Essentials of error-control coding

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Essentials of error-control coding / Jorge Castiñeira Moreira, Patrick Guy Farrell

資料種別:

電子ブック

出版情報:

[Hoboken, N.J.] : Wiley Online Library, 2006

形態:

1 online resource (xxvi, 361 p.)

著者名:

ISBN:

9780470035726 [0470035722] (: electronic bk)

書誌ID:

TT00016115

子書誌情報

フルテキスト

所蔵情報

書誌詳細

注記:

Includes bibliographical references and index
Print published: Chichester : Wiley , c2006
Description based on online resource; title from PDF title page (viewed on August 7, 2019)

主題:

情報理論

言語:

英語

目次情報:

Preface & Acknowledgements

Symbols & Abbreviations

Information and Coding Theory / 1：

Entropy and Information Rate / 1.2：

Extended Discrete Memoryless Source / 1.3：

Channels and Mutual Information / 1.4：

Channel Probability Relationships / 1.5：

The a priori and a posteriori Entropies / 1.6：

Mutual Information / 1.7：

Capacity of a Discrete Channel / 1.8：

Shannon's Theorems / 1.9：

Signal Spaces and the Channel Coding Theorem / 1.10：

Error Control Coding / 1.11：

Limits to Communication and their Consequences / 1.12：

Bibliography and References

Problems

Block Codes / 2：

Error Detection and Correction / 2.1：

Block Codes: Introduction and Parameters / 2.3：

The Vector Space over the Binary Field / 2.4：

Linear Block Codes / 2.5：

Syndrome Error Detection / 2.6：

Minimum Distance of a Block Code / 2.7：

Error Correction Capability of a Block Code / 2.8：

Syndrome Detection and the Standard Array / 2.9：

Hamming Codes / 2.10：

Forward Error Correction (FEC) and Automatic Repeat ReQuest (ARQ) / 2.11：

Cyclic Codes / 3：

Description / 3.1：

Polynomial Representation of Codewords / 3.2：

Generator Polynomial of a Cyclic Code / 3.3：

Cyclic Codes in Systematic Form / 3.4：

Generator Matrix of a Cyclic Code / 3.5：

Syndrome Calculation and Error Detection / 3.6：

Decoding of Cyclic Codes / 3.7：

An Application Example: CRC Code for the Ethernet Standard / 3.8：

BCH Codes / 4：

Introduction: The Minimal Polynomial / 4.1：

Description of BCH Cyclic Codes / 4.2：

Decoding of BCH Codes / 4.3：

Error Location and Error Evaluation Polynomials / 4.4：

The Key Equation / 4.5：

Decoding of BCH Codes using the Euclidean Algorithm / 4.6：

Reed-Solomon Codes / 5：

Introduction / 5.1：

Error Correction Capability of RS Codes: The Vandermonde Determinant / 5.2：

RS Codes in Systematic Form / 5.3：

Syndrome Decoding of RS Codes / 5.4：

The Euclidean Algorithm. Error Location and Evaluation Polynomials / 5.5：

Decoding of RS Codes using the Euclidean Algorithm / 5.6：

Decoding of RS and BCH Codes using the Berlekamp- Massey Algorithm / 5.7：

A Practical Application: Error-Control Coding for the Compact Disc (CD) / 5.8：

Encoding for RS codes C (RS) (28,24) , C (RS) (32,28) and C (RS) (255,251) / 5.9：

