Table of Contents for

Information Theory, Coding and Cryptography

Preface

Information lost means no information. A reliable transmission of information is the basic requirement of communication system. In spite of all the efforts given to the error-free transmission, noise is attributed to communication channel, causing erroneous data at the receiver. It is important that the information at the receiving end is error-free, or if any error occurs, the receiver must detect, locate, and correct the error. Search for the techniques to achieve reliable transmission over noisy communication channel is based on Shannon's theorem at late 1950 that reliable transmission can be achieved with the selection of proper encoding and decoding system, if the signalling rate is less than the channel capacity. This leads to the study of information theory and search for good efficient coding and decoding methods. Both the fields require the extensive background in applied mathematics, modern algebra, and probability theory. Since their inception, these have broadened to find applications in many areas, including data compression, error correction, statistical inference, natural language processing, cryptography, neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, plagiarism detection, and other forms of data analysis.

This book is intended to provide a comprehensive knowledge on information theory, study of different codes and decoding techniques with methods of error correction, and cryptography. The fundamentals of the subject are explained in this book with mathematical illustration wherever necessary. The book is designed in three parts with nine chapters. Part A presents the concepts of information theory and source coding consisting of three chapters; Part B consists of five chapters illustrating different types error control coding and decoding techniques; and Part C provides the basic concepts of cryptography.

In Part A, Chapter 1 provides the fundamentals of probability and random variables. Random processes and noise behaviour are also included in this chapter. Chapter 2 presents the concepts of information theory and channel characteristics with basic theorems and mathematical illustration. Chapter 3 illustrates various types of source codes, their classifications, and algorithms for formatting the codes with necessary mathematical background.

Part B is divided into five chapters, Chapter 4 through Chapter 8. Chapter 4 provides the theory behind error control codes, types of codes, types of errors, and strategies. These are elaborated with mathematical fundamentals and arithmetic of binary field. Galois field and vector spaces related to coding theory are also explained. Linear block codes, cyclic codes, BCH codes, and convolution codes have been illustrated in Chapter 5 through Chapter 8, respectively. Each chapter provides the mathematical background, generation of codes, types of encoders, decoding techniques, error correction, and application for the respective codes.

Part C consists of Chapter 9 that only devotes to cryptography and cryptosystems. This chapter provides the basic principles and fundamentals of cryptography and cryptosystems. Different types of encryption and decryption techniques and algorithms behind them are discussed in this chapter.

Simple lucid language is used throughout the book. Clear diagrams and numerous examples are provided for all the topics to facilitate easy understanding of the concepts. This book can be used as a text for an introductory course on information theory, error-correcting codes, and their applications at graduate or post-graduate level. The book is also designed as self-study guide for engineers in industry who wants to learn the error control codes, their correction techniques, and cryptography.

The authors are greatly thankful to all those who provided help and encouragement during the writing of this book. The authors are thankful to the publisher Pearson Education for providing the wonderful opportunity for publishing the book. The authors express their thanks to their wives and children for their continuous support and enormous patience during the preparation of this book.

Suggestions and corrections are welcome for the improvement of the book.

Arijit Saha
Nilotpal Manna
Surajit Mandal