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Advances in Modern Channel Coding
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Advances in Modern Channel Coding

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 October 2025 | Viewed by 2699

Special Issue Editors

Prof. Dr. Yongpeng Wu

E-Mail Website
Guest Editor
Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China
Interests: MIMO/massive MIMO; massive access; secure communication; power line communication
Dr. Peihong Yuan

E-Mail Website
Guest Editor
Research Laboratory of Electronics (RLE), Massachusetts Institute of Technology (MIT), Cambridge, MA, USA
Interests: applied probability; information theory; coding theory; polar coding; LDPC codes; probabilistic shaping; GRAND

Special Issue Information

Dear Colleagues,

Channel codes are fundamental to the integrity and performance of communication systems. They play a crucial role in ensuring data are transmitted accurately over noisy and unreliable channels. From the inception of classic coding schemes like Hamming codes and Reed–Solomon codes to the more recent breakthroughs in Turbo codes, Low-Density Parity-Check (LDPC) codes and polar codes, the evolution of channel coding techniques has been pivotal in achieving remarkable improvements in data transmission efficiency and error correction capabilities.

In recent years, the demand for higher data rates, improved spectral efficiency, and robust performance in diverse and challenging environments has spurred the development of novel coding paradigms and sophisticated decoding algorithms. This Special Issue aims to capture the essence of these advancements by presenting a collection of original research articles, comprehensive reviews, and insightful perspectives from leading experts in the field.

The contributions in this Special Issue cover a wide spectrum of topics, including, but not limited to, the following:

  • Turbo, LDPC, polar, and product codes;
  • Coded modulation;
  • Joint source-channel coding;
  • Code design for short-packet communications;
  • Coding for optical/wireless communications;
  • Rateless codes;
  • Machine learning for codes and decoder designs;
  • Guess-based decoding;
  • Probabilistic shaping.

Prof. Dr. Yongpeng Wu
Dr. Peihong Yuan
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

  • LDPC codes
  • turbo codes
  • polar coding
  • probabilistic shaping
  • coded modulation

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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

