Searcharxiv⌕ Search

arXiv subjects

Jinlong Wei

Publications and source records attributed to Jinlong Wei.

At least 37 records · Page 2Linked to original sources
arXiv2020

Complexity Reduction of Volterra Nonlinear Equalization for Optical Short-Reach IM/DD Systems

We investigate approaches to reduce the computational complexity of Volterra nonlinear equalizers (VNLEs) for short-reach optical transmission systems using intensity modulation and direct detection (IM/DD). In this contribution we focus on a structural reduction of the number of kernels, i.e. we define rules to decide which terms need to be implemented and which can be neglected before the kernels are calculated. This static complexity reduction is to be distinguished from other approaches like pruning or L1 regularization, that are applied after the adaptation of the full Volterra equalizer e.g. by thresholding. We investigate the impact of the complexity reduction on 90 GBd PAM6 IM/DD experimental data acquired in a back-to-back setup as well as in case of transmission over 1 km SSMF. First, we show, that the third-order VNLE terms have a significant impact on the overall performance of the system and that a high number of coefficients is necessary for optimal performance. Afterwards, we show that restrictions, for example on the tap spacing among samples participating in the same kernel, can lead to an improved tradeoff between performance and complexity compared to a full third-order VNLE. We show an example, in which the number of third-order kernels is halved without any appreciable performance degradation.

eess.SP↗
arXiv2020

Noise and Stability in Reaction-diffusion Equations

We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is firstly established. Then, by using the Lyapunov method, sufficient conditions for mean square and stochastic stability are given. The results show that the multiplicative noise can make the solution stable, but the additive noise will be not.

math.PR↗
arXiv2019

A Kolmogorov type theorem for stochastic fields

We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solutions for nonlocal stochastic parabolic equations driven by non-Gaussian Lévy noises.

math.PR↗
arXiv2019

Impact of noise on parabolic equations

In this short paper, we focus on the blowup phenomenon of stochastic parabolic equations. We first discuss the probability of the event that the solutions keep positive. Then, the blowup phenomenon in the whole space is considered. The probability of the event that the solutions blow up in finite time is given. Lastly, we obtain the probability of the event that blowup time of stochastic parabolic equations large than or less than the deterministic case.

math.PR↗
arXiv2019

Schauder and Sobolev Estimates of Parabolic Equations

In this note, we use the non-homogeneous Poisson stochastic process to show how knowing Schauder and Sobolev estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs. The method is probability. We generalize the result of Krylov-Priola [7].

math.AP↗
arXiv2019

Exceeding the Nonlinear Shannon-Limit in Coherent Optical Communications by MIMO Machine Learning

The nonlinear Shannon capacity limit has been identified as the fundamental barrier to the maximum rate of transmitted information in optical communications. In long-haul high-bandwidth optical networks, this limit is mainly attributed to deterministic Kerr-induced fiber nonlinearities and from the interaction of amplified spontaneous emission noise from cascaded optical amplifiers with fiber nonlinearity: the stochastic parametric noise amplification. Unlike earlier impractical approaches that compensate solely deterministic nonlinearities, here we demonstrate a novel electronic-based deep neural network with multiple-inputs and outputs (MIMO) that tackles the interplay of deterministic and stochastic nonlinearity manifestation in coherent optical signals. Our demonstration shows that MIMO deep learning can compensate nonlinear inter-carrier crosstalk effects even in the presence of frequency stochastic variations, which has hitherto been considered impossible. Our solution significantly outperforms conventional machine learning and gold-standard nonlinear equalizers without sacrificing computational complexity, leading to record-breaking transmission performance for up to 40 Gbit/sec high-spectral-efficient optical signals.

eess.SP↗
arXiv2019

Global existence and non-existence of stochastic parabolic equations

This paper is concerned with the blowup phenomenon of stochastic parabolic equations both on bounded domain and in the whole space. We introduce a new method to study the blowup phenomenon on bounded domain. Comparing with the existing results, we delete the assumption that the solutions to stochastic heat equations are non-negative. Then the blowup phenomenon in the whole space is obtained by using the properties of heat kernel. We obtain that the solutions will blow up in finite time for nontrivial initial data.

math.AP↗
arXiv2019

Blowup solutions of Grushin's operator

In this note, we consider the blowup phenomenon of Grushin's operator. By using the knowledge of probability, we first get expression of heat kernel of Grushin's operator. Then by using the properties of heat kernel and suitable auxiliary function, we get that the solutions will blow up in finite time.

math.AP↗
arXiv2018

Periodic solution of stochastic process in the distributional sense

In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of periodic solution on bounded domain. Lastly, for the case that probability density function exists, we obtain the existence periodic solutions of the probability density function corresponding to the stochastic process by using the technique of deterministic partial differential equations.

math.PR↗
arXiv2018

Fiber-induced nonlinearity compensation in coherent optical systems by affinity propagation soft-clustering

