Related papers: The Shannon Lower Bound is Asymptotically Tight
Direct evaluation of the rate-distortion function has rarely been achieved when it is strictly greater than its Shannon lower bound. In this paper, we consider the rate-distortion function for the distortion measure defined by an…
This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon$,…
Lossy data compression lies at the heart of modern communication and storage systems. Shannon's rate-distortion theory provides the fundamental limit on how much a source can be compressed at a given fidelity, but it assumes infinitely long…
Shannon's rate-distortion theory treats source symbols as unstructured labels. When the source is a knowledge base equipped with a logical proof system, a natural fidelity criterion is closure fidelity: a reconstruction is acceptable if it…
We derive a lower bound on the differential entropy of a log-concave random variable $X$ in terms of the $p$-th absolute moment of $X$. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds…
The Shannon lower bound has been the subject of several important contributions by Berger. This paper surveys Shannon bounds on rate-distortion problems under mean-squared error distortion with a particular emphasis on Berger's techniques.…
We consider a Shannon cipher system for memoryless sources, in which distortion is allowed at the legitimate decoder. The source is compressed using a rate distortion code secured by a shared key, which satisfies a constraint on the…
Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
We derive a few extended versions of the Kraft inequality for lossy compression, which pave the way to the derivation of several refinements and extensions of the well known Shannon lower bound in a variety of instances of rate-distortion…
We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data…
Shannon proved that if we can transmit bits reliably at rates larger than the rate distortion function $R(D)$, then we can transmit this source to within a distortion $D$. We answer the converse question ``If we can transmit a source to…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…
For variable-length coding with an almost-sure distortion constraint, Zhang et al. show that for discrete sources the redundancy is upper bounded by $\log n/n$ and lower bounded (in most cases) by $\log n/(2n)$, ignoring lower order terms.…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of…
This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…
We apply statistical mechanics to an inverse problem of linear mapping to investigate the physics of the irreversible compression. We use the replica symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's result.…
We introduce a new measure of information-theoretic secrecy based on rate-distortion theory and study it in the context of the Shannon cipher system. Whereas rate-distortion theory is traditionally concerned with a single reconstruction…
We study lossy compression of a finite statement source generated in a fixed deductive environment. The source symbols are statements in a knowledge base endowed with a shared proof system, and reconstruction fidelity is measured by…