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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 15 December 2026 | Viewed by 7049

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Editor

Prof. Dr. Tsachy Weissman

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Guest Editor

Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
Interests: information theory; entropy; channel coding; data compression; statistical signal processing; digital communications

Special Issue Information

Dear Colleagues,

Data compression is more critical than ever for enabling our technologies. This Special Issue is geared toward key advancements in this area, with an emphasis on bridging theory and practice.

Topics of interest include, but are not limited to, the following:

New distortion criteria tailored to tasks like perceptual coding and machine learning;
Emerging data types such as graphs and point clouds;
Tradeoffs between compression, distortion, and complexity;
The interplay between compression and other information processing tasks.

Prof. Dr. Tsachy Weissman
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

information theory
data compression (lossless and lossy)
compression complexity
source coding
coding theory
distortion
point clouds

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Published Papers (7 papers)

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Research

24 pages, 2001 KB

Open AccessArticle

A Sequential Markov Probabilistic Aggregation Algorithm for Causal Emergence in Markov Aggregation

by Zhenjie Hou and Xuchu Dai

Entropy 2026, 28(8), 872; https://doi.org/10.3390/e28080872 - 3 Aug 2026

Viewed by 194

Abstract

Causal emergence (CE) is a phenomenon in which macrodynamics provide better effective information (EI) than microdynamics. The CE is widely used as the objective function in Markov aggregation. The existing works focus on deterministic aggregation, which may not offer a good solution since the search space of each step is finite. To solve this problem, we propose a sequential Markov probabilistic aggregation (SMPA) algorithm. We first express the aggregation problem as an optimization problem, then find that the EI is maximized when the transition probability matrix is a permutation matrix, and prove that the optimization problem is a nonconvex function of the probabilistic aggregation matrix. In the SMPA algorithm, the optimization problem is split into multiple univariate optimizations. Compared with the deterministic aggregation algorithm, SMPA can achieve better greedy solutions. The experimental results indicate that probabilistic aggregation generally performs better than deterministic aggregation. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

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25 pages, 1909 KB

Open AccessArticle

Contour-Based Chain-Code Serialization for Lossless Compression of Voxelized 3D Objects

by Esteban-Alejandro Durán-Yáñez, Mario-Alberto Rodríguez-Díaz, Ricardo Mendoza-González, Francisco-Javier Luna-Rosas and Julio-César Martínez-Romo

Entropy 2026, 28(7), 774; https://doi.org/10.3390/e28070774 - 8 Jul 2026

Viewed by 261

Abstract

Voxel representations provide a simple way to represent three-dimensional objects as binary occupancy signals, but dense voxel grids and direct sparse encodings remain costly at medium and high resolutions. This paper addresses the gap between conventional dense-grid, octree, and point-cloud-codec representations and deterministic contour-first source serialization for exact binary voxel occupancy. We propose a contour-based chain-code serialization that decomposes a voxel grid into two-dimensional slices, extracts foreground components and holes, encodes their contours using F4, 3OT, and F8 variants, and separates contour symbols from positional metadata before applying general-purpose lossless compression. The method is evaluated on 3983 ModelNet40-derived voxelized objects across 40 classes and resolutions N = 8, 16, 32, 64, 128, 256, and 512, using the X-axis for the main evaluation. It is compared against OCC1, BINVOX, breadth-first octree masks, and geometry-only G-PCC. The proposed streams are not competitive at N = 8, where zstd-compressed octree masks achieve the best mean bpv. From N = 16 onward, however, the best proposed stream outperforms the strongest evaluated baseline, with gains increasing from 20.93% at N = 16 to 84.37% at N = 512. The best proposed configuration is zstd + 3OT at N = 8 and N = 16, while zstd + F8 dominates from N = 32 through N = 512. Entropy, ablation, timing, memory, and validation analyses further show that the advantage comes from the interaction between contour-aware source serialization and backend compression, rather than from the backend compressor alone. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

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18 pages, 345 KB

Open AccessFeature PaperArticle

Generalized Forms of the Kraft Inequality for Finite-State Encoders

by Neri Merhav

Entropy 2026, 28(3), 278; https://doi.org/10.3390/e28030278 - 1 Mar 2026

Viewed by 619

Abstract

We derive a few extended versions of the Kraft inequality for information lossless finite-state encoders. The main basic contribution is in defining a notion of a Kraft matrix and in establishing the fact that a necessary condition for information losslessness of a finite-state encoder is that none of the eigenvalues of this matrix have modulus larger than unity, or equivalently, the spectral radius of the Kraft matrix cannot exceed one. We then derive several equivalent forms of this condition, which are based on well-known formulas for spectral radius. Even stronger results are presented for the important special case where the finite-state encoder is assumed irreducible. Finally, two extensions are outlined—one concerns the case of side information available to both encoder and decoder, and the other is for lossy compression. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

