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 |