相关论文: One step RSB scheme for the rate distortion functi…
We prove the existence of full replica symmetry breaking (FRSB) for the Sherrington-Kirkpatrick (SK) model at low temperature. More specifically, we prove that slightly beyond the critical temperature, the Parisi measure for the SK model is…
We study the critical properties of the weakly disordered $p$-component random Heisenberg ferromagnet. It is shown that if the specific heat critical exponent of the pure system is positive, the traditional renormalization group (RG) flows…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
We study the one-body reduced density matrix of a system of $N$ one-dimensional impenetrable anyons trapped by a harmonic potential. To this purpose we extend two methods developed to tackle related problems, namely the determinant approach…
We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
The information rate-distortion-perception (RDP) function characterizes the three-way trade-off between description rate, average distortion, and perceptual quality measured by discrepancy between probability distributions and has been…
We extend quantum rate distortion theory by considering auxiliary resources that might be available to a sender and receiver performing lossy quantum data compression. The first setting we consider is that of quantum rate distortion coding…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success…
We use the replica method of statistical mechanics to examine a typical performance of correctly reconstructing $N$-dimensional sparse vector $bx=(x_i)$ from its linear transformation $by=bF bx$ of $P$ dimensions on the basis of…
In the context of lossy compression, Blau & Michaeli (2019) adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider…
Rate distortion dimension describes the theoretical limit of lossy data compression methods as the distortion bound goes to zero. It was originally introduced in the context of information theory, and recently it was discovered that it has…
We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large…
In this paper, we study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint that belongs to the family of…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…
This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
We report large effects of Parisi replica permutation symmetry breaking (RPSB) on elementary excitations of fermionic systems with frustrated magnetic interactions. The electronic density of states is obtained exactly in the zero…
Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these…