Mathematical Theory and Applications of Error Correcting Codes

✍ Scribed by Stefano Spezia (editor)

• Publisher: Arcler Press
• Year: 2020
• Tongue: English
• Leaves: 560
• Category: Library

✦ Synopsis

Mathematical Theory and Applications of Error-Correcting Codes book presents those concepts of mathematics that continue to reveal essentials in making reliable the data exchange between systems and their parts. For such reason, its applications range over many areas, including physical science, engineering, and medicine. In particular, it treats of hard and soft-decision decoding, of cyclic and quasi-cyclic codes, of Reed-Solomon codes, of low density parity check codes, and quantum error-correcting codes.

✦ Table of Contents

Cover
Title Page
Copyright
DECLARATION
ABOUT THE EDITOR
TABLE OF CONTENTS
List of Contributors
List of Abbreviations
Preface
Section 1 Introduction to Error-Correcting Codes
Chapter 1 Error-correcting Codes and Neural Networks
Abstract
Introduction And Summary
Codes And Good Codes
Neural Encodings Of Stimulus Spaces
Acknowledgements
References
Section 2 Hard and Soft Decision Decoding
Chapter 2 Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection
Abstract
Introduction
Basic Definitions
Algorithm Description
Complexity Analysis
Simulation Results and Statistical Analysis
Conclusions
Acknowledgments
Conflicts Of Interest
References
Chapter 3 Soft-Decision Low-Complexity Chase Decoders for the RS (255,239) Code
Abstract
Introduction
Rs Decoders
Low-Complexity Chase Decoder
Decoder Architecture
Implementation Results
Conclusions
References
Chapter 4 Low-energy Error Correction of NAND Flash Memory through Soft-decision Decoding
Abstract
Introduction
Energy Consumption Of Multi-Bit Data Read In Nand Flash Memory
Soft-Decision Error Correcting Performance In Nand Flash Memory
Hardware Performance Of (68254, 65536) Ldpc Decoder
Low-Energy Error Correction Scheme For Nand Flash Memory
Concluding Remarks
Acknowledgements
References
Chapter 5 Performance of Soft Viterbi Decoder enhanced with Non-Transmittable Codewords for Storage Media
Abstract
Public Interest Statement
Introduction
Binary Convolutional Encoding And Decoding
Enhanced Soft Viterbi Algorithm
Developed Model
Result And Discussion
Conclusion
Funding
References
Section 3 Linear Codes: Cyclic and Constacyclic Codes
Chapter 6 The Structure of One Weight Linear and Cyclic Codes Over Zr2 x (Z2 + uZ2)S
Abstract
Introduction
Preliminaries
The Structure of One Weight Z2Z2[u]-Linear Codes
One Weight Z2Z2[u]-Cyclic Codes
Examples Of One Weight Z2Z2[u]-Cyclic Codes
Conclusion
Acknowledgement
References
Chapter 7 (1 + u)-Constacyclic Codes over Z 4 + uZ 4
Abstract
Background
(1 + U)-Constacyclic Codes Over Z4 + UZ 4
Gray Images Of (1 + U)-Constacyclic Codes Over R
Conclusion
Acknowledgements
Competing Interests
References
Section 4 Introduction to Error-Correcting Codes
Chapter 8 Projection Decoding of Some Binary Optimal Linear Codes of Lengths 36 and 40
Abstract
Introduction
Projection of Binary Linear Codes
Construction of Binary Optimal [36, 19, 8] And [40, 22, 8] Codes
Projection Decoding
Examples
Conclusions
Funding
Conflicts of Interest
References
Chapter 9 Reed-Solomon Turbo Product Codes for Optical Communications: From Code Optimization to Decoder Design
Abstract
Introduction
Reed-Solomon Product Codes
Turbo Decoding of RS Product Codes
RS Product Code Design For Optical Communications
