Error-Correction Coding and Decoding : : Bounds, Codes, Decoders, Analysis and Applications.

• Superior document: Signals and Communication Technology Series
• Author: Tomlinson, Martin.
• TeilnehmendeR: Tjhai, Cen Jung.; Ambroze, Marcel A.; Ahmed, Mohammed.; Jibril, Mubarak.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2017.; ©2017.
• Year of Publication: 2017
• Edition: 1st ed.
• Language: English
• Series: Signals and Communication Technology Series
• Physical Description: 1 online resource (527 pages)

Table of Contents

• Intro
• Preface
• Acknowledgements
• Contents
• Acronyms
• Part I Theoretical Performance of Error-Correcting Codes
• 1 Bounds on Error-Correction Coding Performance
• 1.1 Gallager's Coding Theorem
• 1.1.1 Linear Codes with a Binomial Weight Distribution
• 1.1.2 Covering Radius of Codes
• 1.1.3 Usefulness of Bounds
• 1.2 Bounds on the Construction of Error-Correcting Codes
• 1.2.1 Upper Bounds
• 1.2.2 Lower Bounds
• 1.2.3 Lower Bounds from Code Tables
• 1.3 Summary
• References
• 2 Soft and Hard Decision Decoding Performance
• 2.1 Introduction
• 2.2 Hard Decision Performance
• 2.2.1 Complete and Bounded Distance Decoding
• 2.2.2 The Performance of Codes on the Binary Symmetric Channel
• 2.3 Soft Decision Performance
• 2.3.1 Performance Assuming a Binomial Weight Distribution
• 2.3.2 Performance of Self-dual Codes
• 2.4 Summary
• References
• 3 Soft Decision and Quantised Soft Decision Decoding
• 3.1 Introduction
• 3.2 Soft Decision Bounds
• 3.3 Examples
• 3.4 A Hard Decision Dorsch Decoder and BCH Codes
• 3.5 Summary
• References
• Part II Code Construction
• 4 Cyclotomic Cosets, the Mattson--Solomon Polynomial, Idempotents and Cyclic Codes
• 4.1 Introduction
• 4.2 Cyclotomic Cosets
• 4.3 The Mattson--Solomon Polynomial
• 4.4 Binary Cyclic Codes Derived from Idempotents
• 4.4.1 Non-Primitive Cyclic Codes Derived from Idempotents
• 4.5 Binary Cyclic Codes of Odd Lengths from 129 to 189
• 4.6 Summary
• References
• 5 Good Binary Linear Codes
• 5.1 Introduction
• 5.2 Algorithms to Compute the Minimum Hamming Distance of Binary Linear Codes
• 5.2.1 The First Approach to Minimum Distance Evaluation
• 5.2.2 Brouwer's Algorithm for Linear Codes
• 5.2.3 Zimmermann's Algorithm for Linear Codes and Some Improvements
• 5.2.4 Chen's Algorithm for Cyclic Codes
• 5.2.5 Codeword Enumeration Algorithm.
• 5.3 Binary Cyclic Codes of Lengths 129 len le 189
• 5.4 Some New Binary Cyclic Codes Having Large Minimum Distance
• 5.5 Constructing New Codes from Existing Ones
• 5.5.1 New Binary Codes from Cyclic Codes of Length 151
• 5.5.2 New Binary Codes from Cyclic Codes of Length ge 199
• 5.6 Concluding Observations on Producing New Binary Codes
• 5.7 Summary
• References
• 6 Lagrange Codes
• 6.1 Introduction
• 6.2 Lagrange Interpolation
• 6.3 Lagrange Error-Correcting Codes
• 6.4 Error-Correcting Codes Derived from the Lagrange Coefficients
• 6.5 Goppa Codes
• 6.6 BCH Codes as Goppa Codes
• 6.7 Extended BCH Codes as Goppa Codes
• 6.8 Binary Codes from MDS Codes
• 6.9 Summary
• References
• 7 Reed--Solomon Codes and Binary Transmission
• 7.1 Introduction
• 7.2 Reed--Solomon Codes Used with Binary Transmission-Hard Decisions
• 7.3 Reed--Solomon Codes and Binary Transmission Using Soft Decisions
• 7.4 Summary
• References
• 8 Algebraic Geometry Codes
• 8.1 Introduction
• 8.2 Motivation for Studying AG Codes
• 8.2.1 Bounds Relevant to Algebraic Geometry Codes
• 8.3 Curves and Planes
• 8.3.1 Important Theorems and Concepts
• 8.3.2 Construction of AG Codes
• 8.4 Generalised AG Codes
• 8.4.1 Concept of Places of Higher Degree
• 8.4.2 Generalised Construction
• 8.5 Summary
• References
• 9 Algebraic Quasi Cyclic Codes
• 9.1 Introduction
• 9.2 Background and Notation
• 9.2.1 Description of Double-Circulant Codes
• 9.3 Good Double-Circulant Codes
• 9.3.1 Circulants Based Upon Prime Numbers Congruent to pm3 Modulo 8
• 9.3.2 Circulants Based Upon Prime Numbers Congruent to +1 mod 8, or -1 mod 8: Cyclic Codes
• 9.4 Code Construction
• 9.4.1 Double-Circulant Codes from Extended Quadratic Residue Codes
• 9.4.2 Pure Double-Circulant Codes for Primes +3 mod 8, or -3 mod 8
• 9.4.3 Quadratic Double-Circulant Codes.
• 9.5 Evaluation of the Number of Codewords of Given Weight ƒ
• 9.6 Weight Distributions
• 9.6.1 The Number of Codewords of a Given Weight in Quadratic Double-Circulant Codes
