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Entropy
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New Advances in Error-Correcting Codes
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New Advances in Error-Correcting Codes

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 (15 November 2024) | Viewed by 3128

Special Issue Editors

Prof. Dr. Robert H. Morelos-Zaragoza

E-Mail Website
Guest Editor
College of Engineering, San Jose State University, San Jose, CA 95192, USA
Interests: error-correcting codes; coded modulation; signal processing; watermarking
Prof. Dr. T. Aaron Gulliver

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada
Interests: information theory; source coding; error correcting codes

Special Issue Information

Dear Colleagues,

Error-correcting coding is an indispensable part of signal processing in modern communication and computer systems. In recent years, low-density parity-check (LDPC) codes and polar codes have been designed and implemented in practical applications such as wireless networks, satellite communications and memory systems. Furthermore, block codes are being explored for use in quantum computation and communication channels as well as in various watermarking techniques and cryptographic schemes. As technology advances, it is of great importance to investigate the types of error-correcting codes that may be needed in future applications. A good example of this is future wireless networks, which will require a low latency that limits the code length. This offers an opportunity to explore short block codes as alternatives to LDPC codes and polar codes, which are known to have good performance only at moderate to large code lengths. Another important example is quantum error-correcting codes that are fundamental for both enabling powerful computing systems as well as securing network communications. The area of error-correcting coding is therefore a very active one, with new open problems to be solved with innovative designs and implementations.

This Special Issue invites researchers in this area to share results and insights on novel applications of error-correcting codes, including their design, analysis and implementation.

Prof. Dr. Robert H. Morelos-Zaragoza
Prof. Dr. T. Aaron Gulliver
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 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

  • error-correcting codes
  • channel coding
  • forward error correction
  • future networks
  • quantum channels

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Published Papers (4 papers)

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Research

12 pages, 498 KiB  
Article
New Variable-Weight Optical Orthogonal Codes with Weights 3 to 5
by Si-Yeon Pak, Hyo-Won Kim, DaeHan Ahn and Jin-Ho Chung
Entropy 2024, 26(11), 982; https://doi.org/10.3390/e26110982 - 15 Nov 2024
Viewed by 299
Abstract
In optical networks, designing optical orthogonal codes (OOCs) with appropriate parameters is essential for enhancing the overall system performance. They are divided into two categories, constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs), based on the number of distinct Hamming weights present in their [...] Read more.
In optical networks, designing optical orthogonal codes (OOCs) with appropriate parameters is essential for enhancing the overall system performance. They are divided into two categories, constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs), based on the number of distinct Hamming weights present in their codewords. This paper introduces a method for constructing VW-OOCs of length kp by using the structure of an integer ring and the Chinese Remainder Theorem. In particular, we present some specific VW-OOCs with weights of 3, 4, or 5. The results demonstrate that certain optimal VW-OOCs can be obtained with parameters that are not covered in the existing literature. Full article
(This article belongs to the Special Issue New Advances in Error-Correcting Codes)
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12 pages, 1670 KiB  
Article
Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes
by Adriana-Maria Cuc, Florin Lucian Morgoș, Adriana-Marcela Grava and Cristian Grava
Entropy 2024, 26(9), 720; https://doi.org/10.3390/e26090720 - 23 Aug 2024
Viewed by 511
Abstract
In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the [...] Read more.
In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the least squares algorithm in various scenarios. For example, the impulse response of the AWGN channel h was initially estimated using a training sequence. Subsequently, the impulse response was calculated based on the training sequence and then re-estimated once using the sequence estimated from the output of the LDPC decoder. Lastly, the impulse response was calculated based on the training sequence and re-estimated twice using the sequence estimated from the output of the LDPC decoder. Comparisons were made between the performances of the three mentioned situations, with the situation in which a perfect estimate of the impulse response of the channel is assumed. The performance analysis focused on how the bit error rate changes in relation to the signal-to-noise ratio. The BER performance comes close to the scenario of having a perfect estimate of the impulse response when the estimation is performed based on the training sequence and then re-estimated twice from the sequence obtained from the output of the LDPC decoder. Full article
(This article belongs to the Special Issue New Advances in Error-Correcting Codes)
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14 pages, 723 KiB  
Article
Dynamic Injection and Permutation Coding for Enhanced Data Transmission
by Kehinde Ogunyanda, Opeyemi O. Ogunyanda and Thokozani Shongwe
Entropy 2024, 26(8), 685; https://doi.org/10.3390/e26080685 - 13 Aug 2024
Viewed by 626
Abstract
In this paper, we propose a novel approach to enhance spectral efficiency in communication systems by dynamically adjusting the mapping between cyclic permutation coding (CPC) and its injected form. By monitoring channel conditions such as interference levels and impulsive noise strength, the system [...] Read more.
In this paper, we propose a novel approach to enhance spectral efficiency in communication systems by dynamically adjusting the mapping between cyclic permutation coding (CPC) and its injected form. By monitoring channel conditions such as interference levels and impulsive noise strength, the system optimises the coding scheme to maximise data transmission reliability and efficiency. The CPC method employed in this work maps information bits onto non-binary symbols in a cyclic manner, aiming to improve the Hamming distance between mapped symbols. To address challenges such as low data rates inherent in permutation coding, injection techniques are introduced by removing δ column(s) from the CPC codebook. Comparative analyses demonstrate that the proposed dynamic adaptation scheme outperforms conventional permutation coding and injection schemes. Additionally, we present a generalised mathematical expression to describe the relationship between the spectral efficiencies of both coding schemes. This dynamic approach ensures efficient and reliable communication in environments with varying levels of interference and impulsive noise, highlighting its potential applicability to systems like power line communications. Full article
(This article belongs to the Special Issue New Advances in Error-Correcting Codes)
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17 pages, 2914 KiB  
Article
Adaptive Segmented Aggregation and Rate Assignment Techniques for Flexible-Length Polar Codes
by Souradip Saha, Shubham Mahajan, Marc Adrat and Wolfgang Gerstacker
Entropy 2024, 26(7), 584; https://doi.org/10.3390/e26070584 - 9 Jul 2024
Viewed by 620
Abstract
Polar codes have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provable capacity achieving capability. They have been standardized to be used for encoding information on the control channels in 5G wireless networks due to their [...] Read more.
Polar codes have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provable capacity achieving capability. They have been standardized to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The conventional approach to generate polar codes is to recursively use 2×2 kernels and polarize channel capacities. This approach however, has a limitation of only having the ability to generate codewords of length Norig=2n form. In order to mitigate this limitation, multiple techniques have been developed, e.g., polarization kernels of larger sizes, multi-kernel polar codes, and downsizing techniques like puncturing or shortening. However, the availability of so many design options and parameters, in turn makes the choice of design parameters quite challenging. In this paper, the authors propose a novel polar code construction technique called Adaptive Segmented Aggregation which generates polar codewords of any arbitrary codeword length. This approach involves dividing the entire codeword into smaller segments that can be independently encoded and decoded, thereby aggregated for channel processing. Additionally a rate assignment methodology has been derived for the proposed technique, that is tuned to the design requirement. Full article
(This article belongs to the Special Issue New Advances in Error-Correcting Codes)
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