Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

By exploiting a causality property of the nonlinear Fourier transform, a novel decision-feedback detection strategy for nonlinear frequency-division multiplexing (NFDM) systems is introduced. The performance of the proposed strategy is investigated both by simulations and by theoretical bounds and approximations, showing that it achieves a considerable performance improvement compared to previously adopted techniques in terms of Q-factor. The obtained improvement demonstrates that, by tailoring the detection strategy to the peculiar properties of the nonlinear Fourier transform, it is possible to boost the performance of NFDM systems and overcome current limitations imposed by the use of more conventional detection techniques suitable for the linear regime

Resource theory of non-Gaussian operations

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is non-increasing under the set of free super-operations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (1) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition and all Gaussian-dilatable non-Gaussian channels; and (2) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian-dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.Comment: 15 pages, 4 figure

WDM channel capacity and its dependence on multichannel adaptation models

Optical multichannel systems are often characterized by the channel capacity of a single channel, assuming a certain adaptation behavior of the other channels. We investigate some common adaptation models, which lead to dramatically different capacities

Nonlinear Fourier transform for optical data processing and transmission:advances and perspectives

Fiber-optic communication systems are nowadays facing serious challenges due to the fast growing demand on capacity from various new applications and services. It is now well recognized that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been steadily growing interest in the application of a powerful mathematical tool-the nonlinear Fourier transform (NFT)-in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to the Kerr effect can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system, however, constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages, and challenges of various recently emerged system designs employing the NFT, as well as the spectral efficiency estimates available up-to-date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers assess the perspectives, understand the bottlenecks, and envision the development paths in the upcoming NFT-based transmission technologies

Digital backpropagation in the nonlinear Fourier domain

Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schrödinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the nonlinear Schrödinger equation can be reverted analytically in the nonlinear Fourier domain through simple phase-shifts, there is no need to discretize the spatial domain. The proposed algorithm requires only OpDlog2 Dq floating point operations to backpropagate a signal given by D samples, independently of the fiber's length, and is therefore highly promising for real-time implementations. The merits of this new approach are illustrated through numerical simulations

Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with 2n degrees of freedom, where n = 2 and n = 3 correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary n and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of n. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for n = 1; 2; 3. At an SNR of 25 dB, the best lower bounds we developed are approximately 3:68 bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of 25 dB, a 16- ASK constellation yields a rate of approximately 3:45 bit per channel use

On nonlinear Fourier transform-based fibre-optic communication systems for periodic signals

As the demand for information rate grows on a daily basis, new ways of improving the efficiency of fibre-optic communication systems, the backbone of the global data network,are highly anticipated. Nonlinear Fourier transform (NFT) is one of the newly emerged techniques showing promising results in recent studies both in simulation and experiment. Along this path, this method has shown its potential to overcome some difficulties of the fibre-optic communication regarding nonlinear distortions, especially the crosstalk between the user’s bands in wavelength division multiplexing (WDM) systems. NFT-based systems, however, in the conventional, widely considered case of vanishing boundary signals, have exhibited some drawbacks related to the computational complexity and spectral efficiency. Both problems are the direct consequences of large signal duration ensued from the vanishing boundary condition. Considering periodic solutions to the nonlinear Schrödinger equation is among attempts to solve this problem. It helps to decrease the processing window at the receiver and gives full control over the communication-related parameters of the signal. Periodic NFT (PNFT) can also be implemented through fast numerical methods which makes it yet more appealing. In this thesis, a general framework to implement PNFT in fibre-optic communication systems is proposed. As the most challenging part of such a system, the inverse transformation stage is particularly taken attention to, and a few ways to perform it are put forward. From the simplest signals with analytically known nonlinear spectrum to a complete periodic solution with arbitrary, finite number of degrees of freedom, several system configurations are conferred and evaluated in terms of their performance. Common measures such as bit error rate, quality factor and mutual information are considered in scrutinising the systems.Based on simulation results, we conclude that the PNFT can, in fact, improve the mutual information by overcoming some shortcomings of the vanishing boundary NFT

Nonlinear digital compensation for spatial multiplexing systems

We review the latest advances on digital backward-propagation for the compensation of inter-channel nonlinear interference in spatial- and wavelength-multiplexed systems. Different solution methods of the multimode Schrödinger equation are compared for challenging linear mode coupling and differential mode delay conditions, highlighting the significant relaxation of the step size requirements provided by the separate-channels approach