相关论文: Linear Bounds between Contraction Coefficients for…

We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…

We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation…

In this paper, we study the upper and the lower bounds on the joint source-channel coding error exponent with decoder side-information. The results in the paper are non-trivial extensions of the Csiszar's classical paper [5]. Unlike the…

For any channel $P_{Y|X}$ the strong data processing constant is defined as the smallest number $\eta_{KL}\in[0,1]$ such that $I(U;Y)\le \eta_{KL} I(U;X)$ holds for any Markov chain $U-X-Y$. It is shown that the value of $\eta_{KL}$ is…

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the…

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

The goal of this paper is to obtain a better knowledge of the achievable data rate over noncoherent Rician fading channel with time and frequency memory. We assume that the average-power as well as the peak-power of the input signal are…

Statistical distances (SDs), which quantify the dissimilarity between probability distributions, are central to machine learning and statistics. A modern method for estimating such distances from data relies on parametrizing a variational…

The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice…

We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on…

The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain…

Let $f$ and $g$ be holomorphic or Maass cusp forms for $\rm SL_2(\mathbb{Z})$ and let $\chi$ be a primitive Dirichlet character of prime power conductor $q=p^n$. For any given $\varepsilon>0$, we establish the following subconvexity bound…

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…

This paper provides lower bounds on the reconstruction error for transmission of two continuous correlated random vectors sent over both sum and parallel channels using the help of two causal feedback links from the decoder to the encoders…

In this paper, we revisit two multi-terminal lossy source coding problems: the lossy source coding problem with side information available at the encoder and one of the two decoders, which we term as the Kaspi problem (Kaspi, 1994), and the…

An analog source is to be transmitted across a Gaussian channel in more than one channel use per source symbol. This paper derives a lower bound on the asymptotic mean squared error for a strategy that consists of repeatedly quantizing the…

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…

Consider a pair of correlated Gaussian sources (X1,X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear…

We show that the uniform distribution minimizes entropy among all one-dimensional symmetric log-concave distributions with fixed variance, as well as various generalizations of this fact to R\'enyi entropies of orders less than 1 and with…