Digital Back Research Articles

Joint intra and inter-channel nonlinear compensation scheme based on improved learned digital back propagation for WDM systems.

In this paper, we improve the learned digital back propagation (LDBP) and propose a novel joint intra and inter-channel nonlinearity compensation scheme for polarization division multiplexing wavelength-division multiplexed (PDM-WDM) systems. From the perspective of interpretable neural network, the scheme realizes the alternating compensation of chromatic dispersion (CD) and nonlinearity based on physical models. The chromatic dispersion compensation (CDC) adopts one-dimensional convolution operation in the time domain. Moreover, the pulse-broadening effect is introduced into the overlap-and-save method. For nonlinear compensation, the improved joint model is applied, and the impact of the intra-channel pulse broadening and the walk-off effect between different channels caused by CD on the nonlinear effect is considered. To validate the effectiveness of the proposed scheme, we construct an 11-channel simulation system of 36 GBaud PDM uniform 16 quadrature amplitude modulation (PDM-16QAM) 1600 km and 64 GBaud PDM-64QAM 400 km, as well as a 5-channel experimental system of 28 GBaud PDM-16QAM 806.4 km. The simulation results show that the performance of PDM-16QAM with 0.5 steps per span and PDM-64QAM with 2 steps per span improve the Q-factor by approximately 0.75 dB and 0.54 dB at the optimal launch power, compared with the linear compensation scheme. The transmission performance of PDM-16QAM is higher than that of digital back propagation with 5 steps per span (DBP-5StPS), and the complexity is only 31.36% of that of DBP-5StPS. The performance of PDM-64QAM is higher than that of DBP-10StPS, with a complexity of 62.72%. The experimental results show that the performance of PDM-16QAM with 0.5 steps per span is improved with 0.86 dB Q-factor improvement compared with the linear compensation scheme at the optimal launch power, and the performance of the proposed scheme is higher than that of DBP-5StPS with a complexity of only 23.68%.

Nonlinear compensation for few-mode fiber MDM-WDM systems using probabilistic neural network

In this paper, we propose for the first time to apply probabilistic neural network (PNN) to fiber nonlinear compensation (NLC) in a high-speed coherent optical communication system that combines few-mode fiber (FMF) mode division multiplexing (MDM) with wavelength division multiplexing (WDM). By training on a small number of symbols, the PNN equalizer can compute the statistical distribution of the signal nonlinearity, make decisions on test symbols, and thereby compensate for the nonlinear impairments of the signals. To verify the effectiveness of the proposed scheme, we construct a MDM-WDM simulation system with 28 GBaud polarization division multiplexing (PDM) 16-quadrature amplitude modulation(QAM) and 64 GBaud PDM-64QAM, 6 spatial mode signals are transmitted over 11 wavelength channels with link lengths of 1500 km and 400 km, respectively. The results show that the PNN equalizer can make nonlinear judgments on received signals and effectively compensate the signal impairments caused by Kerr nonlinearity and device nonlinearity in a large launch power range after undergoing carrier phase recovery (CPR). Meanwhile, this scheme exhibits strong robustness against residual linear mode coupling (LMC), differential mode group delay (DMGD), and amplified spontaneous emission (ASE) noise. Finally, by the computational complexity comparison, it is proved that the complexity of the probabilistic neural network nonlinear compensation (PNN NLC) scheme is lower than that of digital back propagation (DBP) with comparable performance, which is on the order O(N).

Multichannel meta-imagers for accelerating machine vision.

Rapid developments in machine vision technology have impacted a variety of applications, such as medical devices and autonomous driving systems. These achievements, however, typically necessitate digital neural networks with the downside of heavy computational requirements and consequent high energy consumption. As a result, real-time decision-making is hindered when computational resources are not readily accessible. Here we report a meta-imager designed to work together with a digital back end to offload computationally expensive convolution operations into high-speed, low-power optics. In this architecture, metasurfaces enable both angle and polarization multiplexing to create multiple information channels that perform positively and negatively valued convolution operations in a single shot. We use our meta-imager for object classification, achieving 98.6% accuracy in handwritten digits and 88.8% accuracy in fashion images. Owing to its compactness, high speed and low power consumption, our approach could find a wide range of applications in artificial intelligence and machine vision applications.

