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Coding and Entropy
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Coding and Entropy

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

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 15424

Special Issue Editors

Prof. Dr. Pingyi Fan

E-Mail Website
Guest Editor
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
Interests: B5G technology; network coding; network information theory; machine learning and big data analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Qi Chen

E-Mail Website
Guest Editor
State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China
Interests: Shannon theory; information inequalities and entropy region; network coding
Special Issues, Collections and Topics in MDPI journals
Dr. Suihua Cai

E-Mail Website
Guest Editor
School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China
Interests: information theory; channel coding and its applications
Special Issues, Collections and Topics in MDPI journals
Gangtao Xin

E-Mail
Guest Editor Assistant
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
Interests: semantic communications; information theory; image compression; machine learning and source coding

Special Issue Information

Dear Colleagues,

The Special Issue focuses on new developments in multi-type coding and entropies and their applications in communications, data processing and machine learning.

Shannon’s information theory answers two fundamental questions raised by communication theory: What is the ultimate data compression, and what is the ultimate transmission rate of communication? Entropy is the core concept of this framework, with coding beings its most significant technology, including source coding, channel coding, and network coding. In this context, a number of metrics, such as Shannon entropy, Rényi entropy, message importance measure, sample entropy, fuzzy entropy, and permutation entropy, are introduced to quantify the irregularity or uncertainty of signals and images. Various coding theories and methods have also been proposed to reduce the occupancy of communication and storage resources in order to improve the objective efficiency of the communication network and the subjective experience of clients.

With advances in intelligent vision algorithms and devices, data reprocessing and secondary propagation are becoming increasingly prevalent. the production of a large amount of similar data is becoming more rapid and widespread, resulting in a homogeneity and similarity in data such as images and videos and creating new challenges for information theory. Novel entropy and coding methods may play a significant role in the era of big data.

We invite authors to submit previously unpublished contributions in any field related to developments and applications of information theory in coding and entropy, including but not limited to, the following subtopics:

  • Mathematical extensions for entropy analysis;
  • Source coding and channel coding techniques;
  • Network coding and its related topics;
  • Two- and three-dimensional entropy methods for image analysis;
  • Entropy optimization and modeling for performance enhancement;
  • Entropy-based image, signal processing, and coding;
  • Network information theory and semantic information theory;
  • Compressed sensing and rate-distortion theory;
  • Application of entropy and coding in machine learning;
  • Application of machine learning method to developments of coding and entropy.

Prof. Dr. Pingyi Fan
Dr. Qi Chen
Dr. Suihua Cai
Guest Editors

Gangtao Xin
Guest Editor Assistant

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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind 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
  • entropy
  • data-driven entropy modeling
  • source coding
  • channel coding
  • network coding
  • coding techniques
  • information-theoretic methods
  • entropy-based methods
  • machine learning

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
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Further information on MDPI's Special Issue polices can be found here.

Published Papers (9 papers)

