(1)The investigation of the performance of Raptor codes without fixed code rate under low SNR.Raptor codes,as the codes without fixed code rate,guarantee the false frame rate of all data frames must be 0 by continuously sending the coding information until the decoder can successfully decode them.Therefore,the Raptor codes are firstly investigated in the Binary Input Additive White Gaussian Noise(BI-AWGN)channel.(2)Optimization of multi-dimensional reconciliation algorithm based on Raptor codes without fixed code rate.The multi-dimensional reconciliation algorithm is introduced in detail and Raptor codes are applied to the multi-dimensional reconciliation algorithm,aiming to solve the defects of the fixed-code-rate error correction code MET-LDPC whose performance will be degraded due to the slight changes of signal-to-noise ratio,and to derive the initialization formula of linear packet codes under the multi-dimensional reconciliation condition,so that the initialization of the decoding code has the most accurate log-likelihood ratio value.The algorithm not only truly achieves code rate compatibility,but also achieves high reconciliation efficiency(>95%)at very low signal-tonoise ratio(<-15 d B).(3)Theoretical analysis of the virtual channel in multi-dimensional reconciliation.By comparing the performance of Raptor codes in the BI-AWGN channel and the multi-dimensional reconciliation algorithm,we find that the performance of Raptor codes in the BI-AWGN channel fail to achieve the performance in multi-dimensional reconciliation.So we develop the analysis of the virtual channel constructed in multi-dimensional reconciliation.The difference between these two is found to be that the virtual channel is not exactly a BI-AWGN channel,and there exists a fading coefficient that varies with the signal-to-noise ratio,while its noise satisfies a t-distribution with d as the degree of freedom.In contrast,the noise of BI-AWGN channel satisfies Gaussian distribution,so we perform the analysis to derive the virtual channel capacity whose noise satisfies the t-distribution and compare it with the BI-AWGN channel.