Software-defined meta-optics

Rapid advancements in autonomous systems and the Internet of Things have necessitated the development of compact and low-power image sensors to bridge the gap between the digital and physical world. To that end, sub-wavelength diffractive optics, commonly known as meta-optics, have garnered significant interest from the optics and photonics community due to their ability to achieve multiple functionalities within a small form factor. Despite years of research, however, the performance of meta-optics has often remained inferior compared to that of traditional refractive optics. In parallel, computational imaging techniques have emerged as a promising path to miniaturize optical systems, albeit often at the expense of higher power and latency. The lack of desired performance from either meta-optical or computational solutions has motivated researchers to look into a jointly optimized meta-optical–digital solution. While the meta-optical front end can preprocess the scene to reduce the computational load on the digital back end, the computational back end can in turn relax requirements on the meta-optics. In this Perspective, we provide an overview of this up-and-coming field, termed here as “software-defined meta-optics.” We highlight recent contributions that have advanced the current state of the art and point out directions toward which future research efforts should be directed to leverage the full potential of subwavelength photonic platforms in imaging and sensing applications. Synergistic technology transfer and commercialization of meta-optic technologies will pave the way for highly efficient, compact, and low-power imaging systems of the future.

Review on optical solitons for long haul transmission

Abstract Fiber optics telecommunication is the currently established backbone infrastructure for most of the information flow across the world. New services and applications are causing an exponential increase in Internet traffic, increasing transmission rate, and high bandwidth-demanding applications have been propelling the data rate per wavelength to approach the speed limit of electronics. In a few years, the current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Also, the dispersion phenomenon is a problem for high bit rates and long-haul optical communication systems. An easy solution to this problem is optical solitons pulses that preserve their shape over long distances. An optical soliton is formed by balancing nonlinearity (self-phase modulation) and dispersion phenomenon (group velocity dispersion). In this review article, a detailed study of optical solitons is presented along with its recent progress. Advanced numerical methods such as Darboux transform (DT), digital back propagation, split step Fourier, and forward–backward methods are also discussed in this paper which is used for solving higher-order solitons.

The Role of Virtual Triage in Improving Clinician Experience and Satisfaction: A Narrative Review.

This review examines the literature on improving clinician satisfaction with a focus on what has been most effective in improving experience from the perspective of clinicians, and the potential role that virtual triage (VT) technology can play in delivering positive clinician experiences that improve clinical care, and bring value to health care delivery organizations (HDOs). Review and synthesis of evidence on clinician satisfaction indicating a potential for VT to favorably impact clinician experience, sense of effectiveness, efficiency, and reduction of administrative task burden. Analysis considers how to conceptualize and the value of improving clinician experience, leading clinician dissatisfiers, and the potential role of VT in improving clinician experience/satisfaction. Contributors to poor clinician experience/satisfaction where VT could have a beneficial impact include better managing resource limitations, administrative workload, lack of care coordination, information overload, and payer interactions. VT can improve clinician experience through the technology's ability to leverage real-time actionable data clinicians can use, streamlining patient-clinician communications, personalizing care delivery, optimizing care coordination, and better aligning digital/virtual services with clinical practice. From an organizational perspective, improvements in clinician experience and satisfaction derive from establishing an effective digital back door, increasing the clinical impact of and satisfaction derived from telemedicine and virtual care, and enhancing clinician centricity. By embracing digital transformation and implementing solutions such as VT that focus on improving patient and clinician experience, HDOs can address barriers to delivery of high-quality, efficient, and cost-effective care. VT is a digital health tool that can create a more streamlined and satisfying experience for clinicians and the patients they care for. VT is a technology solution that can help clinicians make faster more informed decisions, reduces avoidable care, improves communication with patients and within care teams, and lowers their administrative burden so they have more quality time to care for patients.

DSP optimization technique based on deep learning to account for the effects of fiber nonlinearity

The first section of this work is the classification of digital signal processing (DSP) techniques for adjusting, minimizing, and utilizing fiber nonlinearities in coherent fiber optic transmission systems. Then, different experimental optimization methods based on the Volterra series of Deep Neural Networks (DNN) and the Digital Back Propagation (DBP) methods are contrasted with the aid of specific instances. Concrete examples reinforce the techniques. The findings demonstrate the viability of a DSP strategy using deep learning for inexpensive optical comms, resulting in significant performance gains and computational efficiencies. The optimal DSP, it is further determined, should balance minimizing transmission flaws with minimizing additional distortions brought on by ineffective linear or nonlinear correction steps as a result of in-line amplifier noise. It is demonstrated that, in addition to improving system performance, machine learning (ML) improves analytical reasoning, provides deeper mathematical comprehension of fiber nonlinearity correction, and advances theoretical knowledge in related fields.

