Related papers: Finite-State Dimension and Lossy Decompressors
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
Today, with the growing demands of information storage and data transfer, data compression is becoming increasingly important. Data Compression is a technique which is used to decrease the size of data. This is very useful when some huge…
In 1959, R\'enyi proposed the information dimension and the $d$-dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stochastic processes by…
This paper proposes the use of deep autoencoders to compress the channel information in a \review{massive} multiple input and multiple output (MIMO) system. Although autoencoders perform lossy compression, they still have adequate…
Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data…
In this paper, a communication-efficient multi-processor compressed sensing framework based on the approximate message passing algorithm is proposed. We perform lossy compression on the data being communicated between processors, resulting…
We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a…
Many scientific codes and instruments generate large amounts of floating-point data at high rates that must be compressed before they can be stored. Typically, only lossy compression algorithms deliver high-enough compression ratios.…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
Rate-distortion theory provides bounds for compressing data produced by an information source to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some loss, or distortion, between the…
Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)].…
It is well known that lossless compression of a discrete memoryless source with near-uniform encoder output is possible at a rate above its entropy if and only if the encoder is randomized. This work focuses on deriving conditions for…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of…
In image compression, with recent advances in generative modeling, existence of a trade-off between the rate and perceptual quality has been brought to light, where the perceptual quality is measured by the closeness of the output and…
We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].…
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and…
Jalali and Poor introduced an asymptotic framework for compressed sensing of stochastic processes, demonstrating that any rate strictly greater than the mean information dimension serves as an upper bound on the number of random linear…
Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…