Papers
Topics
Authors
Recent
2000 character limit reached

End-to-end Optimization of Optical Communication Systems based on Directly Modulated Lasers (2405.09907v1)

Published 16 May 2024 in eess.SP

Abstract: The use of directly modulated lasers (DMLs) is attractive in low-power, cost-constrained short-reach optical links. However, their limited modulation bandwidth can induce waveform distortion, undermining their data throughput. Traditional distortion mitigation techniques have relied mainly on the separate training of transmitter-side pre-distortion and receiver-side equalization. This approach overlooks the potential gains obtained by simultaneous optimization of transmitter (constellation and pulse shaping) and receiver (equalization and symbol demapping). Moreover, in the context of DML operation, the choice of laser-driving configuration parameters such as the bias current and peak-to-peak modulation current has a significant impact on system performance. We propose a novel end-to-end optimization approach for DML systems, incorporating the learning of bias and peak-to-peak modulation current to the optimization of constellation points, pulse shaping and equalization. The simulation of the DML dynamics is based on the use of the laser rate equations at symbol rates between 15 and 25 Gbaud. The resulting output sequences from the rate equations are used to build a differentiable data-driven model, simplifying the calculation of gradients needed for end-to-end optimization. The proposed end-to-end approach is compared to 3 additional benchmark approaches: the uncompensated system without equalization, a receiver-side finite impulse response equalization approach and an end-to-end approach with learnable pulse shape and nonlinear Volterra equalization but fixed bias and peak-to-peak modulation current. The numerical simulations on the four approaches show that the joint optimization of bias, peak-to-peak current, constellation points, pulse shaping and equalization outperforms all other approaches throughout the tested symbol rates.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (108)
  1. N.-P. Diamantopoulos, T. Fujii, S. Yamaoka, H. Nishi, K. Takeda, T. Tsuchizawa, T. Segawa, T. Kakitsuka, and S. Matsuo, “60 GHz Bandwidth Directly Modulated Membrane III-V Lasers on SiO2/Si,” \JournalTitleJournal of Lightwave Technology 40, 3299–3306 (2022).
  2. J. Huang, C. Li, R. Lu, L. Li, and Z. Cao, “Beyond the 100 Gbaud Directly Modulated Laser for Short Reach Applications,” \JournalTitleJournal of Semiconductors 42, 041306 (2021).
  3. D. Che and X. Chen, “Modulation Format and Digital Signal Processing for IM-DD Optics at Post-200G Era,” \JournalTitleJournal of Lightwave Technology 42, 588–605 (2024).
  4. M. S. Alam, R. Maram, K. A. Shahriar, P. Ricciardi, and D. V. Plant, “Chirped Managed Laser for Multilevel Modulation Formats: A Semi-analytical Approach for Efficient Filter Design,” \JournalTitleJournal of Lightwave Technology pp. 1–11 (2023).
  5. X. Pang, T. Salgals, H. Louchet, D. Che, M. Gruen, Y. Matsui, T. Dippon, R. Schatz, M. Joharifar, B. Krüger, F. Pittala, Y. Fan, A. Udalcovs, L. Zhang, X. Yu, S. Spolitis, V. Bobrovs, S. Popov, and O. Ozolins, “200 Gb/s Optical-Amplifier-Free IM/DD Transmissions Using a Directly Modulated O-Band DFB+R Laser Targeting LR Applications,” \JournalTitleJournal of Lightwave Technology 41, 3635–3641 (2023).
  6. G. V. Rajeswari, M. Moehrle, F. Ehrensack, U. Troppenz, A. Sigmund, and M. Schell, “Novel >57 GHz bandwidth O-band InGaAlAs MQW RW DFB,” in Novel In-Plane Semiconductor Lasers XXII, vol. 12440 A. A. Belyanin and P. M. Smowton, eds., International Society for Optics and Photonics (SPIE, 2023), p. 1244007.