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19 pages, 335 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality

by Neri Merhav

Entropy 2026, 28(1), 76; https://doi.org/10.3390/e28010076 - 9 Jan 2026

Cited by 1 | Viewed by 928

Abstract

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 coding. These refinements and extensions include sharper bounds for one-to-one codes and D-semifaithful codes, a Shannon lower bound for distortion measures based on sliding-window functions, and an individual-sequence counterpart of the Shannon lower bound. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

20 pages, 934 KB

Open AccessArticle

Non-Uniform Entropy-Constrained L_∞ Quantization for Sparse and Irregular Sources

by Alin-Adrian Alecu, Mohammad Ali Tahouri, Adrian Munteanu and Bujor Păvăloiu

Entropy 2025, 27(11), 1126; https://doi.org/10.3390/e27111126 - 31 Oct 2025

Viewed by 1041

Abstract

Near-lossless coding schemes traditionally rely on uniform quantization to control the maximum absolute error (

L_{\infty}

norm) of residual signals, often assuming a parametric model for the source distribution. This paper introduces a novel design framework for non-uniform, entropy-aware

L_{\infty}

-oriented [...] Read more.

Near-lossless coding schemes traditionally rely on uniform quantization to control the maximum absolute error (

L_{\infty}

norm) of residual signals, often assuming a parametric model for the source distribution. This paper introduces a novel design framework for non-uniform, entropy-aware

L_{\infty}

-oriented scalar quantizers that leverages a tight and differentiable approximation of the

L_{\infty}

distortion metric and does not require any parametric density function formulations. The framework is evaluated on both synthetic parametric sources and real-world medical depth map video datasets. For smoothly decaying distributions, such as the continuous Laplacian or discrete two-sided geometric distributions, the proposed method naturally converges to near-uniform quantizers, consistent with theoretical expectations. In contrast, for sparse or irregular sources, the algorithm produces highly non-uniform bin allocations that adapt to the local distribution structure and improve rate-distortion efficiency. When embedded in a residual-based near-lossless compression scheme, the resulting codec consistently outperforms versions equipped with uniform or piecewise-uniform quantizers, as well as state-of-the-art near-lossless schemes such as JPEG-LS and CALIC. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

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33 pages, 1024 KB

Open AccessFeature PaperArticle

Graph-Theoretic Limits of Distributed Computation: Entropy, Eigenvalues, and Chromatic Numbers

by Mohammad Reza Deylam Salehi and Derya Malak

Entropy 2025, 27(7), 757; https://doi.org/10.3390/e27070757 - 15 Jul 2025

Cited by 1 | Viewed by 1673

Abstract

We address the problem of the distributed computation of arbitrary functions of two correlated sources,

X_{1}

and

X_{2}

, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source characteristic graphs (and multiple [...] Read more.

We address the problem of the distributed computation of arbitrary functions of two correlated sources,

X_{1}

and

X_{2}

, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source characteristic graphs (and multiple instances using the n-fold OR product of this graph with itself). For regular graphs and general graphs, we establish bounds on the optimal rate—characterized by the chromatic entropy for the n-fold graph products—that allows a receiver for asymptotically lossless computation of arbitrary functions over finite fields. For the special class of cycle graphs (i.e., 2-regular graphs), we establish an exact characterization of chromatic numbers and derive bounds on the required rates. Next, focusing on the more general class of d-regular graphs, we establish connections between d-regular graphs and expansion rates for n-fold graph products using graph spectra. Finally, for general graphs, we leverage the Gershgorin Circle Theorem (GCT) to provide a characterization of the spectra, which allows us to derive new bounds on the optimal rate. Our codes leverage the spectra of the computation and provide a graph expansion-based characterization to succinctly capture the computation structure, providing new insights into the problem of distributed computation of arbitrary functions. Full article

(This article belongs to the Special Issue Information Theory and Data Compression)

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14 pages, 262 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Universal Encryption of Individual Sequences Under Maximal Information Leakage

by Neri Merhav

Entropy 2025, 27(6), 551; https://doi.org/10.3390/e27060551 - 24 May 2025

Viewed by 869

Abstract

We consider the Shannon cipher system in the framework of individual sequences and finite-state encrypters under the metric of maximal information leakage. A lower bound and an asymptotically matching upper bound on the leakage are derived, which lead to the conclusion that asymptotically [...] Read more.

(This article belongs to the Special Issue Information Theory and Data Compression)

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