skip to main content


Title: Physical-layer impairment estimation for arbitrary spectral-shaped signals in optical networks
In long-haul fiber-optic networks, precise modeling of physical-layer impairments (PLIs) is crucial to optimizing network resource usage while ensuring adequate transmission quality. In order to accurately estimate PLIs, many mathematical models have been proposed. Among them, the so-called Gaussian noise (GN) model is one of the most accurate and simple enough to use on complex continental-size networks. However, the closed-form GN model assumes that the signals can be represented as having rectangular spectra, leading to a significant estimation error in typical cases when this assumption is violated. We propose the component-wise Gaussian noise (CWGN) PLI model that can account for arbitrary spectral-shaped demands. The CWGN model is computationally simple and suitable for most network management approaches. Results indicate that the CWGN model can prevent as much as a 136% overestimation of the PLIs resulting from the closed-form GN model applied to network lightpaths containing cascaded filters.  more » « less
Award ID(s):
1718130
NSF-PAR ID:
10475719
Author(s) / Creator(s):
;
Publisher / Repository:
Optica
Date Published:
Journal Name:
Optics Express
Volume:
30
Issue:
10
ISSN:
1094-4087
Page Range / eLocation ID:
17351
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Deep learning holds a great promise of revolutionizing healthcare and medicine. Unfortunately, various inference attack models demonstrated that deep learning puts sensitive patient information at risk. The high capacity of deep neural networks is the main reason behind the privacy loss. In particular, patient information in the training data can be unintentionally memorized by a deep network. Adversarial parties can extract that information given the ability to access or query the network. In this paper, we propose a novel privacy-preserving mechanism for training deep neural networks. Our approach adds decaying Gaussian noise to the gradients at every training iteration. This is in contrast to the mainstream approach adopted by Google's TensorFlow Privacy, which employs the same noise scale in each step of the whole training process. Compared to existing methods, our proposed approach provides an explicit closed-form mathematical expression to approximately estimate the privacy loss. It is easy to compute and can be useful when the users would like to decide proper training time, noise scale, and sampling ratio during the planning phase. We provide extensive experimental results using one real-world medical dataset (chest radiographs from the CheXpert dataset) to validate the effectiveness of the proposed approach. The proposed differential privacy based deep learning model achieves significantly higher classification accuracy over the existing methods with the same privacy budget. 
    more » « less
  2. The nonlinear Gaussian-noise (GN) model is a useful analytical tool for the estimation of the impact of distortion due to Kerr nonlinearity on the performance of coherent optical communications systems with no inline dispersion compensation. The original nonlinear GN model was formulated for coherent optical communications systems with identical single-mode fiber spans. Since its inception, the original GN model has been modified for a variety of link configurations. However, its application to coherent optical communications systems with hybrid fiber spans, each composed of multiple fiber segments with different attributes, has attracted scarcely any attention. This invited paper is dedicated to the extended nonlinear GN model for coherent optical communications systems with hybrid fiber spans. We review the few publications on the topic and provide a unified formalism for the analytical calculation of the nonlinear noise variance. To illustrate the usefulness of the extended nonlinear GN model, we apply it to coherent optical communications systems with fiber spans composed of a quasi-single-mode fiber segment and a single-mode fiber segment in tandem. In this configuration, a quasi-single-mode fiber with large effective area is placed at the beginning of each span, to reduce most of the nonlinear distortion, followed by a single-mode fiber segment with smaller effective-area, to limit the multipath interference introduced by the quasi-single-mode fiber to acceptable levels. We show that the optimal fiber splitting ratio per span can be calculated with sufficient accuracy using the extended nonlinear GN model for hybrid fiber spans presented here. 
    more » « less
  3. The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the classical central limit theorem (CLT) kicks in. This assumption is often made for mathematical convenience, since it enables SGD to be analyzed as a stochastic differential equation (SDE) driven by a Brownian motion. We argue that the Gaussianity assumption might fail to hold in deep learning settings and hence render the Brownian motion-based analyses inappropriate. Inspired by non-Gaussian natural phenomena, we consider the GN in a more general context and invoke the generalized CLT (GCLT), which suggests that the GN converges to a heavy-tailed -stable random variable. Accordingly, we propose to analyze SGD as an SDE driven by a Lévy motion. Such SDEs can incur ‘jumps’, which force the SDE transition from narrow minima to wider minima, as proven by existing metastability theory. To validate the -stable assumption, we conduct extensive experiments on common deep learning architectures and show that in all settings, the GN is highly non-Gaussian and admits heavy-tails. We further investigate the tail behavior in varying network architectures and sizes, loss functions, and datasets. Our results open up a different perspective and shed more light on the belief that SGD prefers wide minima. 
    more » « less
  4. Legged robots with point or small feet are nearly impossible to control instantaneously but are controllable over the time scale of one or more steps, also known as step-to-step control. Previous approaches achieve step-to-step control using optimization by (1) using the exact model obtained by integrating the equations of motion, or (2) using a linear approximation of the step-to-step dynamics. The former provides a large region of stability at the expense of a high computational cost while the latter is computationally cheap but offers limited region of stability. Our method combines the advantages of both. First, we generate input/output data by simulating a single step. Second, the input/output data is curve fitted using a regression model to get a closed-form approximation of the step-to-step dynamics. We do this model identification offline. Next, we use the regression model for online optimal control. Here, using the spring-load inverted pendulum model of hopping, we show that both parametric (polynomial and neural network) and non-parametric (gaussian process regression) approximations can adequately model the step-to-step dynamics. We then show this approach can stabilize a wide range of initial conditions fast enough to enable real-time control. Our results suggest that closed-form approximation of the step-to-step dynamics provides a simple accurate model for fast optimal control of legged robots. 
    more » « less
  5. null (Ed.)
    Abstract Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large data sets have empirically been shown to be able to generate natural images well from a low-dimensional latent representation of the image. Given such a generator network, a noisy image can be denoised by (i) finding the closest image in the range of the generator or by (ii) passing it through an encoder-generator architecture (known as an autoencoder). However, there is little theory to justify this success, let alone to predict the denoising performance as a function of the network parameters. In this paper, we consider the problem of denoising an image from additive Gaussian noise using the two generator-based approaches. In both cases, we assume the image is well described by a deep neural network with ReLU activations functions, mapping a $k$-dimensional code to an $n$-dimensional image. In the case of the autoencoder, we show that the feedforward network reduces noise energy by a factor of $O(k/n)$. In the case of optimizing over the range of a generative model, we state and analyze a simple gradient algorithm that minimizes a non-convex loss function and provably reduces noise energy by a factor of $O(k/n)$. We also demonstrate in numerical experiments that this denoising performance is, indeed, achieved by generative priors learned from data. 
    more » « less