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Key Distribution Data Coordination Optimization with Continuous Variables Based on EXIT Chart

WANG Xiaokai,SUN Yi,GUO Dabo,WANG Yunyan

Published Jun 1, 2016• 0 citations
Publisher

Abstract

In quantum cryptography communication,distributions of the non optimized Low Density Parity Check(LDPC) has low performance and it has low reconciliation efficiency and short transmission distance.Aiming at this problem,a quantum key distribution data coordination algorithm based on continuous variables is proposed.Take the advantage of characteristics of Extrinsic Information Transfer(EXIT) chart,from the results of Guassian approximation based on Particle Swarm Optimization(PSO),EXIT chart selects better performance distributions by comparing the threshold value and optimize LDPC code.Simulation results show that,compared with the density evolution algorithm and the Gauss approximation algorithm,the LDPC code distribution can be optimized effectively by EXIT chart.Meanwhile,when the number of packets of continuous variables is 2×105,compared with of the non optimized LDPC codes,the optimized LDPC codes can reduce the convergence Signal to Noise Ratio(SNR) and improve the reconciliation efficiency and maximum transmission distance.

DOI
10.3969/j.issn.1000-3428.2016.06.027

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In quantum cryptography communication,distributions of the non optimized Low Density Parity Check(LDPC) has low performance and it has low reconciliation efficiency and short transmission distance.Aiming at this problem,a quantum key distribution data coordination algorithm based on continuous variables is proposed.Take the advantage of characteristics of Extrinsic Information Transfer(EXIT) chart,from the results of Guassian approximation based on Particle Swarm Optimization(PSO),EXIT chart selects better performance distributions by comparing the threshold value and optimize LDPC code.Simulation results show that,compared with the density evolution algorithm and the Gauss approximation algorithm,the LDPC code distribution can be optimized effectively by EXIT chart.Meanwhile,when the number of packets of continuous variables is 2×105,compared with of the non optimized LDPC codes,the optimized LDPC codes can reduce the convergence Signal to Noise Ratio(SNR) and improve the reconciliation efficiency and maximum transmission distance.
According to the basic principle of the density evolution for the irregular low-density paritycheck(LDPC)codes,the parity check matrix His optimized and a better performance one is obtained by combining the Gaussian approximation algorithm and the particle swarm optimization(PSO)algorithm.Applied to the data reconciliation of continuous variables coherent states based quantum key distribution,the algorithm gets a lower SNRthreshold and improves reconciliation efficiency so that the communication distance of quantum key distribution is extended.When the SNRof quantum channel is above 4.9dB and the number of packets of continuous variables is 2×105,the simulation results of the algorithm written by C language show that the reliable data reconciliation can be realized.Meanwhile,the reconciliation efficiency can achieve 92.06%and the maximum transmission distance can be extended up to 35.5km.
The current bottleneck of continuous-variable quantum key distribution (CV-QKD) is the computational complexity and performance of key reconciliation algorithms. CV-QKD requires capacity approaching error correcting codes in the low signal-to-noise (SNR) regime (SNR << 0 dB) with very low code rates. Multilevel coding (MLC) combined with multistage decoding (MSD) can solve this challenge. Multi-edge-type low-density parity-check (MET-LDPC) codes are ideal for low code rates in the low SNR regime due to degree one variable nodes. Here, we introduce the concept of generalized extrinsic information transfer (G-EXIT) charts for MET-LDPC codes and demonstrate how this tool can be used to analyze their convergence behavior. We calculate the capacity for each level in the MLC-MSD scheme and use G-EXIT charts to exemplary find the best codes for some given thresholds. In comparison to the traditional density evolution method, G-EXIT charts offer a simple and fast asymptotic analysis tool for MET-LDPC codes.
Non-binary low-density parity-check(LDPC) codes defined over the finite field GF(q=2p) are an extension of binary LDPC codes and have demonstrated improved performance over binary LDPC codes with the same frame length and rate.This paper introduces the principle of extrinsic information transfer(EXIT) charts,analyzes the convergence behavior of non-binary LDPC codes on AWGN channel,and confirms the thresholds of non-binary LDPC codes,which provides the foundation for analysis and design of real communication system using EXIT tool in future work.Simulation result shows that the performance of quaternary LDPC codes is better than that of binary LDPC codes in the same channel,and validates the superiority of using EXIT chart for iterative research.
Information reconciliation in the continuousvariable quantum key distribution (CVQKD) plays a vital role on affecting secret key rate as well as maximum transmission distance. It is necessary to search good error-correcting codes in order to improve the performance of reconciliation efficiency. In this work, we construct Quasi-Cyclic (QC) low-density paritycheck (LDPC) codes based on LDPC codes in the digital video broadcasting second generation terrestrial (DVB-T2) standard, and then combine these codes with information reconciliation in the CVQKD system, which can extremely ameliorate the performance of secret key rate and maximum transmission distance. The simulation results show that our proposed QC-LDPC codes can achieve higher reconciliation efficiency of 93.05% compare to DVB-T2 LDPC codes, which means our proposed QC-LDPC codes can obtain better performance of secret key rate and longer maximum transmission distance.
The extrinsic information transfer (EXIT) charts are used to analyze the sum-product decoding algorithm of low-density parity-check (LDPC) codes. The codes are optimized by performing curve fitting on EXIT charts. This technique is developed for binary erasure channels based on area property and is extended to other channels. We show that on channels where the area property is not valid, the curve fitting approach is a sub-optimal method of optimizing for the best convergence threshold. On Gaussian channels, the messages from variable nodes to check nodes are approximated by a symmetric Gaussian distribution. We prove that the check node detector mutual information transfer function derived using this approximation is an upper bound. So the EXIT chart analysis predicts an optimistic value for the convergence threshold. We give an empirical lower bound for the check node detector mutual information transfer function. For few irregular LDPC codes designed for AWGN channel using density evolution, we have examined the accuracy of convergence thresholds predicted by EXIT charts using these bounds for the check node transfer function. The analysis of EXIT chart technique presented in this paper can be extended to other channels for which the distribution of channel messages can be approximated by a symmetric Gaussian/Gaussian mixture distribution.
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>97%>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.