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Chaotic optical communications at 56 Gbit/s over 100-km fiber transmission based on a chaos generation model driven by long short-term memory networks

Lin Jiang, Jiacheng Feng, Lianshan Yan, Anlin Yi, Song-Sui Li, Hui Yang, Yixian Dong, Longsheng Wang, Anbang Wang, Yuncai Wang, Wei Pan, and Bin Luo

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Abstract

Chaotic optical communication technology is considered as an effective secure communication technology, which can protect information from a physical layer and is compatible with the existing optical networks. At present, to realize long-distance chaos synchronization is still a very difficult problem, mainly because well-matched hardware cannot always be guaranteed between the transmitter and receiver. In this Letter, we introduce long short-term memory (LSTM) networks to learn a nonlinear dynamics model of an opto-electronic feedback loop, and then apply the trained deep learning model to generate a chaotic waveform for encryption and decryption at the transmitter and receiver. Furthermore, to improve the security, we establish a deep learning model pool which consists of different gain trained models and different delay trained models, and use a digital signal to drive chaos synchronization between the receiver and transmitter. The proposed scheme is experimentally verified in chaotic-encrypted 56-Gbit/s PAM-4 systems, and a decrypted performance below 7%FEC threshold (BER = 3.8×10−3) can be achieved over a 100-km fiber transmission.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)
Fig. 1.
Fig. 1. Chaotic waveform generation based on the trained deep learning model. LD, laser diode; PC, polarization controller; MZM, Mach–Zehnder modulator; OC, optical coupler; VOA, variable optical attenuator; PD, photodiode.

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Fig. 2.
Fig. 2. (a) Chaotic time series generated based on the opto-electronic feedback loop. (b) Chaotic time series generated based on the LSTM model. (c) Consistency of the chaotic waveform between actual components and the LSTM model. The illustration is the bandwidth of the chaotic waveform generated by the LSTM model.

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Fig. 3.
Fig. 3. Encryption and synchronization mechanism.

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Fig. 4.
Fig. 4. (a) Time series of the original data. (b) Chaotic time series generated based on the deep learning model. (c) Time series of the encrypted data. ACF of (d) chaotic time series and (e) the time series of the encrypted data.

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Fig. 5.
Fig. 5. Experiment setup. ECL, external cavity laser; MZM, Mach–Zehnder modulator; EDFA, erbium-doped fiber amplifier; SSMF, standard single-mode fiber; DCM, dispersion compensation module; VOA, variable optical attenuator; PD, photodiode.

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Fig. 6.
Fig. 6. BER performance of the encrypted and decrypted signals under different mask coefficients for the B2B and fiber transmission cases.

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Tables (1)

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Table 1. Nonlinear Behavior and Consistency of Time Series Based on Opto-Electronic Feedback Loop and Deep Learning Model

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Equations (5)

Equations on this page are rendered with MathJax. Learn more.

c ( t ) = P 0 cos 2 ( R η 1 g π 2 V π c ( t − △ τ ) ∗ h ( t ) + ϕ 0 ) ,
d ( n ) = C e λ n ,
λ ( x 0 ) = lim n → ∞ ⁡ 1 n ∑ i = 0 n − 1 ln ⁡ | f ′ ( x i ) | ,
P E ( m ) = − ∑ j = 1 k P j ln P j ,
C . C = ∑ i = 0 n − 1 [ ( x i − μ x ) ( y i − μ y ) ] ∑ i = 0 n − 1 ( x i − μ x ) 2 ⋅ ∑ i = 0 n − 1 ( y i − μ y ) 2 ,
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