  7. S. Yamaoka, N.-P. P. Diamantopoulos, H. Nishi, T. Fujii, K. Takeda, T. Hiraki, S. Kanazawa, T. Kakitsuka, and S. Matsuo, “Uncooled 100-GBaud Directly Modulated Membrane Lasers on SiC Substrate,” \JournalTitleJournal of Lightwave Technology 41, 3389–3396 (2023).
  8. A. G. Reza, M. T. Costas, C. Browning, F. D. Otero, and L. Barry, “67.5 Gbit/s PAM-8 Signal Transmissions Over 25-km SMF With a 1550-nm 10G-Class DML Using Machine Learning,” in Conference on Lasers and Electro-Optics, (Optica Publishing Group, 2022), p. SM3J.4.
  9. S. Hernandez, O. Jovanovic, C. Peucheret, F. D. Ros, and D. Zibar, “Differentiable Machine Learning-Based Modeling for Directly-Modulated Lasers,” \JournalTitleIEEE Photonics Technology Letters 36, 266–269 (2024).
  10. S. Li, X. Jin, Y. Xuan, X. Zhou, W. Chen, Y.-X. Wang, and X. Yan, “Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting,” in Proceedings of the 33rd International Conference on Neural Information Processing Systems, (2019).
  11. M. Srinivasan, J. Song, A. Grabowski, K. Szczerba, H. K. Iversen, M. N. Schmidt, D. Zibar, J. Schröder, A. Larsson, C. Häger, and H. Wymeersch, “End-to-End Learning for VCSEL-Based Optical Interconnects: State-of-the-Art, Challenges, and Opportunities,” \JournalTitleJournal of Lightwave Technology 41, 3261–3277 (2023).
  12. L. Minelli, F. Forghieri, A. Shahpari, T. Shao, and R. Gaudino, “TDECQ optimization of VCSEL-MMF nonlinear Digital Pre-Distorters using End-to-end Learning,” in European Conference on Optical Communication (ECOC), (2023), p. Th.B.5.6.
  13. F. A. Aoudia and J. Hoydis, “Model-Free Training of End-to-End Communication Systems,” \JournalTitleIEEE Journal on Selected Areas in Communications 37, 2503–2516 (2019).
  14. M. P. Yankov, O. Jovanovic, D. Zibar, and F. D. Ros, “Recent Advances in Constellation Optimization for Fiber-optic Channels,” in European Conference on Optical Communication (ECOC) 2022, (Optica Publishing Group, 2022), p. Mo3D.4.
  15. T. O’Shea and J. Hoydis, “An Introduction to Deep Learning for the Physical Layer,” \JournalTitleIEEE Transactions on Cognitive Communications and Networking 3, 563–575 (2017).
  16. V. Oliari, B. Karanov, S. Goossens, G. Liga, O. Vassilieva, I. Kim, P. Palacharla, C. Okonkwo, and A. Alvarado, “Hybrid Geometric and Probabilistic Shaping; Is It Really Necessary?” in Optica Advanced Photonics Congress 2022, (2022), p. SpTu1J.4.
  17. A. Soleimanzade, M. Ardakani, and H. Ebrahimzad, “Optimization of the Non-Linearity Tolerant 4D Geometric Shaped Constellations for Optical Fiber Communication Systems Using Neural Networks,” \JournalTitleJournal of Lightwave Technology 42, 670–680 (2024).
  18. E. Sillekens, G. Liga, D. Lavery, P. Bayvel, and R. I. Killey, “High-Cardinality Geometrical Constellation Shaping for the Nonlinear Fibre Channel,” \JournalTitleJournal of Lightwave Technology 40, 6374–6387 (2022).
  19. O. Jovanovic, F. Da Ros, D. Zibar, and M. P. Yankov, “Geometric Constellation Shaping for Fiber-Optic Channels via End-to-End Learning,” \JournalTitleJournal of Lightwave Technology 41, 3726–3736 (2023).
  20. S. Yamaoka, N.-P. Diamantopoulos, H. Nishi, R. Nakao, T. Fujii, K. Takeda, T. Hiraki, T. Tsurugaya, S. Kanazawa, H. Tanobe, T. Kakitsuka, T. Tsuchizawa, F. Koyama, and S. Matsuo, “Directly modulated membrane lasers with 108 GHz bandwidth on a high-thermal-conductivity silicon carbide substrate,” \JournalTitleNature Photonics 15, 28–35 (2021).
