Coding Theory A First Course
Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Cambridge, UK ; New York
Cambridge University Press
12.02.2004
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| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780521529235 0521529239 0521821916 9780521821919 |
| DOI | 10.1017/CBO9780511755279 |
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| Abstract | Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material. |
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| AbstractList | Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material. Based on the authors' teaching experiences, this book provides a thoroughly modern introduction to the coding theory - a subject of central importance for many applications in engineering and computer science. There are numerous examples and exercises, some of which introduce students to novel or more advanced material. |
| Author | Xing, Chaoping Ling, San |
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| Copyright | Cambridge University Press 2004 |
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| Notes | Includes bibliographical references and index |
| OCLC | 80244846 |
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| PageCount | 236 |
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| Snippet | Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance... Based on the authors' teaching experiences, this book provides a thoroughly modern introduction to the coding theory - a subject of central importance for many... |
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| SubjectTerms | Coding theory Data compression (Telecommunication) |
| Subtitle | A First Course |
| TableOfContents | Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Introduction -- Exercises -- 2 Error detection, correction and decoding -- 2.1 Communication channels -- Decoding rule -- 2.2 Maximum likelihood decoding -- 2.3 Hamming distance -- 2.4 Nearest neighbour/minimum distance decoding -- 2.5 Distance of a code -- Exercises -- 3 Finite fields -- 3.1 Fields -- 3.2 Polynomial rings -- 3.3 Structure of finite fields -- 3.4 Minimal polynomials -- Exercises -- 4 Linear codes -- 4.1 Vector spaces over finite fields -- 4.2 Linear codes -- 4.3 Hamming weight -- 4.4 Bases for linear codes -- 4.5 Generator matrix and parity-check matrix -- 4.6 Equivalence of linear codes -- 4.7 Encoding with a linear code -- 4.8 Decoding of linear codes -- 4.8.1 Cosets -- 4.8.2 Nearest neighbour decoding for linear codes -- 4.8.3 Syndrome decoding -- Exercises -- 5 Bounds in coding theory -- 5.1 The main coding theory problem -- 5.2 Lower bounds -- 5.2.1 Sphere-covering bound -- 5.2.2 Gilbert-Varshamov bound -- 5.3 Hamming bound and perfect codes -- 5.3.1 Binary Hamming codes -- Decoding with a binary Hamming code -- 5.3.2 q-ary Hamming codes -- Decoding with a q-ary Hamming code -- 5.3.3 Golay codes -- Binary Golay codes -- Ternary Golay codes -- 5.3.4 Some remarks on perfect codes -- 5.4 Singleton bound and MDS codes -- 5.5 Plotkin bound -- 5.6 Nonlinear codes -- 5.6.1 Hadamard matrix codes -- 5.6.2 Nordstrom-Robinson code -- 5.6.3 Preparata codes -- 5.6.4 Kerdock codes -- 5.7 Griesmer bound -- 5.8 Linear programming bound -- Exercises -- 6 Constructions of linear codes -- 6.1 Propagation rules -- 6.2 Reed-Muller codes -- 6.3 Subfield codes -- Exercises -- 7 Cyclic codes -- 7.1 Definitions -- 7.2 Generator polynomials -- 7.3 Generator and parity-check matrices -- 7.4 Decoding of cyclic codes -- Decoding algorithm for cyclic codes Decoding algorithm for cyclic burst-error-correcting codes -- 7.5 Burst-error-correcting codes -- Exercises -- 8 Some special cyclic codes -- 8.1 BCH codes -- 8.1.1 Definitions -- 8.1.2 Parameters of BCH codes -- 8.1.3 Decoding of BCH codes -- 8.2 Reed-Solomon codes -- 8.3 Quadratic-residue codes -- Exercises -- 9 Goppa codes -- 9.1 Generalized Reed-Solomon codes -- 9.2 Alternant codes -- 9.3 Goppa codes -- 9.4 Sudan decoding for generalized RS codes -- 9.4.1 Generation of the (P, k, t)-polynomial -- 9.4.2 Factorization of the (P, k, t)-polynomial -- Factoring algorithm -- Exercises -- References -- Bibliography -- Index |
| Title | Coding Theory |
| URI | http://dx.doi.org/10.1017/CBO9780511755279 https://doi.org/10.1017/CBO9780511755279?locatt=mode:legacy https://cir.nii.ac.jp/crid/1130000793841265920 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=256665 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780511755279 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781107145849&uid=none |
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