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Research

12 pages, 610 KiB  
Article
New Construction of Asynchronous Channel Hopping Sequences in Cognitive Radio Networks
by Yaoxuan Wang, Xianhua Niu, Chao Qi, Zhihang He and Bosen Zeng
Entropy 2023, 25(10), 1473; https://doi.org/10.3390/e25101473 - 22 Oct 2023
Viewed by 1230
Abstract
The channel-hopping-based rendezvous is essential to alleviate the problem of under-utilization and scarcity of the spectrum in cognitive radio networks. It dynamically allows unlicensed secondary users to schedule rendezvous channels using the assigned hopping sequence to guarantee the self-organization property in a limited [...] Read more.
The channel-hopping-based rendezvous is essential to alleviate the problem of under-utilization and scarcity of the spectrum in cognitive radio networks. It dynamically allows unlicensed secondary users to schedule rendezvous channels using the assigned hopping sequence to guarantee the self-organization property in a limited time. In this paper, we use the interleaving technique to cleverly construct a set of asynchronous channel-hopping sequences consisting of d sequences of period xN2 with flexible parameters, which can generate sequences of different lengths. By this advantage, the new designed CHSs can be used to adapt to the demands of various communication scenarios. Furthermore, we focus on the improved maximum-time-to-rendezvous and maximum-first-time-to-rendezvous performance of the new construction compared to the prior research at the same sequence length. The new channel-hopping sequences ensure that rendezvous occurs between any two sequences and the rendezvous times are random and unpredictable when using licensed channels under asynchronous access, although the full degree-of-rendezvous is not satisfied. Our simulation results show that the new construction is more balanced and unpredictable between the maximum-time-to-rendezvous and the mean and variance of time-to-rendezvous. Full article
(This article belongs to the Special Issue Coding and Entropy)
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25 pages, 354 KiB  
Article
Jeffreys Divergence and Generalized Fisher Information Measures on Fokker–Planck Space–Time Random Field
by Jiaxing Zhang
Entropy 2023, 25(10), 1445; https://doi.org/10.3390/e25101445 - 13 Oct 2023
Cited by 1 | Viewed by 1471
Abstract
In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generalized Fisher information of a single space–time random field with respect [...] Read more.
In this paper, we present the derivation of Jeffreys divergence, generalized Fisher divergence, and the corresponding De Bruijn identities for space–time random field. First, we establish the connection between Jeffreys divergence and generalized Fisher information of a single space–time random field with respect to time and space variables. Furthermore, we obtain the Jeffreys divergence between two space–time random fields obtained by different parameters under the same Fokker–Planck equations. Then, the identities between the partial derivatives of the Jeffreys divergence with respect to space–time variables and the generalized Fisher divergence are found, also known as the De Bruijn identities. Later, at the end of the paper, we present three examples of the Fokker–Planck equations on space–time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and their corresponding De Bruijn identities. Full article
(This article belongs to the Special Issue Coding and Entropy)
14 pages, 609 KiB  
Article
Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback
by Haoheng Yuan, Guangfen Xie and Bin Dai
Entropy 2023, 25(9), 1339; https://doi.org/10.3390/e25091339 - 15 Sep 2023
Cited by 1 | Viewed by 993
Abstract
For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then [...] Read more.
For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key. By secret sharing, any capacity-achieving coding scheme for the AWGN channel without feedback can be secure by itself, which indicates that the capacity of the same model without the secrecy constraint also affords an achievable secrecy rate to the AWGN channel with an eavesdropper and feedback. Then it is natural to ask: is the secret key-based feedback scheme still the optimal scheme for the AWGN multiple-access channel (MAC) with an external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose the optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. This paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of an external eavesdropper and channel feedback. Full article
(This article belongs to the Special Issue Coding and Entropy)
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14 pages, 336 KiB  
Article
Construction of Optimal Frequency Hopping Sequence Set with Low-Hit-Zone
by Xinyu Tian, Hongyu Han, Xianhua Niu and Xing Liu
Entropy 2023, 25(7), 1044; https://doi.org/10.3390/e25071044 - 11 Jul 2023
Cited by 1 | Viewed by 1491
Abstract
In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be [...] Read more.
In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be verified that they are optimal with respect to the Peng–Fan–Lee bound. Full article
(This article belongs to the Special Issue Coding and Entropy)
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17 pages, 510 KiB  
Article
Channel Modeling and Quantization Design for 3D NAND Flash Memory
by Cheng Wang, Zhen Mei, Jun Li, Feng Shu, Xuan He and Lingjun Kong
Entropy 2023, 25(7), 965; https://doi.org/10.3390/e25070965 - 21 Jun 2023
Cited by 1 | Viewed by 2214
Abstract
As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new [...] Read more.
As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new sources of errors, which severely affects the reliability of the system. In this paper, for the first time, we derive the channel probability density function of 3D NAND flash memory by taking major sources of errors. Based on the derived channel probability density function, the mutual information (MI) for 3D flash memory with multiple layers is derived and used as a metric to design the quantization. Specifically, we propose a dynamic programming algorithm to jointly optimize read-voltage thresholds for all layers by maximizing the MI (MMI). To further reduce the complexity, we develop an MI derivative (MID)-based method to obtain read-voltage thresholds for hard-decision decoding (HDD) of error correction codes (ECCs). Simulation results show that the performance with jointly optimized read-voltage thresholds can closely approach that with read-voltage thresholds optimized for each layer, with much less read latency. Moreover, the MID-based MMI quantizer almost achieves the optimal performance for HDD of ECCs. Full article