  21. T. Koch and J. Bowers, “Nature of Wavelength Chirping in Directly Modulated Semiconductor Lasers,” \JournalTitleElectronics Letters 20, 1038–1040 (1984).
  22. A. Villafranca, J. Lasobras, and I. Garces, “Precise Characterization of the Frequency Chirp in Directly Modulated DFB Lasers,” in 2007 Spanish Conference on Electron Devices, (2007), pp. 173–176.
  23. Y. Mao, Z. Ren, L. Guo, H. Wang, R. Zhang, Y. Huang, D. Lu, Q. Kan, C. Ji, and W. Wang, “Modulation Bandwidth Enhancement in Distributed Reflector Laser Based on Identical Active Layer Approach,” \JournalTitleIEEE Photonics Journal 10 (2018).
  24. S. Sulikhah, S. L. Lee, and H. W. Tsao, “Improvement on Direct Modulation Responses and Stability by Partially Corrugated Gratings Based DFB Lasers With Passive Feedback,” \JournalTitleIEEE Photonics Journal 13, 1–14 (2021).
  25. Y. Matsui, R. Schatz, T. Pham, W. A. Ling, G. Carey, H. M. Daghighian, D. Adams, T. Sudo, and C. Roxlo, “55 GHz Bandwidth Distributed Reflector Laser,” \JournalTitleJournal of Lightwave Technology 35, 397–403 (2017).
  26. D. Che, Y. Matsui, R. Schatz, R. Rodes, F. Khan, M. Kwakernaak, and T. Sudo, “200-Gb/s Direct Modulation of a 50-GHz Class Laser With Advanced Digital Modulations,” \JournalTitleJournal of Lightwave Technology 39, 845–852 (2021).
  27. U. Feiste, “Optimization of modulation bandwidth in DBR lasers with detuned Bragg reflectors,” \JournalTitleIEEE Journal of Quantum Electronics 34, 2371–2379 (1998).
  28. M. Chaciński and R. Schatz, “Impact of Losses in the Bragg Section on the Dynamics of Detuned Loaded DBR Lasers,” \JournalTitleIEEE Journal of Quantum Electronics 46, 1360–1367 (2010).
  29. Y. Matsui, R. Schatz, D. Che, F. Khan, M. Kwakernaak, and T. Sudo, “Low-chirp Isolator-free 65-GHz-bandwidth Directly Modulated Lasers,” \JournalTitleNature Photonics 15, 59–63 (2021).
  30. P. Bardella and I. Montrosset, “A New Design Procedure for DBR Lasers Exploiting the Photon–Photon Resonance to Achieve Extended Modulation Bandwidth,” \JournalTitleIEEE Journal of Selected Topics in Quantum Electronics 19, 1502408–1502408 (2013).
  31. G. Morthier, R. Schatz, and O. Kjebon, “Extended Modulation Bandwidth of DBR and External Cavity Lasers by Utilizing a Cavity Resonance for Equalization,” \JournalTitleIEEE Journal of Quantum Electronics 36, 1468–1475 (2000).
  32. S. Guan, Y. Zhang, J. Zheng, J. Su, Z. Sun, L. Lu, T. Fang, L. Li, R. Xiao, Y. Shi, and X. Chen, “Modulation Bandwidth Enhancement and Frequency Chirp Suppression in Two-Section DFB Laser,” \JournalTitleJournal of Lightwave Technology 40, 7383–7389 (2022).
  33. K. Shinohara, R. Miyagoshi, Y. Suzuki, R. Suzuki, G. Sakaino, M. Shimada, and K. Matsumoto, “106-Gbps PAM4 Operation at an Extinction Ratio above 3.5 dB using a Conventional Buried-Heterostructure Directly Modulated Laser,” in Optical Fiber Communication Conference (OFC) 2023, (2023), p. M2D.6.
