New approaches to coding information using inverse scattering transform

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption

Nonlinear Fourier Transform in application to long-haul optical communications

The optical fibres form a basis of the long-haul transmissions systems, and is a significant component of the connectivity infrastructure. Rapidly growing demand in data traffic requires instantaneous imperative actions with long-term effect to meet the future expansion of the digital economy. The current optical networks resources are overstretched, and the further extensive utilisation will ultimately constrain the development of other economic sectors. The intelligent and effective usage of the installed infrastructure can shift forward the existent limitations, keeping the cost low because of avoiding of the reinstallation. One of the principal constrain, which bounds the further optical fibre capacity grows, is the existence of undesirable nonlinear phenomena, the so-called Kerr nonlinearity, causing self-phase, cross-phase modulation and four-wave mixing. The combination of advanced achievements of mathematical physics, together with communication engineering and information theory allowed to implement the so-called nonlinear Fourier transform (NFT) approach to optical communication. In its paradigm, the fibre nonlinearity is considered as a valuable part of the model, and the NFT mapping effectively (de)composes the signal to naturally non-interacting modes. The NFT concept can be applied to the signal propagation model with either vanishing or periodic boundary condition, which involves the different structures of parameters for manipulation. In this thesis, I focused on the investigation of boundary condition cases, discovering analytical properties, available degrees of freedom, developing numerical methods, and coding approaches; then examining their performance via the simulation of optical transmission systems. The results allow us to conclude the existence of several technical limitations, which limit the achievable transmission quality and data-rate. These include: the deviation of the channel model from the purely integrable, nonlinear and not explicit coupling of the resulting signal parameters, numerical methods accuracy and amplifiers noise accumulation. In spite of those, the simulations demonstrate the considerable performance of NFT-based communication systems