Preface

*"Code is poetry, and coding theory is the symphony that orchestrates the harmony of information"*

*Coding Theory Essentials* is an edited book that unveils the intricacies and wonders of a field that lies at the heart of modern communication and information storage. In this digital era, where the transfer and protection of data have become paramount, coding theory plays a vital role in ensuring the reliability and security of our interconnected world.

The essence of coding theory is the art of transforming messages into a language that transcends the boundaries of noise, interference, and errors. By cleverly encoding information and implementing efficient algorithms, coding theorists have paved the way for robust and error-resilient systems, enabling us to transmit data over vast distances and safeguard it from corruption.

This book serves as a comprehensive guide, capturing the fundamental concepts, principles, and techniques that underpin coding theory. Whether you are an aspiring computer scientist, an electrical engineer, or a curious mind seeking to delve into the captivating realm of information theory, this compilation of knowledge will empower you to understand, appreciate, and apply the core tenets of coding theory.

The chapters within have been meticulously crafted by experts in the field, combining theoretical foundations with real-world applications. Through a step-by-step journey, we explore diverse topics, ranging from error-correcting codes and block codes to convolutional codes, channel capacity, and beyond. Each chapter offers a careful balance between theory and practical insights, equipping readers with both the conceptual understanding and the tools necessary to address modern challenges in data transmission and storage.

As you embark on this intellectual expedition, we encourage you to embrace the beauty and elegance that lies within coding theory. Witness how seemingly abstract mathematical concepts transform into tangible solutions that revolutionize our daily lives. Discover the profound impact of error-correcting codes on digital communication, from wireless networks to satellite transmissions, from data centers to deep-space exploration.

Our aim in creating this book is to inspire and empower readers to explore, experiment, and innovate within the realm of coding theory. We hope that the insights gained from these pages will spark new ideas, foster interdisciplinary collaborations, and ignite a passion for the intricate world of information coding.

We extend our deepest gratitude to the contributing authors who have dedicated their expertise, time, and energy to enriching this collection. Their collective wisdom and

dedication have made this book a valuable resource for researchers, students, and practitioners alike.

Finally, we would like to express our gratitude to the readers, whose curiosity and thirst for knowledge motivate us to bring this book to fruition. May *Coding Theory Essentials* serve as a guiding light on your path towards unraveling the mysteries of coding theory and embracing the boundless possibilities it offers.

I owe special thanks to IntechOpen for their kind support and great efforts in bringing the book to fruition. I also appreciate all those who worked tirelessly in the background throughout the publication process.

> **Dr. Dinesh G. Harkut** Head and Associate Professor, Department of Computer Science and Engineering, Professor Ram College of Engineering and Management, Amravati, M.S., India

### **Dr. Kashmira N. Kasat**

**Chapter 1**

Theory

**1. Introduction**

receiver end.

**2. Historical background**

Introductory Chapter: Coding

The field of channel coding is a fundamental part of digital communication systems. Its purpose is to enable reliable transmission of data over noisy and

error-prone communication channels. Channel coding theory deals with the design of error-correcting codes that can tolerate a certain number of errors introduced during transmission, while still allowing for accurate reconstruction of the original data at the

Channel coding is the process of adding redundancy to a message or data stream to protect against errors that may occur during transmission over a noisy communication channel. The redundant information, known as the error-correcting code, enables the receiver to detect and correct errors that occur during transmission. For example, let us say you want to send a message "HELLO" to your friend over a communication channel. During transmission, the message may get corrupted due to noise or interference on the channel. To protect against errors, you can add redundancy to the message by encoding it with an error-correcting code, such as a cyclic redundancy check (CRC) code. The CRC code adds a checksum to the message, which is computed based on the message content using a mathematical algorithm. The receiver also computes the checksum of the received message and compares it with the checksum sent by the transmitter. If the two checksums do not match, it indicates that there was an error in the transmission, and the receiver requests the transmitter to resend the message. In this example, the CRC code serves as a channel coding scheme that protects the message against errors during transmission over the noisy communication channel. By adding redundancy to the message, the receiver can detect and correct errors, ensuring reliable communication between the transmitter and receiver.

The history of channel coding dates back to the early days of telegraphy and radio communication, when engineers first realized the need for error-correcting codes to ensure reliable transmission over noisy and error-prone communication channels. The first error-correcting codes were developed in the 1940s, with the work of Richard Hamming and Claude Shannon laying the foundation for modern channel coding theory [1]. Richard Hamming developed the concept of Hamming codes in 1950, which were the first practical error-correcting codes used in digital communication systems. These codes were designed to detect and correct single-bit errors, and they were widely used in early computer systems and communication protocols [1]. Claude

*Dinesh G. Harkut and Kashmira N. Kasat*

Head and Assistant Professor, Department of Electronics and Telecommunication Engineering, Professor Ram College of Engineering and Management, Amravati, M.S., India

### **Chapter 1**