16 pages, 304 KiB  
Article
LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis
by Hengzhou Xu, Xiaodong Zhang, Mengmeng Xu, Haipeng Yu and Hai Zhu
Entropy 2025, 27(5), 476; https://doi.org/10.3390/e27050476 - 27 Apr 2025
Viewed by 111
Abstract
In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based [...] Read more.
In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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18 pages, 3845 KiB  
Article
Mutual Information Neural-Estimation-Driven Constellation Shaping Design and Performance Analysis
by Xiuli Ji, Qian Wang, Liping Qian and Pooi-Yuen Kam
Entropy 2025, 27(4), 451; https://doi.org/10.3390/e27040451 - 21 Apr 2025
Viewed by 190
Abstract
The choice of constellations largely affects the performance of both wireless and optical communications. To address increasing capacity requirements, constellation shaping, especially for high-order modulations, is imperative in high-speed coherent communication systems. This paper, thus, proposes novel mutual information neural estimation (MINE)-based geometric, [...] Read more.
The choice of constellations largely affects the performance of both wireless and optical communications. To address increasing capacity requirements, constellation shaping, especially for high-order modulations, is imperative in high-speed coherent communication systems. This paper, thus, proposes novel mutual information neural estimation (MINE)-based geometric, probabilistic, and joint constellation shaping schemes, i.e., the MINE-GCS, MINE-PCS, and MINE-JCS, to maximize mutual information (MI) via emerging deep learning (DL) techniques. Innovatively, we first introduce the MINE module to effectively estimate and maximize MI through backpropagation, without clear knowledge of the channel state information. Then, we train encoder and probability generator networks with different signal-to-noise ratios to optimize the distribution locations and probabilities of the points, respectively. Note that MINE transforms the precise MI calculation problem into a parameter optimization problem. Our MINE-based schemes only optimize the transmitter end, and avoid the computational and structural complexity in traditional shaping. All the designs were verified through simulations as having superior performance for MI, among which the MINE-JCS undoubtedly performed the best for additive white Gaussian noise, compared to the unshaped QAMs and even the end-to-end training and other DL-based joint shaping schemes. For example, the low-order 8-ary MINE-GCS could achieve an MI gain of about 0.1 bits/symbol compared to the unshaped Star-8QAM. It is worth emphasizing that our proposed schemes achieve a balance between implementation complexity and MI performance, and they are expected to be applied in various practical scenarios with different noise and fading levels in the future. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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21 pages, 1375 KiB  
Article
Bit-Level Construction for Multiplicative-Repetition-Based Non-Binary Polar Codes
by Rongchi Xu, Peiyao Chen, Ling Liu, Min Zhu and Baoming Bai
Entropy 2025, 27(4), 377; https://doi.org/10.3390/e27040377 - 2 Apr 2025
Viewed by 220
Abstract
In this paper, we discuss non-binary polar codes using a 2×2 matrix over a Galois field GF(2q) as the kernel. Conventional construction of non-binary polar codes divides the synthesized channels into frozen channels and information channels. Each information [...] Read more.
In this paper, we discuss non-binary polar codes using a 2×2 matrix over a Galois field GF(2q) as the kernel. Conventional construction of non-binary polar codes divides the synthesized channels into frozen channels and information channels. Each information channel carries one symbol, i.e., q bits. However, there are many middle channels with insufficient polarization, which cannot carry one symbol of q bits but only i bits, 1≤i<q,i∈Z, at finite block length. In this paper, we consider bit-level construction for multiplicative repetition (MR)-based non-binary polar codes and propose a bit-level construction based on the two following methods. We first calculate the error probability and channel capacity lower bound of each synthesized channel based on the channel degradation method, and then determine both the number and index of the carried bits for each synthesized channel according to the symbol error probability and capacity. To reduce complexity, we also introduce a Monte-Carlo method. We compute the error probability of each synthesized channel carrying i information bits and select the optimal construction that can minimize the union bound of the error probability. Finally, an improved construction-based probabilistic shaping method for MR-based non-binary polar codes is considered. Simulation results show that the proposed construction significantly improved the decoding performance compared with the conventional construction scheme. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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22 pages, 428 KiB  
Article
Restart Mechanisms for the Successive-Cancellation List-Flip Decoding of Polar Codes
by Charles Pillet, Ilshat Sagitov, Alexios Balatsoukas-Stimming and Pascal Giard
Entropy 2025, 27(3), 309; https://doi.org/10.3390/e27030309 - 14 Mar 2025
Viewed by 471
Abstract
Polar codes concatenated with a cyclic redundancy check (CRC) code have been selected in the 5G standard with the successive-cancellation list (SCL) of list size L = 8 as the baseline algorithm. Despite providing great error-correction performance, a large list size increases the [...] Read more.
Polar codes concatenated with a cyclic redundancy check (CRC) code have been selected in the 5G standard with the successive-cancellation list (SCL) of list size L = 8 as the baseline algorithm. Despite providing great error-correction performance, a large list size increases the hardware complexity of the SCL decoder. Alternatively, flip decoding algorithms were proposed to improve the error-correction performance with a low-complexity hardware implementation. The combination of list and flip algorithms, the successive-cancellation list flip (SCLF) and dynamic SCLF (DSCLF) algorithms, provides error-correction performance close to SCL-32 with a list size L = 2 and Tmax = 300 maximum additional trials. However, these decoders have a variable execution time, a characteristic that poses a challenge to some practical applications. In this work, we propose a restart mechanism for list–flip algorithms that allows us to skip parts of the decoding computations without affecting the error-correction performance. We show that the restart location cannot realistically be allowed to occur at any location in a codeword as it would lead to an unreasonable memory overhead under DSCLF. Hence, we propose a mechanism where the possible restart locations are limited to a set and propose various construction methods for that set. The construction methods are compared, and the tradeoffs are discussed. For a polar code of length N = 1024 and rate ¼, under DSCLF decoding with a list size L = 2 and a maximum number of trials Tmax = 300, our proposed approach is shown to reduce the average execution time by 41.7% with four restart locations at the cost of approximately 1.5% in memory overhead. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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24 pages, 1215 KiB  
Article
Network Coding-Enhanced Polar Codes for Relay-Assisted Visible Light Communication Systems
by Congduan Li, Mingyang Zhong, Yiqian Zhang, Dan Song, Nanfeng Zhang and Jingfeng Yang
Entropy 2024, 26(12), 1112; https://doi.org/10.3390/e26121112 - 19 Dec 2024
Viewed by 1034
Abstract
This paper proposes a novel polar coding scheme tailored for indoor visible light communication (VLC) systems. Simulation results demonstrate a significant reduction in bit error rate (BER) compared to uncoded transmission, with a coding gain of at least 5 dB. Furthermore, the reliable [...] Read more.
This paper proposes a novel polar coding scheme tailored for indoor visible light communication (VLC) systems. Simulation results demonstrate a significant reduction in bit error rate (BER) compared to uncoded transmission, with a coding gain of at least 5 dB. Furthermore, the reliable communication area of the VLC system is substantially extended. Building on this foundation, this study explores the joint design of polar codes and physical-layer network coding (PNC) for VLC systems. Simulation results illustrate that the BER of our scheme closely approaches that of the conventional VLC relay scheme. Moreover, our approach doubles the throughput, cuts equipment expenses in half, and boosts effective bit rates per unit time-slot twofold. This proposed design noticeably advances the performance of VLC systems and is particularly well-suited for scenarios with low-latency demands. Full article
(This article belongs to the Special Issue Advances in Modern Channel Coding)
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