Error Correction Coding Mathematical Methods and Algorithms 2nd Edition by Todd Moon 1119567493 9781119567493

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ISBN-10 :  1119567493 

ISBN-13 :  9781119567493

Author:   Todd K. Moon 

Error Correction Coding: Mathematical Methods and Algorithms, 2nd Edition provides a comprehensive introduction to classical and modern methods of error correction. The presentation provides a clear, practical introduction to using a lab-oriented approach.  Readers are encouraged to implement the encoding and decoding algorithms with explicit algorithm statements and the mathematics used in error correction, balanced with an algorithmic development on how to actually do the encoding and decoding. Both block and stream (convolutional) codes are discussed, and the mathematics required to understand them are introduced on a “just-in-time” basis as the reader progresses through the book. 

Error Correction Coding Mathematical Methods and Algorithms 2nd Table of contents:

Part I: Introduction and Foundations
Chapter 1: A Context for Error Correction Coding
1.1 Purpose of This Book
1.2 Introduction: Where Are Codes?
1.3 The Communications System
1.4 Basic Digital Communications
1.5 Signal Detection
1.6 Memoryless Channels
1.7 Simulation and Energy Considerations for Coded Signals
1.8 Some Important Definitions and a Trivial Code: Repetition Coding
1.9 Hamming Codes
1.10 The Basic Questions
1.11 Historical Milestones of Coding Theory
1.12 A Bit of Information Theory
1.14 References
Part II: Block Codes
Chapter 2: Groups and Vector Spaces
2.1 Introduction
2.2 Groups
2.3 Fields: A Prelude
2.4 Review of Linear Algebra
2.25 Exercises
References
Chapter 3: Linear Block Codes
3.1 Basic Definitions
3.2 The Generator Matrix Description of Linear Block Codes
3.3 The Parity Check Matrix and Dual Codes
3.4 Error Detection and Correction Over Hard‐Output Channels
3.5 Weight Distributions of Codes and Their Duals
3.6 Binary Hamming Codes and Their Duals
3.7 Performance of Linear Codes
3.8 Erasure Decoding
3.9 Modifications to Linear Codes
3.10 Best‐Known Linear Block Codes
Exercises
3.12 References
Chapter 4: Cyclic Codes, Rings, and Polynomials
4.1 Introduction
4.2 Basic Definitions
4.3 Rings
4.4 Quotient Rings
4.5 Ideals in Rings
4.6 Algebraic Description of Cyclic Codes
4.7 Nonsystematic Encoding and Parity Check
4.8 Systematic Encoding
4.9 Some Hardware Background
4.10 Cyclic Encoding
4.11 Syndrome Decoding
4.12 Shortened Cyclic Codes
4.13 Binary CRC Codes
Appendix 4.A Linear Feedback Shift Registers
4.14 Exercise
References
Chapter 5: Rudiments of Number Theory and Algebra
5.1 Motivation
5.2 Number Theoretic Preliminaries
5.3 The Chinese Remainder Theorem
5.4 Fields
5.5 Galois Fields: Mathematical Facts
5.6 Implementing Galois Field Arithmetic
5.7 Subfields of Galois Fields
5.8 Irreducible and Primitive Polynomials
5.9 Conjugate Elements and Minimal Polynomials
5.10 Factoring
5.11 Cyclotomic Cosets
Appendix 5.A How Many Irreducible Polynomials Are There?
Exercise
References
Chapter 6: BCH and Reed–Solomon Codes: Designer Cyclic Codes
6.1 BCH Codes
6.2 Reed–Solomon Codes
6.3 Decoding BCH and RS Codes: The General Outline
6.4 Finding the Error Locator Polynomial
6.5 Nonbinary BCH and RS Decoding
6.6 Euclidean Algorithm for the Error Locator Polynomial
6.7 Erasure Decoding for Nonbinary BCH or RS Codes
6.8 Galois Field Fourier Transform Methods
6.9 Variations and Extensions of Reed–Solomon Codes
Appendix 6.A Proof of Newton’s Identities
6.11 Exercise
References
Chapter 7: Alternate Decoding Algorithms for Reed–Solomon Codes
7.1 Introduction: Workload for Reed–Solomon Decoding
7.2 Derivations of Welch–Berlekamp Key Equation
7.3 Finding the Error Values
7.4 Methods of Solving the WB Key Equation
7.5 Erasure Decoding with the WB Key Equation
7.6 The Guruswami–Sudan Decoding Algorithm and Soft RS Decoding
Exercises
7.8 References
Notes
Chapter 8: Other Important Block Codes
8.1 Introduction
8.2 Hadamard Matrices, Codes, and Transforms
8.3 Reed–Muller Codes
8.4 Building Long Codes from Short Codes: The Squaring Construction
8.5 Quadratic Residue Codes
8.6 Golay Codes
8.7 Exercises
References
Chapter 9: Bounds on Codes
9.1 The Gilbert–Varshamov Bound
9.2 The Plotkin Bound