Decoding of RS Codes C (RS) (28,24) and C (RS) (32,28) / 5.10：

Importance of Interleaving Bibliography and References Problems / 5.11：

Conolutional Codes / 6：

Linear Sequential Circuits / 6.1：

Convolutional Codes and Encoders / 6.2：

Description in the D-Transform Domain / 6.3：

Convolutional Encoder Representations / 6.4：

Convolutional Codes in Systematic Form / 6.5：

General Structure of FIR and IIR Finite State Sequential Machines / 6.6：

State Transfer Function Matrix: Calculation of the Transfer Function / 6.7：

Relationship between the Systematic and Non-Systematic Forms / 6.8：

Distance Properti / 6.9：

Preface

Acknowledgements

List of Symbols

Abbreviations

Information / 1.1：

A Measure of Information / 1.1.1：

Extended DMSs

Information Transmission over Discrete Channels / 1.4.1：

Information Channels / 1.4.2：

The A Priori and A Posteriori Entropies

Mutual Information: Definition / 1.7.1：

Mutual Information: Properties / 1.7.2：

The Shannon Theorems

Source Coding Theorem / 1.9.1：

Channel Capacity and Coding / 1.9.2：

Channel Coding Theorem / 1.9.3：

Capacity of the Gaussian Channel / 1.10.1：

Error-Control Coding

Simple Codes: The Repetition Code / 2.2.1：

Vector Subspaces / 2.4.1：

Dual Subspace / 2.4.2：

Matrix Form / 2.4.3：

Dual Subspace Matrix / 2.4.4：

Generator Matrix G / 2.5.1：

Block Codes in Systematic Form / 2.5.2：

Parity Check Matrix H / 2.5.3：

Minimum Distance and the Structure of the H Matrix / 2.7.1：

Error-Correction Capability of a Block Code

Forward Error Correction and Automatic Repeat ReQuest

Forward Error Correction / 2.11.1：

Automatic Repeat ReQuest / 2.11.2：

ARQ Schemes / 2.11.3：

ARQ Scheme Efficiencies / 2.11.4：

Hybrid-ARQ Schemes / 2.11.5：

An Application Example: Cyclic Redundancy Check Code for the Ethernet Standard

Bounds on the Error-Correction Capability of a BCH Code: The Vandermonde Determinant / 4.2.1：

Error-Location and Error-Evaluation Polynomials

Decoding of Binary BCH Codes Using the Euclidean Algorithm

The Euclidean Algorithm / 4.6.1：

Error-Correction Capability of RS Codes: The Vandermonde Determinant

The Euclidean Algorithm: Error-Location and Error-Evaluation Polynomials

Decoding of RS Codes Using the Euclidean Algorithm

Steps of the Euclidean Algorithm / 5.6.1：

Decoding of RS and BCH Codes Using the Berlekamp-Massey Algorithm

B-M Iterative Algorithm for Finding the Error-Location Polynomial / 5.7.1：

B-M Decoding of RS Codes / 5.7.2：

Relationship Between the Error-Location Polynomials of the Euclidean and B-M Algorithms / 5.7.3：

A Practical Application: Error-Control Coding for the Compact Disk

Compact Disk Characteristics / 5.8.1：

Channel Characteristics / 5.8.2：

Coding Procedure / 5.8.3：

Encoding for RS codes C[subscript RS](28, 24), C[superscript RS](32, 28) and C[subscript RS](255, 251)

Decoding of RS Codes C[subscript RS](28, 24) and C[subscript RS](32, 28)