How Accountants Stay in the C-Suite (or Disappear Into the Digital Back Office)

The digital era is hitting the practice of accounting hard. Really hard. So much “accounting” falls right in the oncoming automation rush. So what happens to accounting in the future of work? What value will it provide the C-suite? Will value be defined around incremental changes, or does accounting need to reinvent itself? Or is accounting destined to disappear into the back office?

DBP with modified field intensity averaging for low-complexity digital coherent systems

We numerically and experimentally assessed novel optical nonlinear compensation systems and modified field-intensity averaging digital back propagation (mFIA-DBP). mFIA-DBP achieves a higher performance than DBP with lower computational complexity. For the 50 Gbaud-DP-16QAM system in the simulation, a higher performance was obtained by mFIA-DBP with one steps/span (StPS) over DBP with 2StPS. A comparison of the computational complexity in terms of the number of real multiplications shows that mFIA-DBP can compensate for the signal nonlinearity after a 4000 km transmission with 66.5% of the DBP. We confirmed the superior performance of mFIA-DBP in the high-power range and showed that this trend was consistent in experiments with the simulations.

Adaptive digital back propagation exploiting adjoint-based optimization for fiber-optic communications.

This work proposes a novel and powerful adaptive digital back propagation (A-DBP) method with a fast adaption process. Given that the total transmission distance is known, the proposed A-DBP algorithm blindly compensates for the linear and nonlinear distortions of optical fiber transmission systems and networks, without knowing the launch power and channel parameters. An adjoint-based optimization (ABO) technique is proposed to significantly accelerate the parameters estimation of the A-DBP. The ABO algorithm utilizes a sequential quadratic programming (SQP) method coupled with an adjoint sensitivity analysis (ASA) approach to rapidly solve the A-DBP training problem. The design parameters are optimized using the minimum overhead of only one extra system simulation. Regardless of the number of A-DBP design parameters, the derivatives of the training objective function with respect to all parameters are estimated using only one extra adjoint system simulation per optimization iterate. This is contrasted with the traditional finite-difference (FD)-based optimization methods whose sensitivity analysis calculations cost per iterate scales linearly with the number of parameters. The robustness, performance, and efficiency of the proposed A-DBP algorithm are demonstrated through applying it to mitigate the distortions of 4-span and 20-span optical fiber communication systems. Coarse-mesh A-DBPs with less number of virtual spans are also used to significantly reduce the computational complexity of the equalizer, achieving compensation performance higher than that obtained using the coarse-mesh DBP with the exact channel parameters and full number of virtual spans.

Learning-based digital back propagation to compensate for fiber nonlinearity considering self-phase and cross-phase modulation for wavelength-division multiplexed systems

We propose a learning-based digital back propagation (LDBP) technique that addresses self-phase modulation (SPM) and cross-phase modulation (XPM) of a wavelength-division multiplexed (WDM) optical signal. The LDBP has a structure defined for each of the individual channels of a WDM signal, and connections between the channels address the XPM to effectively compensate for nonlinear waveform distortion of the signal in long-distance optical transmission systems. We attempt to optimize the limited number of parameters used in the structure such as the dispersion, nonlinear coefficient, and walkoff parameter to compensate for the nonlinear phase shift induced by the XPM. We derive equations to update the parameters through an iterative process based on the stochastic gradient descent algorithm. We verify the effectiveness of the proposed LDBP technique through a transmission experiment that uses an 11-channel WDM, 32-Gbaud, dual-polarization 16 quadrature amplitude modulation (QAM), and probabilistically shaped (PS) 64QAM signals. With the focus on the LDBP with a 1-step/span configuration, we operate the learning process using the received 16QAM signal in the experiment. We confirmed the successful convergence of particular parameters of the model of the transmission line after the developed learning procedure. We apply the LDBP with fixed optimized parameters to the received waveforms of the PS-64QAM signals and compare the performance with some DBPs. We observed that the proposed LDBP technique that considers XPM with 1-step/span configuration exhibits the best performance in compensating for nonlinear waveform distortion. Additionally, the learning process is effective for the case considering both SPM and XPM compared with the case of SPM only. Finally, we investigate the computational complexity of the LDBP and reveal that the total calculation cost is of the same order as that of a conventional DBP considering only SPM with a 2-step/span configuration.

