Related papers: Applications of Universal Source Coding to Statist…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
In this work, we consider a distributed source coding problem with a joint distortion criterion depending on the sources and the reconstruction. This includes as a special case the problem of computing a function of the sources to within…
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…
It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error.…
We construct an optimal quantum universal variable-length code that achieves the admissible minimum rate, i.e., our code is used for any probability distribution of quantum states. Its probability of exceeding the admissible minimum rate…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
Since the publication of Shannon's theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv and Berger-Yeung. Specifically, the…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
Universal compression algorithms have been studied in the past for sequential change detection, where they have been used to estimate the post-change distribution in the modified version of the Cumulative Sum (CUSUM) Test. In this paper, we…
We consider the problem of universal decoding for arbitrary unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper…
In this paper, the context dependence multilevel pattern matching(in short CDMPM) grammar transform is proposed; based on this grammar transform, the universal lossless data compression algorithm, CDMPM code is then developed. Moreover we…
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…
Signal processing and Information theory are two disparate fields used for characterizing signals for various scientific and engineering applications. Spectral/Fourier analysis, a technique employed in signal processing, helps estimation of…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…