  34. S. Ohno, M. Onga, T. Nakajima, A. Nakanishi, N. Sasada, S. Tanaka, R. Nakajima, and K. Naoe, “10-km Transmission of 106-Gb/s PAM4 with Directly Modulated DFB Lasers in the CWDM Range,” in Optical Fiber Communication Conference (OFC) 2023, (2023), p. M2D.7.
  35. X. Zhu, J. Guo, H. Li, Z. Li, D. Zhou, L. Zhao, W. Wang, and S. Liang, “High Speed Directly Modulated DFB Lasers Having MQW Based Passive Reflectors,” \JournalTitleIEEE Photonics Technology Letters 35, 333–336 (2023).
  36. H.-T. Cheng, Y.-C. Yang, T.-H. Liu, and C.-H. Wu, “Recent Advances in 850 nm VCSELs for High-Speed Interconnects,” \JournalTitlePhotonics 9 (2022).
  37. M. Hoser, W. Kaiser, D. Quandt, J. Bueno, S. Saintenoy, and S. Eitel, “Highly Reliable 106 Gb/s PAM-4 850 nm Multi-Mode VCSEL for 800G Ethernet Applications,” in Optical Fiber Communication Conference (OFC) 2022, (2022), p. Tu2D.5.
  38. D. Wu, X. Yu, H. Wu, W. Fu, and M. Feng, “Single-mode 850nm VCSELs Demonstrate 96 Gb/s PAM4 OM4 Fiber Link for Extended Reach to 1km,” in Optical Fiber Communication Conference (OFC) 2022, (2022), p. W2A.7.
  39. J. Wang, Y. Ji, Z. Yang, H. Hu, J. Chen, H. Li, F. Li, S. Li, J. Kapraun, C. Shen, and C. J. Chang-Hasnain, “300-m Multimode Fiber Transmission of 106Gbps PAM-4 Using 850nm High-Contrast-Grating Few-mode VCSELs,” in European Conference on Optical Communication (ECOC), (2022), p. Tu3E.3.
  40. C. Ge, L. Dong, X. Gu, and F. Koyama, “1060nm Single-mode Intra-cavity Metal-aperture VCSEL for over 2km Standard 1300nm SMF Transmission,” in CLEO 2023, (2023), p. STh4Q.2.
  41. J. Chi, X. Li, C. Niu, and J. Zhao, “Output Optical Power Enhancement of Push-Pull Modulated DFB Laser With Asymmetric Structure,” \JournalTitleIEEE Photonics Journal 15, 1–8 (2023).
  42. D. Che, Y. Matsui, X. Chen, R. Schatz, and P. Iannone, “400-Gb/s Direct Modulation using a DFB+++R Laser,” \JournalTitleOpt. Lett. 45, 3337–3339 (2020).
  43. J. Chi, C. Niu, and J. Zhao, “Parameter Extraction For Quantum Well DFB Lasers Based on 1D Traveling Wave Model,” \JournalTitleIEEE Photonics Journal 14, 1–8 (2022).
  44. L. Bjerkan, A. Royset, L. Hafskjaer, and D. Myhre, “Measurement of Laser Parameters for Simulation of High-Speed Fiberoptic Systems,” \JournalTitleJournal of Lightwave Technology 14, 839–850 (1996).
  45. J. Cartledge and R. Srinivasan, “Extraction of DFB Laser Rate Equation Parameters for System Simulation Purposes,” in Conference Proceedings LEOS’96 9th Annual Meeting IEEE Lasers and Electro-Optics Society, vol. 2 (1996), pp. 248–249.
  46. I. Tomkos, I. Roudas, R. Hesse, N. Antoniades, A. Boskovic, and R. Vodhanel, “Extraction of Laser Rate Equations Parameters for Representative Simulations of Metropolitan-area Transmission Systems and Networks,” \JournalTitleOptics Communications 194, 109–129 (2001).
  47. A. Marchisio, E. Ghillino, V. Curri, A. Carena, and P. Bardella, “Particle Swarm Optimization-assisted Approach for the Extraction of VCSEL Model Parameters,” \JournalTitleOpt. Lett. 49, 125–128 (2024).