• 9.6.2 The Number of Codewords of a Given Weight in Extended Quadratic Residue Codes
• 9.7 Minimum Distance Evaluation: A Probabilistic Approach
• 9.8 Conclusions
• 9.9 Summary
• References
• 10 Historical Convolutional Codes as Tail-Biting Block Codes
• 10.1 Introduction
• 10.2 Convolutional Codes and Circulant Block Codes
• 10.3 Summary
• References
• 11 Analogue BCH Codes and Direct Reduced Echelon Parity Check Matrix Construction
• 11.1 Introduction
• 11.2 Analogue BCH Codes and DFT Codes
• 11.3 Error-Correction of Bandlimited Data
• 11.4 Analogue BCH Codes Based on Arbitrary Field Elements
• 11.5 Examples
• 11.5.1 Example of Simple (5,3,3) Analogue Code
• 11.5.2 Example of Erasures Correction Using (15,10,4) Binary BCH code
• 11.5.3 Example of (128, 112, 17) Analogue BCH Code and Error-Correction of Audio Data (Music) Subjected to Impulsive Noise
• 11.6 Conclusions and Future Research
• 11.7 Summary
• References
• 12 LDPC Codes
• 12.1 Background and Notation
• 12.1.1 Random Constructions
• 12.1.2 Algebraic Constructions
• 12.1.3 Non-binary Constructions
• 12.2 Algebraic LDPC Codes
• 12.2.1 Mattson--Solomon Domain Construction of Binary Cyclic LDPC Codes
• 12.2.2 Non-Binary Extension of the Cyclotomic Coset-Based LDPC Codes
• 12.3 Irregular LDPC Codes from Progressive Edge-Growth Construction
• 12.4 Quasi-cyclic LDPC Codes and Protographs
• 12.4.1 Quasi-cyclic LDPC Codes
• 12.4.2 Construction of Quasi-cyclic Codes Using a Protograph
• 12.5 Summary
• References
• Part III Analysis and Decoders
• 13 An Exhaustive Tree Search for Stopping Sets of LDPC Codes
• 13.1 Introduction and Preliminaries.
• 13.2 An Efficient Tree Search Algorithm
• 13.2.1 An Efficient Lower Bound
• 13.2.2 Best Next Coordinate Position Selection
• 13.3 Results
• 13.3.1 WiMax LDPC Codes
• 13.4 Conclusions
• 13.5 Summary
• References
• 14 Erasures and Error-Correcting Codes
• 14.1 Introduction
• 14.2 Derivation of the PDF of Correctable Erasures
• 14.2.1 Background and Definitions
• 14.2.2 The Correspondence Between Uncorrectable Erasure Patterns and Low-Weight Codewords
• 14.3 Probability of Decoder Error
• 14.4 Codes Whose Weight Enumerator Coefficients Are Approximately Binomial
• 14.5 MDS Shortfall for Examples of Algebraic, LDPC and Turbo Codes
• 14.5.1 Turbo Codes with Dithered Relative Prime (DRP) Interleavers
• 14.5.2 Effects of Weight Spectral Components
• 14.6 Determination of the dmin of Any Linear Code
• 14.7 Summary
• References
• 15 The Modified Dorsch Decoder
• 15.1 Introduction
• 15.2 The Incremental Correlation Dorsch Decoder
• 15.3 Number of Codewords that Need to Be Evaluated to Achieve ƒ
• 15.4 Results for Some Powerful Binary Codes
• 15.4.1 The (136, 68, 24) Double-Circulant Code
• 15.4.2 The (255, 175, 17) Euclidean Geometry (EG) Code
• 15.4.3 The (513, 467, 12) Extended Binary Goppa Code
• 15.4.4 The (1023, 983, 9) BCH Code
• 15.5 Extension to Non-binary Codes
• 15.5.1 Results for the (63, 36, 13) GF(4) BCH Code
• 15.6 Conclusions
• 15.7 Summary
• References
• 16 A Concatenated Error-Correction System Using the 69640972 u69640972 u+v69640972 Code Construction
• 16.1 Introduction
• 16.2 Description of the System
• 16.3 Concatenated Coding and Modulation Formats
• 16.4 Summary
• References
• Part IV Applications
• 17 Combined Error Detection and Error-Correction
• 17.1 Analysis of Undetected Error Probability
• 17.2 Incremental-Redundancy Coding System
• 17.2.1 Description of the System
• 17.3 Summary.
• References
• 18 Password Correction and Confidential Information Access System
• 18.1 Introduction and Background
• 18.2 Details of the Password System
• 18.3 Summary
• References
• 19 Variations on the McEliece Public Key Cryptoystem
• 19.1 Introduction and Background
• 19.1.1 Outline of Different Variations of the Encryption System
• 19.2 Details of the Encryption System
• 19.3 Reducing the Public Key Size
• 19.4 Reducing the Cryptogram Length Without Loss of Security
• 19.5 Security of the Cryptosystem
• 19.5.1 Probability of a k timesk Random Matrix Being Full Rank
• 19.5.2 Practical Attack Algorithms
• 19.6 Applications
• 19.7 Summary
• References
• 20 Error-Correcting Codes and Dirty Paper Coding
• 20.1 Introduction and Background
• 20.2 Description of the System
• 20.3 Summary
• References
• Index.