Perturbation Theory-Aided Learned Digital Back-Propagation Scheme for Optical Fiber Nonlinearity Compensation

Derived from the regular perturbation treatment of the nonlinear Schr&#x00F6;dinger equation, a machine learning-based scheme to mitigate the intra-channel optical fiber nonlinearity is proposed. Referred to as the perturbation theory-aided (PA) learned digital back propagation (LDBP), the proposed scheme constructs a deep neural network (DNN) in a way similar to the split-step Fourier method: linear and nonlinear operations alternate. Inspired by the perturbation analysis, the intra-channel cross phase modulation term is conveniently represented by matrix operations in the DNN. The introduction of this term in each nonlinear operation considerably improves the performance, as well as enables the flexibility of PA-LDBP by adjusting the numbers of spans per step. The proposed scheme is evaluated by numerical simulations of a single-carrier optical fiber communication system operating at 32 Gbaud with 64-quadrature amplitude modulation and 20 &#x00D7; 80 km transmission distance. The results show that the proposed scheme achieves approximately 1 dB, 1.2 dB, 1.2 dB, and 0.5 dB performance gain in terms of <inline-formula><tex-math notation="LaTeX">${\it Q}$</tex-math></inline-formula> factor over LDBP, when the numbers of spans per step are 1, 2, 4, and 10, respectively. Two methods are proposed to reduce the complexity of PA-LDBP, i.e., pruning the number of perturbation coefficients and chromatic dispersion compensation in the frequency domain for multi-span per step cases. Investigation of the performance and complexity suggests that PA-LDBP attains improved performance gains with reduced complexity when compared to LDBP in the cases of 4 and 10 spans per step.

Fiber nonlinear impairments compensation based on nonlinear step size and modified adaptive digital back propagation

Abstract In this paper, we propose a low-complexity fiber nonlinearity impairments compensation scheme based on nonlinear step size and modified adaptive digital back propagation. To verify the feasibility of the proposed algorithm, we construct a simulation system of single channel 12.5 GBaud polarization division multiplexing 16-ary quadrature amplitude modulation (PDM-16QAM) optical transmission system. Comprehensive numerical simulation results demonstrate that the proposed scheme can not only search for the fiber nonlinear coefficient adaptively, but also has the characteristics of high performance and low complexity.

Optical nonlinear impairment compensation based on Deep Neural Network (DNN) for coherent modulation systems

One and most important of the intrinsic challenges facing the optical fibers communication systems and main restriction to limited the system capacity is the fiber nonlinearity impairments. Classical Nonlinear Impairments Compensation (NLC) techniques are widely used and exist on the basis of the approximate Nonlinear Schrodinger Equation (NLSE) solution, their use and requires excessive signal resources, and high-level knowledge accuracy. In addition, their parameterizations can be numerically unstable. Algorithms of Artificial Intelligence (AI) are utilized to determine and resolve the deficiencies by learning from the receiving information itself. To the best of our knowledge, this novel approach is implemented. Therefore, this article proposes a system nonlinearity and single-step compensation algorithm according to a Deep Neural Network (DNN) as a new alternative framework for future optical communications. So, we proposed to use the DNN to compensation the nonlinearity impairments in optical communication systems. The suggested DNN is accessible to higher-order QAM modulations with achieving greater gain in nonlinear impairments compensation compare to classical NLC techniques based on Digital Back Propagation (DBP). Its performance is evaluated experimentally on coherent 65536-bit sequence length with 25 Gbaud single polarization 4-16-64 QAM with 50 and 120 Gb/s back-to-back measurements through using pre-distort symbols at the transmitter for showing Q factor development after 5000 km standard single-mode fiber transmission link. The DNN's weights are to train data with the intrachannel cross-phase modulation (XPM) and self-phase modulation (SPM) that used as input features.