  48. S. J. Zhang, N. H. Zhu, E. Y. B. Pun, and P. S. Chung, “Rate-equation-based Circuit Model of High-speed Semiconductor Lasers,” \JournalTitleMicrowave and Optical Technology Letters 49, 539–542 (2007).
  49. A. Griewank, “A mathematical view of automatic differentiation,” \JournalTitleActa Numerica 12, 321–398 (2003).
  50. A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind, “Automatic differentiation in machine learning: a survey,” \JournalTitleJ. Mach. Learn. Res. 18, 5595–5637 (2017).
  51. W. W. Feng and N. H. Zhu, “Analysis of Chirp Characteristics of DFB Lasers and Integrated Laser-modulators,” \JournalTitleOptical and Quantum Electronics 36, 1237–1245 (2004).
  52. Q. Ding, Q. Yang, J. Li, C. Gu, Z. Li, X. Tan, F. Gao, X. Chen, and Q. Niu, “Efficient and systematic parameter extraction based on rate equations by DFB equivalent circuit model,” \JournalTitleOptics Express 31, 40604–40619 (2023).
  53. J. Katz, S. Margalit, C. Harder, D. Wilt, and A. Yariv, “The Intrinsic Electrical Equivalent Circuit of a Laser Diode,” \JournalTitleIEEE Journal of Quantum Electronics 17, 4–7 (1981).
  54. I. Habermayer, “Nonlinear Circuit Model for Semiconductor Lasers,” \JournalTitleOptical and Quantum Electronics 13, 461–468 (1981).
  55. R. S. Tucker, “Circuit model of double-heterojunction laser below threshold,” \JournalTitleIEEE Proceedings I (Solid-State and Electron Devices) 128, 101–106(5) (1981).
  56. S. Ghoniemy, L. MacEachern, and S. Mahmoud, “Extended Robust Semiconductor Laser Modeling for Analog Optical Link Simulations,” \JournalTitleIEEE Journal of Selected Topics in Quantum Electronics 9, 872–878 (2003).
  57. A. Horri, S. Z. Mirmoeini, and R. Faez, “The Noise Equivalent Circuit Model of Quantum-dot Lasers,” \JournalTitleJournal of Russian Laser Research 33, 217–226 (2012).
  58. E. Mortazy, V. Ahmadi, and M. Moravvej-Farshi, “An Integrated Equivalent Circuit Model for Relative Intensity Noise and Frequency Noise Spectrum of a Multimode Semiconductor Laser,” \JournalTitleIEEE Journal of Quantum Electronics 38, 1366–1371 (2002).
  59. T. Jakaša, I. Andročec, and P. Sprčić, “Electricity Price Forecasting — ARIMA Model Approach,” in 2011 8th International Conference on the European Energy Market (EEM), (2011), pp. 222–225.
  60. D. R. Irmawati, R. M. Atok, and Suhartono, “Hybrid Singular Spectrum Analysis-ARIMA Modelling for Direct and Indirect Forecasting of Farmer’s Term of Trade in East Java,” in 2018 International Conference on Information and Communications Technology (ICOIACT), (2018), pp. 889–894.
  61. S. Zhang and Y. Liu, “Forecasting Model of Total Import and Export based on ARIMA Algorithm Optimized by BP Neural Network,” in 2023 IEEE 3rd International Conference on Data Science and Computer Application (ICDSCA), (2023), pp. 1534–1538.
  62. L. Ljung, C. Andersson, K. Tiels, and T. B. Schön, “Deep Learning and System Identification,” \JournalTitle21st IFAC World Congress 53, 1175–1181 (2020).
  63. J. Schoukens and L. Ljung, “Nonlinear System Identification: A User-Oriented Road Map,” \JournalTitleIEEE Control Systems Magazine 39, 28–99 (2019).
  64. H.-Y. Chen, C.-C. Wei, C.-Y. Lin, L.-W. Chen, I.-C. Lu, and J. Chen, “Frequency- and Time-domain Nonlinear Distortion Compensation in High-speed OFDM-IMDD LR-PON with High Loss Budget,” \JournalTitleOpt. Express 25, 5044–5056 (2017).
