Related papers: Estimating the probability law of the codelength a…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…
Lossless variable-length source coding with codeword cost is considered for general sources. The problem setting, where we impose on unequal costs on code symbols, is called the variable-length coding with codeword cost. In this problem,…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements…
Fractal image compression, Culik's image compression and zerotree prediction coding of wavelet image decomposition coefficients succeed only because typical images being compressed possess a significant degree of self-similarity. Besides…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential…
We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform,…
Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…
We show that for a wide range of channels and code ensembles with pairwise-independent codewords, with probability tending to 1 with the code length, expurgating an arbitrarily small fraction of codewords from a randomly selected code…
Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error $\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$, for…
By interpreting the well-known, qualitative criteria for the existence of quantum error correction (QEC) codes by Knill and Laflamme from a quantitative perspective, we propose a figure of merit for assessing a QEC scheme based on the…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…