Neural network-aided receivers for soliton communication impaired by solitonic interaction

In this paper, different neural network-based methods are proposed to improvethe achievable information rate in amplitude-modulated soliton communication systems. The proposed methods use simulated data to learn effective soliton detection by suppressing nonlinear impairments beyond amplifier noise, including intrinsic inter-soliton interaction, Gordon-Haus effect-induced timing jitter, and their combined impact. We first present a comprehensive study of these nonlinear impairments based on numerical simulations. Then, two neural network designs are developed based on a regression network and a classifier. We estimate the achievable information rates of the proposed learning-based soliton detection schemes as well as two modelbased benchmark schemes, including the nonlinear Fourier transform eigenvalue estimation and continuous spectrum-aided eigenvalue estimation schemes. Our results demonstrate that bothlearning-based designs lead to substantial performance gains when compared to the benchmark schemes. Importantly, we highlight that exploiting the channel memory, introduced by solitonic interactions, can yield additional gains in the achievable information rate. Through a comparative analysis of the two neural network designs, we establish that the classifier design exhibits superioradaptability to interaction impairment and is more suitable for symbol detection tasks in the context of the investigated scenarios

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission

We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse

For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics of the received nonlinear spectrum in the presence of additive white Gaussian noise (AWGN) is an open problem. We present a novel method, based on the Fourier collocation algorithm, to compute these statistics.Comment: Accepted for presentation at European Conference on Optical Communications (ECOC) 201

Microresonator solitons for massively parallel coherent optical communications

Optical solitons are waveforms that preserve their shape while propagating, relying on a balance of dispersion and nonlinearity. Soliton-based data transmission schemes were investigated in the 1980s, promising to overcome the limitations imposed by dispersion of optical fibers. These approaches, however, were eventually abandoned in favor of wavelength-division multiplexing (WDM) schemes that are easier to implement and offer improved scalability to higher data rates. Here, we show that solitons may experience a comeback in optical communications, this time not as a competitor, but as a key element of massively parallel WDM. Instead of encoding data on the soliton itself, we exploit continuously circulating dissipative Kerr solitons (DKS) in a microresonator. DKS are generated in an integrated silicon nitride microresonator by four-photon interactions mediated by Kerr nonlinearity, leading to low-noise, spectrally smooth and broadband optical frequency combs. In our experiments, we use two interleaved soliton Kerr combs to transmit a data stream of more than 50Tbit/s on a total of 179 individual optical carriers that span the entire telecommunication C and L bands. Equally important, we demonstrate coherent detection of a WDM data stream by using a pair of microresonator Kerr soliton combs - one as a multi-wavelength light source at the transmitter, and another one as a corresponding local oscillator (LO) at the receiver. This approach exploits the scalability advantages of microresonator soliton comb sources for massively parallel optical communications both at the transmitter and receiver side. Taken together, the results prove the significant potential of these sources to replace arrays of continuous-wave lasers in high-speed communications.Comment: 10 pages, 3 figure

Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the Inverse Scattering Transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. Corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODE's for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure

Highly tunable repetition-rate multiplication of mode-locked lasers using all-fibre harmonic injection locking

Higher repetition-rate optical pulse trains have been desired for various applications such as high-bit-rate optical communication, photonic analogue-to-digital conversion, and multi- photon imaging. Generation of multi GHz and higher repetition-rate optical pulse trains directly from mode-locked oscillators is often challenging. As an alternative, harmonic injection locking can be applied for extra-cavity repetition-rate multiplication (RRM). Here we have investigated the operation conditions and achievable performances of all-fibre, highly tunable harmonic injection locking-based pulse RRM. We show that, with slight tuning of slave laser length, highly tunable RRM is possible from a multiplication factor of 2 to >100. The resulting maximum SMSR is 41 dB when multiplied by a factor of two. We further characterize the noise properties of the multiplied signal in terms of phase noise and relative intensity noise. The resulting absolute rms timing jitter of the multiplied signal is in the range of 20 fs to 60 fs (10 kHz - 1 MHz) for different multiplication factors. With its high tunability, simple and robust all-fibre implementation, and low excess noise, the demonstrated RRM system may find diverse applications in microwave photonics, optical communications, photonic analogue-to-digital conversion, and clock distribution networks.Comment: 25 pages, 9 figure