(This article belongs to the Special Issue Coding and Entropy)
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13 pages, 887 KiB  
Article
Windowed Joint Detection and Decoding with IR-HARQ for Asynchronous SCMA Systems
by Mengsheng Guan, Min Zhu and Baoming Bai
Entropy 2023, 25(6), 930; https://doi.org/10.3390/e25060930 - 13 Jun 2023
Viewed by 1232
Abstract
To improve the decoding performance of asynchronous sparse code multiple access (SCMA) systems over additive white Gaussian noise (AWGN) channels, this paper proposes a novel windowed joint detection and decoding algorithm for a rate-compatible (RC), LDPC code-based, incremental redundancy (IR) hybrid automatic repeat [...] Read more.
To improve the decoding performance of asynchronous sparse code multiple access (SCMA) systems over additive white Gaussian noise (AWGN) channels, this paper proposes a novel windowed joint detection and decoding algorithm for a rate-compatible (RC), LDPC code-based, incremental redundancy (IR) hybrid automatic repeat quest (HARQ) scheme. Since incremental decoding can exchange information iteratively with the detections made at previous consecutive time units, we propose a windowed joint detection and decoding algorithm. The extrinsic information exchanging process is performed between the decoders and the previous w detectors at different consecutive time units. Simulation results show that the sliding-window IR-HARQ scheme for the SCMA system outperforms the original IR-HARQ scheme with a joint detection and decoding algorithm. The throughput of the SCMA system with the proposed IR-HARQ scheme is also improved. Full article
(This article belongs to the Special Issue Coding and Entropy)
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15 pages, 514 KiB  
Article
Transformer-Based Detection for Highly Mobile Coded OFDM Systems
by Leijun Wang, Wenbo Zhou, Zian Tong, Xianxian Zeng, Jin Zhan, Jiawen Li and Rongjun Chen
Entropy 2023, 25(6), 852; https://doi.org/10.3390/e25060852 - 26 May 2023
Cited by 1 | Viewed by 2162
Abstract
This paper is concerned with mobile coded orthogonal frequency division multiplexing (OFDM) systems. In the high-speed railway wireless communication system, an equalizer or detector should be used to mitigate the intercarrier interference (ICI) and deliver the soft message to the decoder with the [...] Read more.
This paper is concerned with mobile coded orthogonal frequency division multiplexing (OFDM) systems. In the high-speed railway wireless communication system, an equalizer or detector should be used to mitigate the intercarrier interference (ICI) and deliver the soft message to the decoder with the soft demapper. In this paper, a Transformer-based detector/demapper is proposed to improve the error performance of the mobile coded OFDM system. The soft modulated symbol probabilities are computed by the Transformer network, and are then used to calculate the mutual information to allocate the code rate. Then, the network computes the codeword soft bit probabilities, which are delivered to the classical belief propagation (BP) decoder. For comparison, a deep neural network (DNN)-based system is also presented. Numerical results show that the Transformer-based coded OFDM system outperforms both the DNN-based and the conventional system. Full article
(This article belongs to the Special Issue Coding and Entropy)
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12 pages, 409 KiB  
Article
Adaptive Bit-Labeling Design for Probabilistic Shaping Based on Residual Source Redundancy
by Chen Chen, Qiwang Chen, Sanya Liu and Lin Zhou
Entropy 2023, 25(4), 586; https://doi.org/10.3390/e25040586 - 29 Mar 2023
Cited by 2 | Viewed by 1432
Abstract
By using the residual source redundancy to achieve the shaping gain, a joint source-channel coded modulation (JSCCM) system has been proposed as a new solution for probabilistic amplitude shaping (PAS). However, the source and channel codes in the JSCCM system should be designed [...] Read more.
By using the residual source redundancy to achieve the shaping gain, a joint source-channel coded modulation (JSCCM) system has been proposed as a new solution for probabilistic amplitude shaping (PAS). However, the source and channel codes in the JSCCM system should be designed specifically for a given source probability to ensure optimal PAS performance, which is undesirable for systems with dynamically changing source probabilities. In this paper, we propose a new shaping scheme by optimizing the bit-labeling of the JSCCM system. Instead of the conventional fixed labeling, the proposed bit-labelings are adaptively designed according to the source probability and the source code. Since it is simple to switch between different labelings according to the source probability and the source code, the proposed design can be considered as a promising low complexity alternative to obtain the shaping gain for sources with different probabilities. Numerical results show that the proposed bit-labelings can significantly improve the bit-error rate (BER) performance of the JSCCM system. Full article
(This article belongs to the Special Issue Coding and Entropy)
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15 pages, 418 KiB  
Article
Design and Analysis of Joint Group Shuffled Scheduling Decoding Algorithm for Double LDPC Codes System
by Qiwang Chen, Yanzhao Ren, Lin Zhou, Chen Chen and Sanya Liu
Entropy 2023, 25(2), 357; https://doi.org/10.3390/e25020357 - 15 Feb 2023
Cited by 3 | Viewed by 1854
Abstract
In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to [...] Read more.
In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to each group; the grouping relies on the types or the length of the variable nodes (VNs). By comparison, the conventional shuffled scheduling decoding algorithm can be regarded as a special case of this proposed algorithm. A novel joint extrinsic information transfer (JEXIT) algorithm for the D-LDPC codes system with the JGSSD algorithm is proposed, by which the source and channel decoding are calculated with different grouping strategies to analyze the effects of the grouping strategy. Simulation results and comparisons verify the superiority of the JGSSD algorithm, which can adaptively trade off the decoding performance, complexity and latency. Full article
(This article belongs to the Special Issue Coding and Entropy)
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