arXiv subjects

Kaikai Yang

Publications and source records attributed to Kaikai Yang.

4 recordsLinked to original sources

arXiv2026

Brownian Bridge Diffusion-Based Joint Channel Estimation and Data Detection for Jamming-Resilient Receivers

In next-generation wireless networks, the growing density of devices and limited spectrum resources pose severe jamming challenges to fragile legitimate communication links in the wireless electromagnetic environment. Crucially, when jamming overlaps with pilot and data symbols in both time and frequency domains, it inflicts a severe bottleneck on receiver-side joint estimation and detection. Existing schemes often lack an effective framework to combat such jamming contamination, thereby failing to guarantee reliable transmission. To address this issue, we propose a Brownian bridge diffusion-based joint channel estimation and data detection framework (BBD-JCED) for jamming-resilient receivers. Specifically, the proposed framework comprises two core modules: the first extracts jamming features in the short-time Fourier transform (STFT) domain and suppresses jamming samples, thereby improving the signal-to-jamming-plus-noise ratio (SJNR) of the received signal; the second introduces a Brownian bridge diffusion (BBD) process to model the evolution of the suppressed signal and the encoded bits in the presence of channel estimation errors, thereby enabling enhanced joint channel estimation and data detection. To alleviate the computational burden of the BBD process in the second module, we further derive a fast ordinary differential equation (ODE) solver that enables its low-complexity iterative evolution. Finally, we design a multi-module training algorithm to improve the data recovery capability of the proposed framework. Simulation results demonstrate that the proposed framework achieves superior bit recovery performance compared with baseline schemes while maintaining a lower number of model parameters and competitive computational complexity.

cs.IT↗

arXiv2024

Multilinear fractional maximal and integral operators with homogeneous kernels, Hardy--Littlewood--Sobolev and Olsen-type inequalities

Let $m\in \mathbb{N}$ and $0<α<mn$.In this paper, we will use the idea of Hedberg to reprove that the multilinear operators $\mathcal{T}_{Ω,α;m}$ and $\mathcal{M}_{Ω,α;m}$ are bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)\times\cdots\times L^{p_m}(\mathbb R^n)$ into $L^q(\mathbb R^n)$ provided that $\vecΩ=(Ω_1,Ω_2,\dots,Ω_m)\in L^s(\mathbf{S}^{n-1})$, $s'<p_1,p_2,\dots,p_m<n/α$, \begin{equation*} \frac{\,1\,}{p}=\frac{1}{p_1}+\frac{1}{p_2}+\cdots+\frac{1}{p_m} \quad \mbox{and} \quad \frac{\,1\,}{q}=\frac{\,1\,}{p}-\fracα{n}. \qquad (*) \end{equation*} We also prove that under the assumptions that $\vecΩ=(Ω_1,Ω_2,\dots,Ω_m)\in L^s(\mathbf{S}^{n-1})$, $s'\leq p_1,p_2,\dots,p_m<n/α$ and $(*)$, the multilinear operators $\mathcal{T}_{Ω,α;m}$ and $\mathcal{M}_{Ω,α;m}$ are bounded from $L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n)\times \cdots\times L^{p_m}(\mathbb R^n)$ into $L^{q,\infty}(\mathbb R^n)$, which are completely new. Moreover, we will use the idea of Adams to show that $\mathcal{T}_{Ω,α;m}$ and $\mathcal{M}_{Ω,α;m}$ are bounded from $L^{p_1,κ}(\mathbb R^n)\times L^{p_2,κ}(\mathbb R^n)\times \cdots\times L^{p_m,κ}(\mathbb R^n)$ into $L^{q,κ}(\mathbb R^n)$ whenever $s'<p_1,p_2,\dots,p_m<n/α$, $0<κ<1$, \begin{equation*} \frac{\,1\,}{p}=\frac{1}{p_1}+\frac{1}{p_2}+\cdots+\frac{1}{p_m} \quad \mbox{and} \quad \frac{\,1\,}{q}=\frac{\,1\,}{p}-\fracα{n(1-κ)},\qquad (**) \end{equation*} and also bounded from $L^{p_1,κ}(\mathbb R^n)\times L^{p_2,κ}(\mathbb R^n)\times \cdots\times L^{p_m,κ}(\mathbb R^n)$ into $WL^{q,κ}(\mathbb R^n)$ whenever $s'\leq p_1,p_2,\dots,p_m<n/α$, $0<κ<1$ and $(**)$.