  65. Y. Xu, L. Huang, W. Jiang, L. Xue, W. Hu, and L. Yi, “Automatic Optimization of Volterra Equalizer With Deep Reinforcement Learning for Intensity-Modulated Direct-Detection Optical Communications,” \JournalTitleJournal of Lightwave Technology 40, 5395–5406 (2022).
  66. N. Stojanovic, F. Karinou, Z. Qiang, and C. Prodaniuc, “Volterra and Wiener Equalizers for Short-Reach 100G PAM-4 Applications,” \JournalTitleJournal of Lightwave Technology 35, 4583–4594 (2017).
  67. F. P. Guiomar, S. B. Amado, C. S. Martins, and A. N. Pinto, “Time-Domain Volterra-Based Digital Backpropagation for Coherent Optical Systems,” \JournalTitleJournal of Lightwave Technology 33, 3170–3181 (2015).
  68. S. Elliott, “8 - Active Control of Nonlinear Systems,” in Signal Processing for Active Control, (Academic Press, 2001), Signal Processing and its Applications, pp. 367–409.
  69. K. L. J. Tsimbinos, “Computational Complexity of Volterra based Nonlinear Compensators,” \JournalTitleElectronics Letters 32, 852–854(2) (1996).
  70. J. Tsimbinos and K. Lever, “The Computational Complexity of Nonlinear Compensators based on the Volterra Inverse,” in Proceedings of 8th Workshop on Statistical Signal and Array Processing, (1996), pp. 387–390.
  71. M. J. Korenberg, S. B. Bruder, and P. J. McLlroy, “Exact Orthogonal Kernel Estimation from Finite Data Records: Extending Wiener’s Identification of Nonlinear Systems,” \JournalTitleAnnals of Biomedical Engineering 16, 201–214 (1988).
  72. E. Thomas, J. van Hemmen, and W. Kistler, “Calculation of Volterra Kernels for Solutions of Nonlinear Differential Equations,” \JournalTitleSiam Journal on Applied Mathematics 61 (2000).
  73. S. Orcioni, M. Pirani, and C. Turchetti, “Advances in Lee-Schetzen Method for Volterra Filter Identification,” \JournalTitleMultidimensional Systems and Signal Processing 16, 265–284 (2005).
  74. A. Wills, T. B. Schön, L. Ljung, and B. Ninness, “Identification of Hammerstein–Wiener Models,” \JournalTitleAutomatica 49, 70–81 (2013).
  75. X. Liu, Y. Fan, Y. Zhang, M. Cai, L. Liu, L. Yi, W. Hu, and Q. Zhuge, “Fusing Physics to Fiber Nonlinearity Model for Optical Networks Based on Physics-Guided Neural Networks,” \JournalTitleJournal of Lightwave Technology 40, 5793–5802 (2022).
  76. Y. Song, Y. Zhang, C. Zhang, J. Li, M. Zhang, and D. Wang, “PINN for Power Evolution Prediction and Raman Gain Spectrum Identification in C+++L-Band Transmission System,” in Optical Fiber Communication Conference (OFC) 2023, (2023), p. Th1F.5.
  77. U. C. de Moura, D. Zibar, A. Margareth Rosa Brusin, A. Carena, and F. Da Ros, “Fiber-Agnostic Machine Learning-Based Raman Amplifier Models,” \JournalTitleJournal of Lightwave Technology 41, 83–95 (2023).
  78. D. Wang, Y. Song, J. Li, J. Qin, T. Yang, M. Zhang, X. Chen, and A. C. Boucouvalas, “Data-driven Optical Fiber Channel Modeling: A Deep Learning Approach,” \JournalTitleJournal of Lightwave Technology 38, 4730–4743 (2020).
  79. A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, and K. J. Lang, “Phoneme Recognition Using Time-Delay Neural Networks,” \JournalTitleReadings in Speech Recognition pp. 393–404 (1990).