9.3 The Griesmer Bound
9.4 The Linear Programming and Related Bounds
9.5 The McEliece–Rodemich–Rumsey–Welch Bound
9.6 Exercises
9.7 References
Chapter 10: Bursty Channels, Interleavers, and Concatenation
10.1 Introduction to Bursty Channels
10.2 Interleavers
10.3 An Application of Interleaved RS Codes: Compact Discs
10.4 Product Codes
10.5 Reed–Solomon Codes
10.6 Concatenated Codes
10.7 Fire Codes
10.9 References
Chapter 11: Soft‐Decision Decoding Algorithms
11.1 Introduction and General Notation
11.2 Generalized Minimum Distance Decoding
11.3 The Chase Decoding Algorithms
11.4 Halting the Search: An Optimality Condition
11.5 Ordered Statistic Decoding
11.6 Soft Decoding Using the Dual Code: The Hartmann Rudolph Algorithm
11.8 References
Part III: Codes on Graphs
Chapter 12: Convolutional Codes
12.1 Introduction and Basic Notation
12.2 Definition of Codes and Equivalent Codes
12.3 Decoding Convolutional Codes
12.4 Some Performance Results
12.5 Error Analysis for Convolutional Codes
12.6 Tables of Good Codes
12.7 Puncturing
12.8 Suboptimal Decoding Algorithms for Convolutional Codes
12.9 Convolutional Codes as Block Codes and Tailbiting Codes
12.10 A Modified Expression for the Path Metric
12.11 Soft Output Viterbi Algorithm (SOVA)
12.12 Trellis Representations of Block and Cyclic Codes
References
Chapter 13: Trellis‐Coded Modulation
13.1 Adding Redundancy by Adding Signals
13.2 Background on Signal Constellations
13.3 TCM Example
13.4 Some Error Analysis for TCM Codes
13.5 Decoding TCM Codes
13.6 Rotational Invariance
13.7 Multidimensional TCM
13.8 Multidimensional TCM Example: The V.34 Modem Standard
13.9 Exercises
13.10 References
Part IV: Iteratively Decoded Codes
Chapter 14: Turbo Codes
14.1 Introduction
14.2 Encoding Parallel Concatenated Codes
14.3 Turbo Decoding Algorithms
14.4 On the Error Floor and Weight Distributions
14.5 EXIT Chart Analysis
14.6 Block Turbo Coding
14.7 Turbo Equalization
Exercise
References
Chapter 15: Low‐Density Parity‐Check Codes: Introduction, Decoding, and Analysis
15.1 Introduction
15.2 LDPC Codes: Construction and Notation
15.3 Tanner Graphs
15.4 Decoding LDPC Codes
15.5 Why Low‐Density Parity‐Check Codes?
15.6 The Iterative Decoder on General Block Codes
15.7 Density Evolution
15.8 EXIT Charts for LDPC Codes
15.9 Irregular LDPC Codes
15.10 More on LDPC Code Construction
15.11 Encoding LDPC Codes
15.12 A Variation: Low‐Density Generator Matrix Codes
Exercise
References
Chapter 16: Low‐Density Parity‐Check Codes: Designs and Variations
16.1 Introduction
16.2 Repeat‐Accumulate Codes
16.3 LDPC Convolutional Codes
16.4 Quasi‐Cyclic Codes
16.5 Construction of LDPC Codes Based on Finite Fields
16.6 Code Design Based on Finite Geometries
16.7 Ensembles of LDPC Codes
16.8 Constructing LDPC Codes by Progressive Edge Growth (PEG)
16.9 Protograph and Multi‐Edge‐Type LDPC Codes
16.10 Error Floors and Trapping Sets
16.11 Importance Sampling
16.12 Fountain Codes
16.13 References
Notes
Part V: Polar Codes
Chapter 17: Polar Codes
17.1 Introduction and Preview
17.2 Notation and Channels
17.3 Channel Polarization, Channel
17.4 Channel Polarization, Channels
17.5 Some Theorems of Polar Coding Theory
17.6 Designing Polar Codes
17.7 Perspective: The Channel Coding Theorem
17.8 Systematic Encoding of Polar Codes
17.9 List Decoding of Polar Codes
17.10 LLR‐Based Successive Cancellation List Decoding
17.11 Simplified Successive Cancellation Decoding
17.12 Relations with Reed–Muller Codes
17.13 Hardware and Throughput Performance Results
17.14 Generalizations, Extensions, and Variations
Appendix 17.A is a Bit‐Reverse Permutation
17.15 Exercises
References
Part VI: Applications
Chapter 18: Some Applications of Error Correction in Modern Communication Systems
18.1 Introduction
18.2 Digital Video Broadcast T2 (DVB‐T2)
18.3 Digital Cable Television
18.4 E‐UTRA and Long‐Term Evolution
18.5 References
Part VII: Space-Time Coding
Chapter 19: Fading Channels and Space‐Time Codes
19.1 Introduction
19.2 Fading Channels
19.3 Diversity Transmission and Reception: The MIMO Channel
19.4 Space‐Time Block Codes
19.5 Space‐Time Trellis Codes
19.6 How Many Antennas?
19.7 Estimating Channel Information
19.8 Exercises
19.9 References

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