There is a tremendous need to maximize signal capacity without sacrificing energy consumption and complexity in optical fiber communications due to the rise of network traffic demand and critical latency-aware services such as telemedicine and the Internet-of-Things. In this work, the first system-agnostic and training-data-free fiber nonlinearity compensator (NLC) using affinity propagation (AP) clustering is experimentally demonstrated. It is shown that compared to linear equalization, AP can increase the signal quality-factor up to about 5 dB in 16-quadrature-amplitude-modulated coherent optical systems by effectively tackling deterministic and stochastic nonlinearities. AP outperforms benchmark clustering algorithms and complex deterministic schemes such as K-means, fuzzy-logic, digital-back propagation and Volterra-based NLC, offering a power margin extension of up to 4 dB.

eess.SP↗
arXiv2018

The effect of noise intensity on stochastic parabolic equations

In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabolic equations. By utilising Itô's formula and the energy estimate method, we obtain the excitation indices of the energy solutions $u$ at any finite time $t$. Furthermore, we improve certain existing results in the literature by presenting a comparably simple method to show those existing results.

math.PR↗
arXiv2018

Regularity of stochastic nonlocal diffusion equations

In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem, we first show the Hölder continuity (locally in the whole state space $\mathbb{R}^d$) for mild solutions of stochastic nonlocal diffusion equations in the sense that the solutions $u$ belong to the space $C^γ(D_T;L^p(Ω))$ with the optimal Hölder continuity index $γ$ (which is given explicitly), where $D_T:=[0,T]\times D$ for $T>0$, and $D\subset\mathbb{R}^d$ being a bounded domain. Then, by utilising tail estimates, we are able to obtain the estimates of mild solutions in $L^p(Ω;C^{γ^*}(D_T))$. What's more, we give an explicit formula between the two index $γ$ and $γ^*$. Moreover, we prove Hölder continuity for mild solutions on bounded domains. Finally, we present a new criteria to justify Hölder continuity for the solutions on bounded domains. The novelty of this paper is that our method are suitable to the case of time-space white noise.

math.PR↗
arXiv2018

Well-posedness of nonlinear transport equation by stochastic perturbation

We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator estimates, we gain the existence and uniqueness of stochastic entropy solutions. Besides, for $BV$ initial data, the $BV$ and Hölder regularities are also derived for the unique stochastic entropy solution. Particularly, for the transport equation, we gain a regularization result, i.e. while the existence fails for the transport equation, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be another explicit example (the first example is given in [22]) of a PDE of fluid dynamics that becomes well-posed under the influence of a multiplicative Brownian type noise.

math.PR↗
arXiv2018

On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems

We obtain a new quantitative deformation lemma, and then gain a new mountain pass theorem. More precisely, the new mountain pass theorem is independent of the functional value on the boundary of the mountain, which improves the well known results (\cite{AR,PS1,PS2,Qi,Wil}). Moreover, by our new mountain pass theorem, new existence of nontrivial periodic solutions for some nonlinear second-order discrete systems is obtained, which greatly improves the result in \cite{Z04}.

math.DS↗
arXiv2017

On weak solutions of stochastic differential equations with sharp drift coefficients

We extend Krylov and Röckner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\times{\mathbb R}^d\rightarrow{\mathbb R}^d$ be Borel measurable, where $T>0$ is arbitrarily fixed. Consider $$X_t=x+\int_0^tb(s,X_s)ds+W_t,\quad t\in[0,T], \, x\in{\mathbb R}^d,$$ where $\{W_t\}_{t\in[0,T]}$ is a $d$-dimensional standard Wiener process. If $b=b_1+b_2$ such that $b_1(T-\cdot)\in\mathcal{C}_q^0((0,T];L^p({\mathbb R}^d))$ with $2/q+d/p=1$ for $p,q\ge1$ and $\|b_1(T-\cdot)\|_{\mathcal{C}_q((0,T];L^p({\mathbb R}^d))}$ is sufficiently small, and that $b_2$ is bounded and Borel measurable, then there exits a unique weak solution to the above equation. Furthermore, we obtain the strong Feller property of the semi-group and existence of density associated with above SDE. Besides, we extend the classical partial differential equations (PDEs) results for $L^q(0,T;L^p({\mathbb R}^d))$ coefficients to $L^\infty_q(0,T;L^p({\mathbb R}^d))$ ones, and derive the Lipschitz regularity for solutions of second order parabolic PDEs (see Lemma 2.1).

math.AP↗
arXiv2017

Existence and uniqueness of $W^{1,r}_{loc}$-solutions for stochastic transport equations

We investigate a stochastic transport equation driven by a multiplicative noise. For $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,r}({\mathbb R}^d)$ initial data, we obtain the existence and uniqueness of stochastic strong solutions (in $W^{1,r}_{loc}({\mathbb R}^d))$.In particular, when $r=\infty$, we establish a Lipschitz estimate for solutions and this question is opened by Fedrizzi and Flandoli in case of $L^q(0,T;L^p({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient. Moreover, opposite to the deterministic case where $L^q(0,T;W^{1,p}({\mathbb R}^d;{\mathbb R}^d))$ drift coefficient and $W^{1,p}({\mathbb R}^d)$ initial data may induce non-existence for strong solutions (in $W^{1,p}_{loc}({\mathbb R}^d)$), we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. It is an interesting example of a deterministic PDE that becomes well-posed under the influence of a multiplicative Brownian type noise. We extend the existing results \cite{FF2,FGP1} partially.

math.AP↗