Parameter prediction of classical<bold>-</bold>quantum signals co<bold>-</bold>fiber transmission system based on BP neural network

SUN Yishi; SUN Yi

doi:10.3969/j.issn.1007-5461.2023.04.014

Chinese Journal of Quantum Electronics, Volume. 40, Issue 4, 546(2023)

Parameter prediction of classical-quantum signals co-fiber transmission system based on BP neural network

SUN Yishi and SUN Yi^*

Author Affiliations

College of Communication and Information Technology, Xi'an University of Science and Technology, Xi'an 710054, China

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Figures & Tables(11)

Fig. 1. Structure diagram of WDM-QKD system

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Fig. 2. Comparison of the detection rates of SRS noise, FWM noise and out-band noise

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Fig. 3. The secure key transmission relationship under different decoy state methods with statistical fluctuations

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Fig. 4. Training performance of neural network with different distribution of neurons. (a) Neuron setup (3, 2, 1); (b) Neuron setup (6, 4, 1); (c) Neuron setup (15, 10, 1); (d) Neuron setup (48, 24, 1)

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Fig. 5. Training performance of neural network with LM variable gradient algorithm

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Fig. 6. Training performance of neural network with Bayesian regularization algorithm

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Fig. 7. Training performance of neural network with SCG algorithm

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Fig. 8. BP neural network model

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Fig. 9. Light source prediction results using BP neural network. (a) Imitative effect; (b) Training error

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Table 1. Propagation algorithm of BP neural network

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Table 1. Propagation algorithm of BP neural network

输入: 训练集 $D = {\{(x_{k}, y_{k})\}}_{k = 1}^{m}$ ; 学习率 $η$

输出: 连接权值或阈值确定的多层前馈神经网络

1: function $B P (D, η)$

2: 在 (0, 1) 范围内随机初始化网络中的所有连接权值和阈值

3: repeat

4: for all $(x_{k}, y_{k}) \in D$ do

5: 计算当前样本输出 ${\hat{y}}^{k} = f (β_{j} - θ_{j})$

6: 计算输出神经元梯度

$\begin{array}{l} g_{j} = - \frac{\partial E_{k}}{\partial {\hat{y}}^{k}} \cdot \frac{\partial {\hat{y}}^{k}}{\partial β_{j}} \\ = - ({\hat{y}}_{j}^{k} - y_{j}^{k}) f^{'} (β_{j} - θ_{j}) \\ = {\hat{y}}_{j}^{k} (1 - {\hat{y}}_{j}^{k}) ({\hat{y}}_{j}^{k} - y_{j}^{k}) \end{array}$

7: 计算隐层的神经元梯度项

$\begin{array}{l} e_{h} = - \frac{\partial E_{k}}{\partial b_{h}} \cdot \frac{\partial b_{h}}{a_{h}} \\ = - \sum_{j = 1}^{l} \frac{\partial E_{k}}{\partial β_{j}} \cdot \frac{\partial β_{j}}{b_{h}} f^{'} (a_{h} - γ_{h}) \\ = \sum_{j = 1}^{l} w_{h j} g_{j} f^{'} (a_{h} - γ_{h}) \\ = b_{h} (1 - b_{h}) \sum_{j = 1}^{l} w_{h j} g_{j} \end{array}$

8: 更新权值

$Δ w_{h j} = n g_{j} b_{h}$

$Δ v_{i h} = η e_{h} x_{i}$

9: 更新阈值

$Δ θ_{j} = - η g_{j}$

$Δ γ_{h} = - η e_{h}$

10: end for

11: until 达到停止条件

12: end function

Table 2. Parameters used for the numerical simulation of WDM-QKD

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Table 2. Parameters used for the numerical simulation of WDM-QKD

Parameter	Value
$I$ (波分复用器的插入损耗)/dB	1.5
$α_{c}$ (光纤衰减系数)/(dB·km^-1)	0.21
$ξ$ (波分复用器的隔离度)/dB	80
$τ_{D}$ (单光子探测器门宽)/ps	100
$η_{D}$ (单光子探测器探测效率)	0.045
$h$ (普朗克常数)/(J·s)	6.63×10^-34
$c$ (光速)/(m·s^-1)	299792458
$t_{F}^{c}$ (滤波后带外噪声的透过率)	0.01
$t_{F}$ (滤波后带内噪声的透过率)	0.95
$t_{B o b}$ (来自内部光学器件的透过率)	0.9
$β$ (自发拉曼散射系数)/(km·nm)	2×10^-9
$Δ λ$ (滤波器带宽)/pm	35.23
$χ$ (光纤非线性系数)/(W·km)	1.2
$D_{i j k}$ (简并因子)	3
$D_{c}$ (光纤色散系数)/(ps·nm^-1·km^-1)	18
$d D_{c} / d λ$ (光纤色散斜率)/(ps·nm^-2·km^-1)	0.056
$e_{d}$ (未对准引起的误码率)	0.033
$P_{d}$ (探测器的暗记数率)	3×10^-6
$f (E_{μ})$ (纠错系数)	1.22

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Yishi SUN, Yi SUN. Parameter prediction of classical-quantum signals co-fiber transmission system based on BP neural network[J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 546

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