Optical Coding Theory with Prime

Contents

List of Figures

List of Tables

Preface

About the Authors

Chapter 1  Fundamental Materials and Tools

1.1    Galois Fields

1.1.1    Primitive Elements

1.2    Vector Space

1.2.1    Linear Operations in Vector Space over a Field

1.3    Matrix Theory

1.3.1    Basic Definitions

1.3.2    Basic Operations and Properties

1.3.3    Determinant

1.3.4    Eigenvalues and Eigenvectors

1.4    Hamming Distance and Weight

1.5    Correlation Functions

1.5.1    1-D Auto- and Cross-Correlation Functions

1.5.2    2-D Auto- and Cross-Correlation Functions

1.6    Cardinality Upper Bound

1.7    Markov Chain

1.8    Algebraic Tools for Performance Analysis

1.8.1    Gaussian Approximation for Unipolar Codes

1.8.2    Gaussian Approximation for Bipolar Codes

1.8.3    Combinatorial ...