مقدمه‌ای بر نظریه کدگذاری جبری و ترکیبی

“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. 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