An Introduction to Algebraic and Combinatorial Coding Theory

✍ Scribed by Olga Moreira (editor)

• Publisher: Arcler Press
• Year: 2024
• Tongue: English
• Leaves: 401
• Category: Library

✦ Synopsis

“An Introduction to Algebraic and Combinatorial Coding Theory” is a comprehensive book that offers a thorough exploration of the principles and techniques of coding theory. It serves as a valuable resource for readers interested in gaining a deeper understanding of error detection and correction in communication systems. With its well-structured chapters covering coding theory fundamentals, algebraic codes, cyclic codes, block codes, and advanced coding techniques, this book caters to the needs of students, researchers, and professionals in the field. It provides a solid foundation in coding theory and showcases its practical applications in various domains, including telecommunications, data storage, and cryptography.

✦ Table of Contents

Cover
HalfTitle Page
Title Page
Copyright
Declaration
About the Editor
Table of Contents
List of Contributors
List of Abbreviations
Preface
Chapter 1: Introduction
Fundamental Concepts in Coding Theory
Fundamental Concepts of Algebraic Coding Theory
Fundamental Concepts of Combinatorial Coding Theory
Applications and Future Directions in Coding Theory
References
Chapter 2: Digital Image Information Hiding Algorithm Research Based on LDPC Code
Abstract
Introduction
Chaotic Sequence Encryption
The Research Method—application of Ldpc Code in Hiding Algorithm
Improved Encryption Algorithm Based on Ldpc Code and Chaotic Sequence
Analysis of Simulation Experiments Results and Discussions
Conclusions
References
Chapter 3: Rate-Adaptive BCH Codes for Distributed Source Coding
Abstract
Introduction
Rate-adaptive Bch Codes
A Model for the Performance of Rateadaptive Bch Codes
Hierarchical Check of Rate-adaptive Bch Codes
Experimental Results
Conclusions
Appendix
References
Chapter 4: Reducing the Overhead of BCH Codes: New Double Error Correction Codes
Abstract
Introduction
Coding Theory and Bch Codes
Low Redundancy and Reduced Overhead (IRRO) Double Error Correction Codes
Evaluation and Comparison
Conclusions
References
Chapter 5: Ideals of Numerical Semigroups and Error-Correcting Codes
Abstract
Introduction
Numerical Semigroups
Ideals of Numerical Semigroups
One-point Algebraic-geometry Codes
Ideals and the Length of Algebraic-geometry Codes
Ideals and Isometry-dual Sequences of One-point Algebraic-geometry Codes
Ideals and Generalized Hamming Weights
Further Reading
Conclusions
Acknowledgments
References
Chapter 6: Turbo Codes for Multi-Hop Wireless Sensor Networks with Decode-andForward Mechanism
Abstract
Introduction
Related Work
Channel Model
Error Correction Codes and Their Processing Power
Evaluation
Conclusions
References
Chapter 7: Entanglement-Assisted Quantum Codes from Cyclic Codes
Abstract
Introduction
Preliminaries
New Entanglement-assisted Quantum-error-correcting Cyclic Codes
Code Examples
Conclusions
Author Contributions
References
Chapter 8: Low-Complexity Chase Decoding of Reed–Solomon Codes Using Channel Evaluation
Abstract
Introduction
Lcc Decoding Algorithm
Time-varying Channel Adaptive LCC Algorithm
The Proposed Time-varying Channel Adaptive LCC Decoder
Implementation Results
Conclusions
References
Chapter 9: How Reed-Solomon Codes Can Improve Steganographic Schemes
Abstract
Introduction
A Word on Coding Theory
Syndrome Coding
What Reed-solomon Codes Are, and why they May be Interesting
Conclusion
Appendix
Acknowledgments
References
Chapter 10: A New Minimize Matrix Computation Coding Method for Distributed Storage Systems
Abstract
Introduction
Background and Motivation
The Proposed Scheme of Optrs Codes
The Performance Comparison Between CRS Codes and OPTRS Codes
The Architecture of the Storage System
Evaluation
Related Works
Conclusion
Data Availability
Conflicts Of Interest
Acknowledgments
References
Chapter 11: Permutation-Based Block Code for Short Packet Communication Systems
Abstract
Introduction
Materials and Methods
Results
Conclusions
References
Chapter 12: A Simple Neural-Network-Based Decoder for Short Binary Linear Block Codes
Abstract
Introduction
Preliminaries of Conventional Soft Decision Decoder
Deep Learning-based Decoder
Proposed Multi-class Neural Network-based Decoder
Dataset Generation and Neural Network Training
Experimental Results of Decoding by Proposed Multi-class Nn-based Decoder
Conclusions
References
Chapter 13: An Analytical Approach to Error Detection and Correction for Onboard Nanosatellites
Abstract
Introduction
Related Works
Methods
Edac Mechanism V-1.1
Edac Mechanism V-1.2
Edac Mechanism V-1.3
Results and Discussion
Limitations and Future Works
Conclusions
References
Chapter 14: Application of Forward Error Correction (FEC) Codes in Wireless Acoustic Emission Structural Health Monitoring on Rail
Abstract
Introduction
AE SHM Setup
Carbody Shell Application
Selection of FEC Codes for the Railway Application
Simulation—results
Conclusions and Future Work
Author Contributions
References
Chapter 15: Blind Recognition of Forward Error Correction Codes Based on Recurrent Neural Network
Abstract
Introduction
The Recognition Process
The Proposed Approach
Simulation Results
Conclusions
Author Contributions
Acknowledgments
References
Index
Back Cover