  80. A. G. Reza and J.-K. K. Rhee, “Nonlinear Equalizer Based on Neural Networks for PAM-4 Signal Transmission Using DML,” \JournalTitleIEEE Photonics Technology Letters 30, 1416–1419 (2018).
  81. K. Cho, B. van Merrienboer, C. Gulcehre, F. Bougares, H. Schwenk, and Y. Bengio, “Learning phrase representations using RNN encoder-decoder for statistical machine translation,” in Conference on Empirical Methods in Natural Language Processing (EMNLP 2014), (2014).
  82. S. Hochreiter and J. Schmidhuber, “Long Short-Term Memory,” \JournalTitleNeural Computation 9, 1735–1780 (1997).
  83. T. K. Rusch and S. Mishra, “UnICORNN: A recurrent model for learning very long time dependencies,” in Proceedings of the 38th International Conference on Machine Learning, vol. 139 M. Meila and T. Zhang, eds. (2021), pp. 9168–9178.
  84. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, and I. Polosukhin, “Attention is All you Need,” in Advances in Neural Information Processing Systems, vol. 30 I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, eds. (2017).
  85. N. Zhang, H. Yang, Z. Niu, L. Zheng, C. Chen, S. Xiao, and L. Yi, “Transformer-Based Long Distance Fiber Channel Modeling for Optical OFDM Systems,” \JournalTitleJournal of Lightwave Technology 40, 7779–7789 (2022).
  86. Y. Zhu, J. Ye, L. Yan, T. Zhou, P. Li, X. Zou, and W. Pan, “Transformer-Based High-Fidelity Modeling Method for Radio Over Fiber Link,” \JournalTitleJournal of Lightwave Technology 41, 2657–2665 (2023).
  87. B. Li, Q. Du, T. Zhou, Y. Jing, S. Zhou, X. Zeng, T. Xiao, J. Zhu, X. Liu, and M. Zhang, “ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence Generation,” in Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), S. Muresan, P. Nakov, and A. Villavicencio, eds. (2022), pp. 8335–8351.
  88. A. Gatto, M. Rapisarda, P. Parolari, and P. Boffi, “Discrete Multitone Modulation for Short-Reach Mode Division Multiplexing Transmission,” \JournalTitleJournal of Lightwave Technology 37, 5185–5192 (2019).
  89. G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems,” \JournalTitleJournal of Lightwave Technology 37, 230–244 (2019).
  90. D. Che and W. Shieh, “Approaching the Capacity of Colored-SNR Optical Channels by Multicarrier Entropy Loading,” \JournalTitleJournal of Lightwave Technology 36, 68–78 (2018).
  91. D. Kim and H. Kim, “Capacity-achieving Symbol Distributions for Directly Modulated Laser and Direct Detection Systems,” \JournalTitleOptics Express 31, 12609–12623 (2023).
  92. N.-P. Diamantopoulos, H. Yamazaki, S. Yamaoka, M. Nagatani, H. Nishi, H. Tanobe, R. Nakao, T. Fujii, K. Takeda, T. Kakitsuka, H. Wakita, M. Ida, H. Nosaka, F. Koyama, Y. Miyamoto, and S. Matsuo, “>>>100-GHz Bandwidth Directly-Modulated Lasers and Adaptive Entropy Loading for Energy-Efficient >>>300-Gbps/λ𝜆\lambdaitalic_λ IM/DD Systems,” \JournalTitleJournal of Lightwave Technology 39, 771–778 (2021).
  93. C. Kottke, C. Caspar, V. Jungnickel, R. Freund, M. Agustin, and N. N. Ledentsov, “High Speed 160 Gb/s DMT VCSEL Transmission Using Pre-equalization,” in Optical Fiber Communication Conference, (Optica Publishing Group, 2017), p. W4I.7.
  94. D. Dasalukunte, F. Rusek, and V. Owall, “Multicarrier Faster-Than-Nyquist Transceivers: Hardware Architecture and Performance Analysis,” \JournalTitleIEEE Transactions on Circuits and Systems I: Regular Papers 58, 827–838 (2011).
