A High-Security Probabilistic Constellation Shaping Transmission Scheme Based on Recurrent Neural Networks
Abstract
:1. Introduction
2. Principle
2.1. Training Framework Setup Based on RNN Probability Distribution
Algorithm 1: Training process of RNN |
Definition 1. Build the RNN as shown in Figure 2; 2. Obtain the coding-side data s; 3. Obtain the decoding-side data r; 4. Define the optimization objective as the optimal transmission performance; Initialization 1. Set the RNN hyperparameters as shown in Table 1; 2. Set the coefficients lr = 0.01, decay = 0.001 for SGD; 3. Set the coefficients Training batch size = 400; Training do Iteratively compute the values of p. until Achieve the optimization objective. return p. |
2.2. 4D Biplane Fractional Order Chaotic Systems
2.3. RNN-PS-OFDM Encryption Scheme
3. Experimental Setup
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Pan, C.; Kschischang, F.R. Probabilistic 16-QAM shaping in WDM systems. J. Light. Technol. 2016, 34, 4285–4292. [Google Scholar] [CrossRef]
- Böcherer, G.; Schulte, P.; Steiner, F. Probabilistic shaping and forward error correction for fiber-optic communication systems. J. Light. Technol. 2019, 37, 230–244. [Google Scholar] [CrossRef]
- Ren, J.; Liu, B.; Wu, X. Three-dimensional probabilistically shaped CAP modulation based on constellation design using regular tetrahedron cells. J. Light. Technol. 2019, 38, 1728–1734. [Google Scholar] [CrossRef]
- Zhou, S.; Liu, X.; Gao, R.; Jiang, Z.; Zhang, H.; Xin, X. Adaptive Bayesian neural networks nonlinear equalizer in a 300-Gbit/s PAM8 transmission for IM/DD OAM mode division multiplexing. Opt. Lett. 2023, 48, 464–467. [Google Scholar] [CrossRef]
- Musumeci, F.; Rottondi, C.; Nag, A. An overview on application of machine learning techniques in optical networks. IEEE Commun. Surv. Tutor. 2018, 21, 1383–1408. [Google Scholar] [CrossRef]
- Gümüş, K.; Alvarado, A.; Chen, B. End-to-end learning of geometrical shaping maximizing generalized mutual information. In Proceedings of the IEEE 2020 Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 8–12 March 2020; pp. 1–3. [Google Scholar]
- Schulte, P.; Böcherer, G. Constant Composition Distribution Matching. IEEE Trans. Inf. Theory 2016, 62, 430–434. [Google Scholar] [CrossRef]
- Zhang, J.; Yu, J.; Li, X. 200 Gbit/s/λ PDM-PAM-4 PON system based on intensity modulation and coherent detection. J. Opt. Commun. Netw. 2020, 12, A1–A8. [Google Scholar] [CrossRef]
- Xu, X.; Liu, B.; Wu, X. A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation. Opt. Express 2018, 26, 26576–26589. [Google Scholar] [CrossRef]
- Ullah, R. Flattened Optical Multicarrier Generation Technique for Optical Line Terminal Side in Next Generation WDM-PON Supporting High Data Rate Transmission. IEEE Access 2018, 6, 6183–6193. [Google Scholar] [CrossRef]
- Ullah, R.; Ullah, S.; Ali, A. Optical 1.56 Tbps coherent 4-QAM transmission across 60 km SSMF employing OFC scheme. AEU-Int. J. Electron. Commun. 2019, 105, 78–84. [Google Scholar] [CrossRef]
- Wu, T.; Zhang, C.; Wei, H. PAPR and security in OFDM-PON via optimum block dividing with dynamic key and 2D-LASM. Opt. Express 2019, 27, 27946–27961. [Google Scholar] [CrossRef]
- Bi, M.; Fu, X.; Zhou, X. A key space enhanced chaotic encryption scheme for physical layer security in OFDM-PON. IEEE Photonics J. 2017, 9, 1–10. [Google Scholar] [CrossRef]