B-M Decoding / 5.10.1：

Alternative Decoding Methods / 5.10.2：

Direct Solution of Syndrome Equations / 5.10.3：

Importance of Interleaving

Convolutional Codes

Representation of Connections / 6.4.1：

State Diagram Representation / 6.4.2：

Trellis Representation / 6.4.3：

General Structure of Finite Impulse Response and Infinite Impulse Response FSSMs

Finite Impulse Response FSSMs / 6.6.1：

Infinite Impulse Response FSSMs / 6.6.2：

State Transfer Function for FIR FSSMs / 6.7.1：

State Transfer Function for IIR FSSMs / 6.7.2：

Relationship Between the Systematic and the Non-Systematic Forms

Distance Properties of Convolutional Codes

Minimum Free Distance of a Convolutional Code / 6.10：

Maximum Likelihood Detection / 6.11：

Decoding of Convolutional Codes: The Viterbi Algorithm / 6.12：

Extended and Modified State Diagram / 6.13：

Error Probability Analysis for Convolutional Codes / 6.14：

Hard and Soft Decisions / 6.15：

Maximum Likelihood Criterion for the Gaussian Channel / 6.15.1：

Bounds for Soft-Decision Detection / 6.15.2：

An Example of Soft-Decision Decoding of Convolutional Codes / 6.15.3：

Punctured Convolutional Codes and Rate-Compatible Schemes / 6.16：

Turbo Codes / 7：

A Turbo Encoder / 7.1：

Decoding of Turbo Codes / 7.2：

The Turbo Decoder / 7.2.1：

Probabilities and Estimates / 7.2.2：

Symbol Detection / 7.2.3：

The Log Likelihood Ratio / 7.2.4：

Markov Sources and Discrete Channels / 7.3：

The BCJR Algorithm: Trellis Coding and Discrete Memoryless Channels / 7.4：

Iterative Coefficient Calculation / 7.5：

The BCJR MAP Algorithm and the LLR / 7.6：

The BCJR MAP Algorithm: LLR Calculation / 7.6.1：

Calculation of Coefficients [gama iota](u[prime], u) / 7.6.2：

Turbo Decoding / 7.7：

Initial Conditions of Coefficients [alpha][subscript [iota]-1] (u[prime]) and [Beta iota] (u) / 7.7.1：

Construction Methods for Turbo Codes / 7.8：

Interleavers / 7.8.1：

Block Interleavers / 7.8.2：

Convolutional Interleavers / 7.8.3：

Random Interleavers / 7.8.4：

Linear Interleavers / 7.8.5：

Code Concatenation Methods / 7.8.6：

Turbo Code Performance as a Function of Size and Type of Interleaver / 7.8.7：

Other Decoding Algorithms for Turbo Codes / 7.9：

Exit Charts for Turbo Codes / 7.10：

Introduction to Exit Charts / 7.10.1：

Construction of the Exit Chart / 7.10.2：

Extrinsic Transfer Characteristics of the Constituent Decoders / 7.10.3：

Low-Density Parity Check Codes / 8：

Different Systematic Forms of a Block Code / 8.1：

Description of LDPC Codes / 8.2：

Construction of LDPC Codes / 8.3：

Regular LDPC Codes / 8.3.1：

Irregular LDPC Codes / 8.3.2：

Decoding of LDPC Codes: The Tanner Graph / 8.3.3：

The Sum-Product Algorithm / 8.4：

Sum-Product Algorithm for LDPC Codes: An Example / 8.5：

Simplifications of the Sum-Product Algorithm / 8.6：

A Logarithmic LDPC Decoder / 8.7：

Initialization / 8.7.1：

Horizontal Step / 8.7.2：

Vertical Step / 8.7.3：

Summary of the Logarithmic Decoding Algorithm / 8.7.4：

Construction of the Look-up Tables / 8.7.5：

Extrinsic Information Transfer Charts for LDPC Codes / 8.8：

Iterative Decoding of Block Codes / 8.8.1：

Exit Chart Construction for LDPC Codes / 8.8.3：

Mutual Information Function / 8.8.4：

Exit Chart for the SND / 8.8.5：

Exit Chart for the PCND / 8.8.6：

Fountain and LT Codes / 8.9：

Fountain Codes / 8.9.1：

Linear Random Codes / 8.9.3：

Luby Transform Codes / 8.9.4：

LDPC and Turbo Codes / 8.10：

Error Probability in the Transmission of Digital Signals / Appendix A：

Galois Fields GF(q) / Appendix B：

Answers to Problems

Index

Preface & Acknowledgements

Symbols & Abbreviations

Information and Coding Theory / 1：

Entropy and Information Rate / 1.2：

Extended Discrete Memoryless Source / 1.3：

Channels and Mutual Information / 1.4：

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