  95. N. Bamiedakis, D. G. Cunningham, and R. V. Penty, “Linearisation Method of DML-Based Transmitters for Optical Communications Part I: Theory and Simulation Studies,” \JournalTitleJournal of Lightwave Technology 39, 5815–5827 (2021).
  96. Q.-A. Ding, Huixin-Liu, X. Cheng, X.-J. Wang, W. Huang, L. Du, G. Zhu, L. Zheng, and Q. Yang, “Suppressing DFB Lasers Relaxation Oscillations by High-Order Continuous Shaping Current With CNN Prediction,” \JournalTitleIEEE Journal of Quantum Electronics 59, 1–11 (2023).
  97. Z. Feng, N. Li, W. Li, P. He, M. Luo, Q. Hu, L. Huang, and Y. Jiang, “A Simplified Volterra Equalizer Based on System Characteristics for Direct Modulation Laser (DML)-Based Intensity Modulation and Direct Detection (IM/DD) Transmission Systems,” \JournalTitlePhotonics 10 (2023).
  98. N.-P. Diamantopoulos, H. Nishi, W. Kobayashi, K. Takeda, T. Kakitsuka, and S. Matsuo, “On the Complexity Reduction of the Second-Order Volterra Nonlinear Equalizer for IM/DD Systems,” \JournalTitleJournal of Lightwave Technology 37, 1214–1224 (2019).
  99. Z. Xu, C. Sun, T. Ji, H. Ji, and W. Shieh, “Cascade Recurrent Neural Network Enabled 100-Gb/s PAM4 Short-Reach Optical Link Based on DML,” in Optical Fiber Communication Conference (OFC) 2020, (2020), p. W2A.45.
  100. F. Tian and C. Yang, “Deep Belief Network-Hidden Markov Model-based Nonlinear Equalizer for VCSEL based Optical Interconnect,” \JournalTitleScience China Information Sciences 63 (2020).
  101. F. A. Aoudia and J. Hoydis, “End-to-End Learning of Communications Systems Without a Channel Model,” in 2018 52nd Asilomar Conference on Signals, Systems, and Computers, (2018), pp. 298–303.
  102. M. Srinivasan, J. Song, C. Häger, K. Szczerba, H. Wymeersch, and J. Schröder, “Learning Optimal PAM Levels for VCSEL-based Optical Interconnects,” in European Conference on Optical Communication (ECOC) 2022, (2022), p. We2C.3.
  103. L. Minelli, F. Forghieri, T. Shao, A. Shahpari, and R. Gaudino, “TDECQ-Based Optimization of Nonlinear Digital Pre-Distorters for VCSEL-MMF Optical Links Using End-to-End Learning,” \JournalTitleJ. Lightwave Technol. 42, 621–635 (2024).
  104. B. Karanov, M. Chagnon, F. Thouin, T. A. Eriksson, H. Bülow, D. Lavery, P. Bayvel, and L. Schmalen, “End-to-End Deep Learning of Optical Fiber Communications,” \JournalTitleJournal of Lightwave Technology 36, 4843–4855 (2018).
  105. R. T. Jones, T. A. Eriksson, M. P. Yankov, and D. Zibar, “Deep Learning of Geometric Constellation Shaping Including Fiber Nonlinearities,” in 2018 European Conference on Optical Communication (ECOC), (2018).
  106. P. Freire, S. Srivallapanondh, B. Spinnler, A. Napoli, N. Costa, J. E. Prilepsky, and S. K. Turitsyn, “Computational Complexity Optimization of Neural Network-Based Equalizers in Digital Signal Processing: A Comprehensive Approach,” \JournalTitleJournal of Lightwave Technology pp. 1–25 (2024).
  107. J. Cartledge and G. Burley, “The effect of laser chirping on lightwave system performance,” \JournalTitleJournal of Lightwave Technology 7, 568–573 (1989).
  108. J. Cartledge and R. Srinivasan, “Extraction of dfb laser rate equation parameters for system simulation purposes,” \JournalTitleJournal of Lightwave Technology 15, 852–860 (1997).
Citations (3)

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Collections

Sign up for free to add this paper to one or more collections.

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.