Optical Coding Theory with Prime

Wing C. Kwong, Guu-Chang Yang

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9781466567801
• eBook ISBN: 9781351831925
• Topic: Computer Science
• Subtopic: Cryptography
• Index: Computer Science

Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theory—until now. Written by renowned authorities in the field, Optical Coding Theory with Prime gathers together in one volume the fundamentals and developments of optical coding theory, with a focus on families of prime codes, supplemented with several families of non-prime codes. The book also explores potential applications to coding-based optical systems and networks.

Learn How to Construct and Analyze Optical Codes

The authors use a theorem-proof approach, breaking down theories into digestible form so that readers can understand the main message without searching through tedious proofs. The book begins with the mathematical tools needed to understand and apply optical coding theory, from Galois fields and matrices to Gaussian and combinatorial analytical tools. Using a wealth of examples, the authors show how optical codes are constructed and analyzed, and detail their performance in a variety of applications. The book examines families of 1-D and 2-D asynchronous and synchronous, multilength, and 3-D prime codes, and some non-prime codes.

Get a Working Knowledge of Optical Coding Theory to Help You Design Optical Systems and Networks

Prerequisites include a basic knowledge of linear algebra and coding theory, as well as a foundation in probability and communications theory. This book draws on the authors' extensive research to offer an authoritative reference on the emerging field of optical coding theory. In addition, it supplies a working knowledge of the theory and optical codes to help readers in the design of coding-based optical systems and networks.

For more on the technological aspects of optical CDMA, see Optical Code Division Multiple Access: Fundamentals and Applications (CRC Press 2005).

1	Fundamental Materials and Tools

Modern algebra [1–5] provides mathematical concepts and tools fundamental to the study of Optical Coding Theory. The theory finds applications in coding-based optical systems and networks, for example, involving optical code-division multiple access (O-CDMA) and multiplexing [6–22]. Various families of the prime codes studied in this book are based on the arithmetic of finite or Galois fields of some prime numbers [1, 2, 21–23].

This chapter covers the essential concepts and algebraic tools that are useful for understanding the subject matter in this book. It begins with a review of Galois fields, followed by vector and matrix theories. Important code parameters, such as Hamming weight and distance, correlation functions, and cardinality upper bound, that characterize optical codes are defined. Afterward, the concept of Markov chains is studied [24,25]. Algebraic tools to analyze the performances of optical codes are also developed. In particular, Gaussian approximation is a quick, utilitarian tool for performance analysis, especially in the absence of structural information of the optical codes under study [21, 22, 24–26]. More accurate combinatorial tools for analyzing code performances with soft-limiting and hard-limiting receivers, and with and without the classical chip-synchronous assumption, are also formulated [27–37]. Finally, the definition of spectral efficiency, another figure of merit for comparing optical codes, is introduced [38–43].

1.1 GALOIS FIELDS

Optical coding theory relies on modern algebra, which uses a different arithmetic system, rather than the familiar real and complex number systems. A field in modern algebra ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• List of Figures
• List of Tables
• Preface
• About the Authors
• Chapter 1 Fundamental Materials and Tools
• Chapter 2 Optical Coding Schemes
• Chapter 3 1-D Asynchronous Prime Codes
• Chapter 4 1-D Synchronous Prime Codes
• Chapter 5 2-D Asynchronous Prime Codes
• Chapter 6 2-D Synchronous Prime Codes
• Chapter 7 Multilength Prime Codes
• Chapter 8 3-D Prime Codes
• Index