Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation

We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the NFT-Net as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. This advantage becomes more pronounced when the noise level is sufficiently high, and we train the neural network on the noise-corrupted field profiles. The maximum restoration quality corresponds to the case where the signal-to-noise ratio of the training data coincides with that of the validation signals. Finally, we also demonstrate that the NFT b-coefficient important for optical communication applications can be recovered with high accuracy and denoised by the neural network with the same architecture

Advanced optical fibre communication via nonlinear Fourier transform

Optical fibre communication using the Nonlinear Fourier transform (NFT) is one of the potential solutions to tackle the so-called capacity crunch problem in long-haul optical fibre networks. The NFT transforms the nonlinear propagation of temporal signal, governed by the nonlinear Schr¨odinger equation (NLSE), into simple linear evolutions of continuous and discrete spectra in the so-called nonlinear spectral domain. These spectra and the corresponding nonlinear spectral domain, defined by the NFT, are the generalized counterparts of the linear spectrum and frequency domain defined by the ordinary Fourier transform. Using the NFT, the optical fibre channel is effectively linearised, and the basic idea is to utilize degrees of freedom in the nonlinear spectral domain for data transmission. However, many aspects of this concept require rigorous investigation due to complexity and infancy of the approach. In this thesis, the aim is to provide a comprehensive investigation of data transmission over mainly the continues spectrum (CS) and partly over of the discrete spectrum (DS) of nonlinear optical fibres. First, an optical fibre communication system is defined, in which solely the CS carries the information. A noise model in the nonlinear spectral domain is derived for such a system by asymptotic analysis as well as extensive simulations for different scenarios of practical interest. It is demonstrated that the noise added to the signal in CS is severely signal-dependent such that the effective signalling space is limited. The variance normalizing transform (VNT) is used to mathematically verify the limits of signalling spaces and also estimate the channel capacity. The numerical results predict a remarkable capacity for signalling only on the CS (e.g., 6 bits/symbol for a 2000-km link), yet it is demonstrated that the capacity saturates at high power. Next, the broadening effect of chromatic dispersion is analysed, and it is confirmed that some system parameters, such as symbol rate in the nonlinear spectral domain, can be optimized so that the required temporal guard interval between the subsequently transmitted data packets is minimized, and thus the effective data rate is significantly enhanced. Furthermore, three modified signalling techniques are proposed and analysed based on the particular statistics of the noise added to the CS. All proposed methods display improved performance in terms of error rate and reach distance. For instance, using one of the proposed techniques and optimized parameters, a 7100-km distance can be reached by signalling on the CS at a rate of 9.6 Gbps. Furthermore, the impact of polarization mode dispersion (PMD) is examined for the first time, as an inevitable impairment in long-haul optical fibre links. By semi-analytical and numerical investigation, it is demonstrated that the PMD affects the CS by causing signal-dependent phase shift and noise-like errors. It is also verified that the noise is still the dominant cause of performance degradation, yet the effect of PMD should not be neglected in the analysis of NFT-based systems. Finally, the capacity of soliton communication with amplitude modulation (part of the degrees of freedom of DS) is also estimated using VNT. For the first time, the practical constraints, such as the restricted signalling space due to limited bandwidth, are included in this capacity analysis. Furthermore, the achievable data rates are estimated by considering an appropriately defined guard time between soliton pulses. Moreover, the possibility of transmitting data on DS accompanied by an independent CS signalling is also validated, which confirms the potentials of the NFT approach for combating the capacity crunch

Biometrics

Biometrics uses methods for unique recognition of humans based upon one or more intrinsic physical or behavioral traits. In computer science, particularly, biometrics is used as a form of identity access management and access control. It is also used to identify individuals in groups that are under surveillance. The book consists of 13 chapters, each focusing on a certain aspect of the problem. The book chapters are divided into three sections: physical biometrics, behavioral biometrics and medical biometrics. The key objective of the book is to provide comprehensive reference and text on human authentication and people identity verification from both physiological, behavioural and other points of view. It aims to publish new insights into current innovations in computer systems and technology for biometrics development and its applications. The book was reviewed by the editor Dr. Jucheng Yang, and many of the guest editors, such as Dr. Girija Chetty, Dr. Norman Poh, Dr. Loris Nanni, Dr. Jianjiang Feng, Dr. Dongsun Park, Dr. Sook Yoon and so on, who also made a significant contribution to the book