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Coding Theory and Its Applications
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Coding Theory and Its Applications

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

Deadline for manuscript submissions: 31 May 2026 | Viewed by 7162

Special Issue Editors

Dr. Yauhen Yakimenka

E-Mail Website
Guest Editor
Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA
Interests: coding theory; information theory; private information retrieval; compressed sensing
Dr. Eirik Rosnes

E-Mail Website
Guest Editor
Information Theory Section, Simula UiB, N-5008 Bergen, Norway
Interests: information and coding theory and their applications to distributed storage and computing, privacy, and security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In an era where the reliable transmission and storage of information are paramount, coding theory stands at the forefront of ensuring data integrity and security across diverse applications. From classical error-correcting codes to cutting-edge developments in quantum coding and network information theory, coding theory is continually evolving to meet the challenges posed by emerging technologies.

Advancements such as polar codes, low-density parity-check (LDPC) codes, and turbo codes have significantly enhanced the efficiency and reliability of communication systems. The proliferation of big data, cloud computing, and the Internet of Things (IoT) demands innovative coding techniques that are capable of handling massive data volumes with minimal errors. Additionally, the integration of coding theory with machine learning is opening new horizons for intelligent error correction and data compression.

This Special Issue aims to compile original research articles and comprehensive reviews that reflect the latest developments and future directions in coding theory and its applications. We encourage submissions presenting novel ideas, theoretical advancements, practical implementations, and interdisciplinary approaches. Each submission will undergo a formal peer review process.

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

  • The design and analysis of error-correcting codes;
  • Network coding and applications in communication networks;
  • Quantum coding and quantum error correction;
  • Coding for distributed storage and cloud computing;
  • Combinatorial and algebraic coding theory;
  • LDPC codes, turbo codes, and polar codes;
  • Coding techniques for wireless and optical communications;
  • Applications in cryptography and information security;
  • Coding for DNA storage and bioinformatics;
  • Machine learning approaches in coding theory;
  • Lattice codes and advanced modulation techniques;
  • Source coding and data compression methods;
  • Codes for multimedia transmission and data streaming;
  • Coding strategies for the Internet of Things (IoT).

We look forward to receiving your contributions to this dynamic and evolving field.

Dr. Yauhen Yakimenka
Dr. Eirik Rosnes
Guest Editors

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-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

  • coding theory
  • error-correcting codes
  • network coding
  • quantum codes
  • distributed storage
  • LDPC codes
  • polar codes
  • machine learning in coding
  • data compression