Full-Parallel Turbo Decoding Architecture Dedicated to Product Codes
Complexity and Throughput Analysis of The Full-Parallel Reed-Solomon Turbo Decoders
Implementation of an RS Turbo Decoder For Ultra High Throughput Communication
Conclusion
Acknowledgments
References
Chapter 10 Enhancing BER Performance Limit of BCH and RS Codes Using Multipath Diversity
Abstract
Introduction
Related Work
Forward Error Correction
Multipath Propagation
Methodology
Column Weight Multipath Combiner (Cwmc)
Results
Conclusions
Acknowledgements
Conflicts Of Interest
Abbreviations
References
Section 5 Quasi Cyclic Codes
Chapter 11 Quasi-Cyclic Codes via Unfolded Cyclic Codes and Their Reversibility
Abstract
Section I
Introduction
Section II
Preliminaries
Section III
Generator Polynomial Matrix Of F.(C)
Section IV
Reversibility of Unfolded Cyclic Codes
Section V
Numerical Examples
Section VI
Conclusion
References
Chapter 12 Skew Cyclic and Quasi-Cyclic Codes of Arbitrary Length over Galois Rings
Abstract
Preliminaries
Skew Cyclic Codes
Skew Quasi-Cyclic Codes
Examples
References
Section 6 Low Density Parity Check Codes
Chapter 13 On the use of Ordered Statistics Decoders For Low-Density Parity-Check Codes In Space Telecommand Links
Abstract
Introduction
Ldpc Codes For Space Telecommand Links
Decoding Algorithms
Error Rate Versus Complexity Tradeoff Evaluation
Impact Of Limited Memory
Conclusions
Endnote
Appendix
Acknowledgements
Competing Interests
References
Chapter 14 Optimization of LDPC Codes over the Underwater Acoustic Channel
Abstract
Introduction
Underwater Acoustic Channel Model
Iterative DFE-LDPC Structure and Its Exit Charts
Optimization Of LDPC Codes
Conclusions
Conflict Of Interests
Acknowledgments
References
Chapter 15 Augmented Decoders for LDPC Codes
Abstract
Introduction
Brief Overview LDPC Codes
Method
Numerical Results
Conclusions
Abbreviations
References
Chapter 16 Adaptive Rate-Compatible Non-Binary LDPC Coding Scheme for the B5G Mobile System
Abstract
Introduction
The Construction of RC-NB-LDPC Codes
Channel Clustering Based on The K-Means++ Algorithm
Design And Performance Simulation Of The Adaptive RC-NB-LDPC Coding Scheme
Conclusions
Conflicts of Interest
References
Chapter 17 Improved Symbol Value Selection for Symbol Flipping-based Non-binary LDPC Decoding
Abstract
Introduction
System Model
Non-Binary LDPC Decoding
Proposed Symbol Value Selection Algorithm
Computational Complexity
Simulation Results and Discussion
Conclusions
Acknowledgments
References
Chapter 18 DNA Barcoding through Quaternary LDPC Codes
Abstract
Introduction
Results
Discussion
Methods
Acknowledgments
Funding Statement
References
Chapter 19 High Speed and Adaptable Error Correction for Megabit/s Rate Quantum Key Distribution
Abstract
Introduction
Results
Discussion
Methods
Acknowledgements
References
Section 7 Introduction to Error-Correcting Codes
Chapter 20 Duality of Quantum and Classical Error Correction Codes: Design Principles and Examples
Abstract
Section I
Section II
Quantum Decoherence
Section III
Quantum Coding Theory
Section IV
Section V
Stabilizer Formalism
Section VI
Quantum-To-Classical Isomorphism
Section VII
Taxonomy Of Stabilizer Codes
Section VIII
Design Examples
Section IX
Conclusion & Design Guidelines
References
Chapter 21 Dynamic Concatenation of Quantum Error Correction in Integrated Quantum Computing Architecture
Abstract
Introduction
Results
Discussion
Acknowledgements
References
Index
Back Cover