math.CA↗

arXiv2023

ACE: Zero-Shot Image to Image Translation via Pretrained Auto-Contrastive-Encoder

Image-to-image translation is a fundamental task in computer vision. It transforms images from one domain to images in another domain so that they have particular domain-specific characteristics. Most prior works train a generative model to learn the mapping from a source domain to a target domain. However, learning such mapping between domains is challenging because data from different domains can be highly unbalanced in terms of both quality and quantity. To address this problem, we propose a new approach to extract image features by learning the similarities and differences of samples within the same data distribution via a novel contrastive learning framework, which we call Auto-Contrastive-Encoder (ACE). ACE learns the content code as the similarity between samples with the same content information and different style perturbations. The design of ACE enables us to achieve zero-shot image-to-image translation with no training on image translation tasks for the first time. Moreover, our learning method can learn the style features of images on different domains effectively. Consequently, our model achieves competitive results on multimodal image translation tasks with zero-shot learning as well. Additionally, we demonstrate the potential of our method in transfer learning. With fine-tuning, the quality of translated images improves in unseen domains. Even though we use contrastive learning, all of our training can be performed on a single GPU with the batch size of 8.

cs.CV↗

arXiv2022

Homogeneous fractional integral operators on Lebesgue and Morrey spaces, Hardy--Littlewood--Sobolev and Olsen-type inequalities

Let $T_{Ω,α}$ be the homogeneous fractional integral operator defined as \begin{equation*} T_{Ω,α}f(x):=\int_{\mathbb R^n}\frac{Ω(x-y)}{|x-y|^{n-α}}f(y)\,dy, \end{equation*} and the related fractional maximal operator $M_{Ω,α}$ is given by \begin{equation*} M_{Ω,α}f(x):=\sup_{r>0}\frac{1}{|B(x,r)|^{1-α/n}}\int_{|x-y|<r}|Ω(x-y)f(y)|\,dy. \end{equation*} In this article, we will use the idea of Hedberg to reprove that the operators $T_{Ω,α}$ and $M_{Ω,α}$ are bounded from $L^p(\mathbb R^n)$ to $L^q(\mathbb R^n)$ provided that $Ω\in L^s(\mathbf{S}^{n-1})$, $s'<p<n/α$ and $1/q=1/p-α/n$, which was obtained by Muckenhoupt and Wheeden. We also reprove that under the assumptions that $Ω\in L^s(\mathbf{S}^{n-1})$, $s'\leq p<n/α$ and $1/q=1/p-α/n$, the operators $T_{Ω,α}$ and $M_{Ω,α}$ are bounded from $L^p(\mathbb R^n)$ to $L^{q,\infty}(\mathbb R^n)$, which was obtained by Chanillo, Watson and Wheeden. We will use the idea of Adams to show that $T_{Ω,α}$ and $M_{Ω,α}$ are bounded from $L^{p,κ}(\mathbb R^n)$ to $L^{q,κ}(\mathbb R^n)$ whenever $s'<p<n/α$ and $1/q=1/p-α/{n(1-κ)}$, and bounded from $L^{p,κ}(\mathbb R^n)$ to $WL^{q,κ}(\mathbb R^n)$ whenever $s'\leq p<n/α$ and $1/q=1/p-α/{n(1-κ)}$. Some new estimates in the limiting cases are also established. The results obtained are substantial improvements and extensions of some known results. Moreover, we will apply these results to several well-known inequalities such as Hardy--Littlewood--Sobolev and Olsen-type inequalities.

math.CA↗