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

20 pages, 1721 KB  
Article
RL-Based Parallel LDPC Decoding with Clustered Scheduling
by Yusuf Ozkan, Yauhen Yakimenka and Jörg Kliewer
Entropy 2026, 28(2), 215; https://doi.org/10.3390/e28020215 - 12 Feb 2026
Viewed by 521
Abstract
We propose a reinforcement learning (RL)-based decoding framework for high-throughput parallel decoding of low-density parity-check (LDPC) codes using clustered scheduling. Parallel LDPC decoders must balance error-correction performance and decoding latency while avoiding memory conflicts. To address this trade-off, we construct clusters of check [...] Read more.
We propose a reinforcement learning (RL)-based decoding framework for high-throughput parallel decoding of low-density parity-check (LDPC) codes using clustered scheduling. Parallel LDPC decoders must balance error-correction performance and decoding latency while avoiding memory conflicts. To address this trade-off, we construct clusters of check nodes that satisfy a two-edge independence property, which enables conflict-free row-parallel belief propagation. An RL agent is trained offline to assign Q-values to clusters and to prioritize their update order during decoding. To overcome the exponential storage requirements of existing RL-based scheduling methods, we introduce the Q-Sum method, which approximates cluster-level Q-values as the sum of Q-values of individual check nodes, reducing storage complexity from exponential to linear in the number of check nodes. We further propose an On-the-Fly clustering strategy that enforces two-edge independence dynamically during decoding and provides additional flexibility when static clustering is not feasible. Simulation results for array-based LDPC codes over additive white Gaussian noise (AWGN) channels show that the proposed methods improve the latency-versus-performance trade-off of parallel LDPC decoders, achieving lower decoding latency and higher throughput while maintaining error rates comparable to state-of-the-art decoding methods. Full article
(This article belongs to the Special Issue Coding Theory and Its Applications)
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21 pages, 1073 KB  
Article
Near-Optimal Decoding Algorithm for Color Codes Using Population Annealing
by Fernando Martínez-García, Francisco Revson F. Pereira and Pedro Parrado-Rodríguez
Entropy 2026, 28(1), 91; https://doi.org/10.3390/e28010091 - 12 Jan 2026
Viewed by 649
Abstract
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. [...] Read more.
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. In this work, we implement a decoder that finds the recovery operation with the highest success probability by mapping the decoding problem to a spin system and using Population Annealing to estimate the free energy of the different error classes. We study the decoder performance on a 4.8.8 color code lattice under different noise models, including code capacity with bit-flip and depolarizing noise, and phenomenological noise, which considers noisy measurements, with performance reaching near-optimal thresholds for bit-flip and depolarizing noise, and the highest reported threshold for phenomenological noise. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum Low-Density Parity Check (qLDPC) codes. Full article
(This article belongs to the Special Issue Coding Theory and Its Applications)
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15 pages, 342 KB  
Article
On the Application of a Hybrid Incomplete Exponential Sum to Aperiodic Hamming Correlation of Some Frequency-Hopping Sequences
by Peihua Li and Hongyu Han
Entropy 2025, 27(9), 988; https://doi.org/10.3390/e27090988 - 21 Sep 2025
Cited by 1 | Viewed by 728
Abstract
Frequency-hopping sequences are essential in frequency-hopping spread spectrum communication systems due to their strong anti-interference capabilities, low probability of interception, and high confidentiality. Existing research has predominantly focused on the periodic Hamming correlation properties of sequences, whereas the aperiodic Hamming correlation performance more [...] Read more.
Frequency-hopping sequences are essential in frequency-hopping spread spectrum communication systems due to their strong anti-interference capabilities, low probability of interception, and high confidentiality. Existing research has predominantly focused on the periodic Hamming correlation properties of sequences, whereas the aperiodic Hamming correlation performance more accurately reflects the actual system performance. Owing to the complexity of its application scenarios and considerable research challenges, results in this area remain scarce. In this paper, we utilize exponential sums over finite fields to derive an upper bound on a hybrid incomplete exponential sum. Then, based on this upper bound, we derive bounds on the aperiodic Hamming correlation of some frequency-hopping sequence sets constructed by trace functions. Finally, by analyzing the maximum estimation error between the average and actual frequency collision numbers of such sequence sets, the validity of the derived bound is demonstrated. Full article
(This article belongs to the Special Issue Coding Theory and Its Applications)
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26 pages, 367 KB  
Article
Construction of Binary Locally Repairable Codes with Nonuniform Locality and Availability Using Combinatorial Designs
by Yu Zhang and Xiangqiong Zeng
Entropy 2025, 27(3), 269; https://doi.org/10.3390/e27030269 - 5 Mar 2025
Cited by 1 | Viewed by 1454
Abstract
In this paper, we generalize the construction of locally repairable codes (LRCs) by leveraging pairwise balanced designs (PBDs) and balanced incomplete block designs (BIBDs) to construct codes with nonuniform locality or nonuniform availability. Our constructions prioritize binary implementations for practical deployment while achieving [...] Read more.
In this paper, we generalize the construction of locally repairable codes (LRCs) by leveraging pairwise balanced designs (PBDs) and balanced incomplete block designs (BIBDs) to construct codes with nonuniform locality or nonuniform availability. Our constructions prioritize binary implementations for practical deployment while achieving optimal or near-optimal performance in terms of rate, minimum distance, and repair efficiency. Specifically, we propose distance-optimal LRCs with nonuniform localities and message-symbol (r,t)-availability. These binary constructions achieve optimal minimum distance under known bounds and have higher code rates than existing works. We also address open problems in the literature, including constructions where r∤k, and demonstrate that our constructions encompass or outperform several prior works. Full article
(This article belongs to the Special Issue Coding Theory and Its Applications)
22 pages, 444 KB  
Article
Some New Constructions of q-ary Codes for Correcting a Burst of at Most t Deletions
by Wentu Song, Kui Cai and Tony Q. S. Quek
Entropy 2025, 27(1), 85; https://doi.org/10.3390/e27010085 - 18 Jan 2025
Cited by 2 | Viewed by 1648
Abstract
In this paper, we construct q-ary codes for correcting a burst of at most t deletions, where t,q≥2 are arbitrarily fixed positive integers. We consider two scenarios of error correction: the classical error correcting codes, which recover each [...] Read more.
In this paper, we construct q-ary codes for correcting a burst of at most t deletions, where t,q≥2 are arbitrarily fixed positive integers. We consider two scenarios of error correction: the classical error correcting codes, which recover each codeword from one read (channel output), and the reconstruction codes, which allow to recover each codeword from multiple channel reads. For the first scenario, our construction has redundancy logn+8loglogn+o(loglogn) bits, encoding complexity O(q7tn(logn)3) and decoding complexity O(nlogn). For the reconstruction scenario, our construction can recover the codewords with two reads and has redundancy 8loglogn+o(loglogn) bits. The encoding complexity of this construction is Oq7tn(logn)3, and decoding complexity is Oq9t(nlogn)3. Both of our constructions have lower redundancy than the best known existing works. We also give explicit encoding functions for both constructions that are simpler than previous works. Full article
(This article belongs to the Special Issue Coding Theory and Its Applications)
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