Research On Efficient QKD Error Correction Algorithm Based On GE Model And LDPC Code

Error correction is an important step in the post-processing process of quantum key distribution.At present,most studies are based on binary symmetric models,which ignore the channel noise distribution characteristics,resulting in bit rate distortion,and ultimately affect the error correction efficiency.LDPC code has high error correction efficiency and is a modern error correction code emerging in recent years.It only needs to exchange adjoint information once for error correction and has low sensitivity to the delay of communication links.In order to accurately describe QKD post-processing error correction sources and channels,Gilbert-Elliott（GE）model based on Hidden Markov Model（HMM）is applied to evaluate the model accuracy,and GE node is introduced to improve the confidence propagation algorithm.Finally,the feasibility of the algorithm is verified according to the simulation data and actual QKD data set.This paper presents an improved LDPC code confidence propagation algorithm with GE node.After obtaining the initial information bit state or the information bit state determined after the last iteration,baum-Welch algorithm was used to re-estimate the GE channel model parameters,and the output probability of code word sequence was calculated by forward-backward algorithm.Finally,the likelihood ratio information was passed into the traditional LDPC code BP decoding algorithm for iterative calculation.In this paper,the model matching degree is verified by the occurrence probability of k consecutive"1"in actual QKD data.An improved multi-bit rate decoder based on IEEE802.16e standard is built.The simulation results show that for the memory characteristics of source and channel,the BP decoding algorithm of GE node can improve BER from 10^-4 to10^-5.FER increased to 10^-4 from 10^-3.The negotiation efficiency is generally reduced,some of which can reach the level of less than 1,reflecting the advantages of the improved BP decoder in error correction efficiency.Finally,the algorithm is applied to a real QKD system.The actual QKD data of Quantumctek are used to verify the error characteristics of source and channel respectively.For the memory characteristics on the source,the bit error rate of the improved decoder increases by an order of magnitude,and the number of iterations decreases.The improved decoder can fully restore and correct the memory characteristics of the channel,while the traditional decoder still has an error rate of about 5%.This paper improves the error correction efficiency of BP decoding algorithm of QKD system and has important application value in military communication field.