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Zhuhong Zhang

Publications and source records attributed to Zhuhong Zhang.

7 recordsLinked to original sources
arXiv2024

Application of Transformers for Nonlinear Channel Compensation in Optical Systems

In this paper, we introduce a new nonlinear optical channel equalizer based on Transformers. By leveraging parallel computation and attending directly to the memory across a sequence of symbols, we show that Transformers can be used effectively for nonlinear compensation (NLC) in coherent long-haul transmission systems. For this application, we present an implementation of the encoder part of the Transformer and analyze its performance over a wide range of different hyper-parameters. It is shown that by proper embeddings and processing blocks of symbols at each iteration and also carefully selecting subsets of the encoder's output to be processed together, an efficient nonlinear equalization can be achieved for different complexity constraints. To reduce the computational complexity of the attention mechanism, we further propose the use of a physic-informed mask inspired by nonlinear perturbation theory. We also compare the Transformer-NLC with digital back-propagation (DBP) under different transmission scenarios in order to demonstrate the flexibility and generalizability of the proposed data-driven solution.

cs.IT↗
arXiv2023

Neural Network Architectures for Optical Channel Nonlinear Compensation in Digital Subcarrier Multiplexing Systems

In this work, we propose to use various artificial neural network (ANN) structures for modeling and compensation of intra- and inter-subcarrier fiber nonlinear interference in digital subcarrier multiplexing (DSCM) optical transmission systems. We perform nonlinear channel equalization by employing different ANN cores including convolutional neural networks (CNN) and long short-term memory (LSTM) layers. We start to compensate the fiber nonlinearity distortion in DSCM systems by a fully connected network across all subcarriers. In subsequent steps, and borrowing from fiber nonlinearity analysis, we gradually upgrade the designs towards modular structures with better performance-complexity advantages. Our study shows that putting proper macro structures in design of ANN nonlinear equalizers in DSCM systems can be crucial for practical solutions in future generations of coherent optical transceivers.

cs.IT↗
arXiv2021

Transmitter IQ Skew Calibration using Direct Detection

We propose a transmitter skew calibration based on direct detection of coherent signals with estimation errors of +/-0.2ps, providing a reliable, accurate and low-cost scheme to calibrate skew for coherent transceivers. In October 2019, this work was submitted / was exposed to Optical Fiber Communication Conference 2020 but an acceptance was not granted. We claimed the first time to use a direct detection-based feedback method for coherent transmitter calibration.

eess.SP↗
arXiv2016

A gap theorem of four-dimensional gradient shrinking solitons

In this paper, we will prove a gap theorem for four-dimensional gradient shrinking soliton. More precisely, we will show that any complete four-dimensional gradient shrinking soliton with nonnegative and bounded Ricci curvature, satisfying a pinched Weyl curvature, either is flat, or $λ_1 + λ_2\ge c_0 R>0$ everywhere for some $c_0\approx 0.29167$, where $\{λ_i\}$ are the two least eigenvalues of Ricci curvature. Furthermore, we will show that $λ_1 + λ_2\ge \frac 13R>0$ under a better pinched Weyl tensor assumption. We point out that the lower bound $\frac 13R$ is sharp.

math.DG↗
arXiv2016

Four-dimensional Einstein manifolds with sectional curvature bounded from above

Given an Einstein structure with positive scalar curvature on a four-dimensional Riemannian manifolds, that is $Ric=λg$ for some positive constant $λ$. For convenience, the Ricci curvature is always normalized to $Ric=1$. A basic problem is to classify four-dimensional Einstein manifolds with positive or nonnegative curvature and $Ric=1$. In this paper, we firstly show that if the sectional curvature satisfies $K\le M_1= \frac{\sqrt{3}}2\approx 0.866025$, then the sectional curvature will be nonnegative. Next, we prove a family of rigidity theorems of Einstein four-manifolds with nonnegative sectional curvature, and satisfies $K_{ik}+sK_{ij}\ge K_s = \frac{1 + \sqrt{2}}3 - \frac{\sqrt{4+2\sqrt{2}}}4 + \frac{2-\sqrt{2}}6 s$ for every orthonormal basis $\{e_i\}$ with $K_{ik}\ge K_{ij}$, where $s$ is any nonnegative constant. Indeed, we will show that these Einstein manifolds must be isometric either $S^4$, $RP^4$ or $CP^2$ with standard metrics. As a corollary, we give a rigidity result of Einstein four-manifolds with $Ric=1$, and the sectional curvature satisfies $K \le M_2 = \frac {2-\sqrt{2}}6 + \frac{\sqrt{4+2\sqrt{2}}}4 \approx 0.750912$.

math.DG↗
arXiv2013

Local pinching estimates in 3-dim Ricci flow

We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature as special cases. A local version of Hamilton-Ivey estimates is also obtained.

math.DG↗