- Sultan, A.; Yang, X.; Hajomer, A.A.E. Chaotic constellation mapping for physical-layer data encryption in OFDM-PON. IEEE Photonics Technol. Lett. 2018, 30, 339–342. [Google Scholar] [CrossRef]
- Zhang, C.; Zhang, W.; Chen, C. Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding. J. Light. Technol. 2018, 36, 1706–1712. [Google Scholar] [CrossRef]
- Zhu, H.; Zhao, Y.; Song, Y. 2D logistic-modulated-sine-coupling-logistic chaotic map for image encryption. IEEE Access 2019, 7, 14081–14098. [Google Scholar] [CrossRef]
- Shen, J.; Liu, B.; Mao, Y. Enhancing the reliability and security of OFDM-PON using modified Lorenz chaos based on the linear properties of FFT. J. Light. Technol. 2021, 39, 4294–4299. [Google Scholar] [CrossRef]
- Zhang, Y.Q.; Hao, J.L.; Wang, X.Y. An efficient image encryption scheme based on S-boxes and fractional-order differential logistic map. IEEE Access 2020, 8, 54175–54188. [Google Scholar] [CrossRef]
- Iskakova, K.; Alam, M.M.; Ahmad, S. Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis. Math. Comput. Simul. 2023, 208, 219–245. [Google Scholar] [CrossRef]
- Stark, M.; Aoudia, F.A.; Hoydis, J. Joint Learning of Geometric and Probabilistic Constellation Shaping. In Proceedings of the 2019 IEEE Globecom Workshops (GC Wkshps), Waikoloa, HI, USA, 9–13 December 2019; IEEE: Piscataway, NJ, USA, 2019; pp. 1–6. [Google Scholar]
- Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; MIT Press: Cambridge, MA, USA, 2016. [Google Scholar]
- Nair, V.; Hinton, G.E. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (ICML-10), Haifa, Israel, 21–24 June 2010; pp. 807–814. [Google Scholar]
- Caputo, M. Linear models of dissipation whose Q is almost frequency independent-II. Geophys. J. Int. 1967, 13, 529–539. [Google Scholar] [CrossRef]
- Li, C.; Qian, D.; Chen, Y.Q. On Riemann-Liouville and caputo derivatives. Discret. Dyn. Nat. Soc. 2011, 2011, 562494. [Google Scholar] [CrossRef]
- Garg, V.; Singh, K. An improved Grunwald-Letnikov fractional differential mask for image texture enhancement. Int. J. Adv. Comput. Sci. Appl. 2013, 3, 130–135. [Google Scholar] [CrossRef]
Hyperparameter | Title 2 |
---|---|
Layers | 2 |
Hidden units per layer | 32 |
Learning rate | 0.001 |
Activation function | ReLU [22] |
Optimization method | SGD |
Training batch size | Integral multiple of M |
Upsampling frequency | 10 GHz |
Downsampling frequency | 10 GHz |
PdBm | −2 |
Training data points | 10,000 |
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Zhou, S.; Liu, B.; Ren, J.; Mao, Y.; Wu, X.; Guo, Z.; Zhu, X.; Ding, Z.; Wu, M.; Wang, F.; et al. A High-Security Probabilistic Constellation Shaping Transmission Scheme Based on Recurrent Neural Networks. Photonics 2023, 10, 1078. https://doi.org/10.3390/photonics10101078
Zhou S, Liu B, Ren J, Mao Y, Wu X, Guo Z, Zhu X, Ding Z, Wu M, Wang F, et al. A High-Security Probabilistic Constellation Shaping Transmission Scheme Based on Recurrent Neural Networks. Photonics. 2023; 10(10):1078. https://doi.org/10.3390/photonics10101078
Chicago/Turabian StyleZhou, Shuyu, Bo Liu, Jianxin Ren, Yaya Mao, Xiangyu Wu, Zeqian Guo, Xu Zhu, Zhongwen Ding, Mengjie Wu, Feng Wang, and et al. 2023. "A High-Security Probabilistic Constellation Shaping Transmission Scheme Based on Recurrent Neural Networks" Photonics 10, no. 10: 1078. https://doi.org/10.3390/photonics10101078