DIGITAL TECHNOLOGIES IN AGRICULTURAL ENTERPRISE MANAGEMENT

Abstract. The article investigates the theoretical and practical principles of using digital technologies in the management of agricultural enterprises. The dynamics of Ukraine’s position in the world ranking of digital competitiveness is analyzed, the leading countries in digital transformation of economic systems are identified in order to study the progressive experience of digitalization of the economy, its spheres, agriculture in particular. The evolution of technologies and business ideas in agriculture, which can be represented as a two — factor model of development, is studied. The comparative analysis of approaches to conducting agrarian business is carried out. It is noted that almost all large holdings in Ukraine are now actively investing and implementing digital solutions, it can also be seen that at all levels of agricultural production the country already has its leaders with extensive experience in implementing digital technologies. It is hypothesized that an important indicator of the development of digitalization are digital technologies formed with world experience. They can be divided into eight main areas of activity: FMS (farm management systems); data collection and aggregation (for precision farming), forecasting; marketplaces; robotic equipment and drones; sensors; reasonable irrigation; animal husbandry; next generation farms. Based on world experience, the peculiarities of the application of certain digital technologies in certain areas of agriculture are considered and assumptions are made about the possibility of their use in the realities of domestic agricultural production. It is concluded that the path or vector of digitalization in agriculture can be represented as three stages for agricultural holdings and two stages (without the last) for relatively small farmers: the first stage characterizes the agricultural company with efficient business processes (here must be implemented and fully integrated internal accounting systems). and a single digital back office); the second stage of development is a digital technology company (it uses innovative technologies such as precision farming, artificial intelligence (AI), computer vision (CV), machine learning (ML), etc.); the third stage is the ecosystem of the agricultural holding (a whole infrastructure of innovations has already been built here). Keywords: digitalization, digital technologies, agriculture, digitalization of agricultural production, digital infrastructure of agricultural enterprise. JEL Classification Q16 Formulas: 0; fig.: 3; tabl.: 0; bibl.: 13.

Effect of optical pulse shaping and adaptive equalization on the performance of 100G DP-QPSK WDM system

Abstract Dual polarization quadrature phase shifting keying (DP-QPSK) modulation format along with coherent receiver helps in increasing the data carrying capability of existing optical networks without any major change in existing transmission infrastructure. The various linear and nonlinear fiber effects, frequency and phase errors are corrected in electrical domain at the receiver end with digital back propagation algorithms (DBP) instead of in-line compensation. In such a case the selection of optimum values of system parameters make the task easier for DBP algorithms. This paper highlights the importance of finding optimum operating point of continuous modulus algorithm (CMA) for better adaptive equalization (AE). The paper also discusses the optical pulse shaping using Gaussian optical band-pass filter to improve the spectral characteristics of DP-QPSK signal.

An Adjoint Sensitivity Analysis Approach Exploiting Inverse Nonlinear Schrödinger Equation

This paper presents a computationally inexpensive adjoint sensitivity analysis (ASA) approach that is based on the inverse nonlinear Schrodinger equation (INLSE). The introduced algorithm significantly accelerates the parameter estimation of adaptive digital back propagation (ADPB), used for blindly mitigating the linear and nonlinear distortions of optical fiber communication systems and networks. The approach efficiency is illustrated here through a numerical example.

Nonlinear/dispersion compensation in dual polarization 128-QAM system incorporating optical backpropagation

Abstract In order to cater long distance optical network units (subscribers), optical networks with prolonged reach are needed. In this study, an optical back propagation (OBP) dual polarization (DP)-128 QAM-based system is proposed to cope with nonlinear impairments in wavelength division multiplexing (WDM) systems. In pre, post and symmetrical configurations, the OBP module consisting of the optical phase conjugator (OPC), Raman fiber amplifier (RFA) and erbium doped fiber amplifier (EDFAs) is examined. Using dispersion compensation fiber (DCF) as RFA with dual directional pumping, ideal OBP conditions are simulated. DP-128 quadrature amplitude modulation (QAM) system is proposed with symmetrical OBP and compared with single channel digital back propagation (DBP), wideband DBP, pre OBP-forward pumping, pre OBP with backward pumping, pre OBP with dual directional pumping, post OBP with dual directional pumping. It is observed that symmetrical OBP configuration with dual direction pumping provide enhanced results and successfully cover 6500 km at bit error rate (BER) 10−3.

Comparison of Short Blocklength Sphere Shaping and Nonlinearity Compensation in WDM Systems

In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achieves similar performance in terms of finite length bit-metric decoding rate to uniform signaling with one step per span DBP. In the context of a dense wavelength-division multiplexing (WDM) transmission system, we show that ESS outperforms uniform signaling with DBP for different step sizes.

Compensation of nonlinear distortion in coherent optical OFDM systems using a MIMO deep neural network-based equalizer.

A novel nonlinear equalizer based on a multiple-input multiple-output (MIMO) deep neural network (DNN) is proposed and experimentally demonstrated for compensation of inter-subcarrier nonlinearities in a 40 Gb/s coherent optical orthogonal frequency division multiplexing system. Experimental results reveal that MIMO-DNN can extend the power margin by 4 dB at 2000 km of standard single-mode fiber transmission when compared to linear compensation or conventional single-input single-output DNN. It is also found that MIMO-DNN outperforms digital back propagation by increasing up to 1 dB the effectiveQ-factor and reducing by a factor of three the computational cost.