Error-Correction Coding and Decoding : : Bounds, Codes, Decoders, Analysis and Applications.
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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
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Physical Description: | 1 online resource (527 pages) |
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Tomlinson, Martin. Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. 1st ed. Cham : Springer International Publishing AG, 2017. ©2017. 1 online resource (527 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Signals and Communication Technology Series 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 -- 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 -- 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. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. Tjhai, Cen Jung. Ambroze, Marcel A. Ahmed, Mohammed. Jibril, Mubarak. Print version: Tomlinson, Martin Error-Correction Coding and Decoding Cham : Springer International Publishing AG,c2017 9783319511023 ProQuest (Firm) https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6422907 Click to View |
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Tomlinson, Martin. |
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Tomlinson, Martin. Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. Signals and Communication Technology Series 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 -- 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 -- 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. |
author_facet |
Tomlinson, Martin. Tjhai, Cen Jung. Ambroze, Marcel A. Ahmed, Mohammed. Jibril, Mubarak. |
author_variant |
m t mt |
author2 |
Tjhai, Cen Jung. Ambroze, Marcel A. Ahmed, Mohammed. Jibril, Mubarak. |
author2_variant |
c j t cj cjt m a a ma maa m a ma m j mj |
author2_role |
TeilnehmendeR TeilnehmendeR TeilnehmendeR TeilnehmendeR |
author_sort |
Tomlinson, Martin. |
title |
Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
title_sub |
Bounds, Codes, Decoders, Analysis and Applications. |
title_full |
Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
title_fullStr |
Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
title_full_unstemmed |
Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
title_auth |
Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
title_new |
Error-Correction Coding and Decoding : |
title_sort |
error-correction coding and decoding : bounds, codes, decoders, analysis and applications. |
series |
Signals and Communication Technology Series |
series2 |
Signals and Communication Technology Series |
publisher |
Springer International Publishing AG, |
publishDate |
2017 |
physical |
1 online resource (527 pages) |
edition |
1st ed. |
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 -- 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 -- 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. |
isbn |
9783319511030 9783319511023 |
callnumber-first |
T - Technology |
callnumber-subject |
TK - Electrical and Nuclear Engineering |
callnumber-label |
TK5101-5105 |
callnumber-sort |
TK 45101 45105.9 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=6422907 |
illustrated |
Not Illustrated |
dewey-hundreds |
000 - Computer science, information & general works |
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Error-Correction Coding and Decoding : Bounds, Codes, Decoders, Analysis and Applications. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>10180nam a22005053i 4500</leader><controlfield tag="001">5006422907</controlfield><controlfield tag="003">MiAaPQ</controlfield><controlfield tag="005">20240229073838.0</controlfield><controlfield tag="006">m o d | </controlfield><controlfield tag="007">cr cnu||||||||</controlfield><controlfield tag="008">240229s2017 xx o ||||0 eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783319511030</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783319511023</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(MiAaPQ)5006422907</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(Au-PeEL)EBL6422907</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)975018188</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">MiAaPQ</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="e">pn</subfield><subfield code="c">MiAaPQ</subfield><subfield code="d">MiAaPQ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">TK5101-5105.9</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003.54</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tomlinson, Martin.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Error-Correction Coding and Decoding :</subfield><subfield code="b">Bounds, Codes, Decoders, Analysis and Applications.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1st ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham :</subfield><subfield code="b">Springer International Publishing AG,</subfield><subfield code="c">2017.</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2017.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (527 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Signals and Communication Technology Series</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">9.5 Evaluation of the Number of Codewords of Given Weight -- 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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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 -- 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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. 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