Error Correction Coding

Building on the success of the first edition, which offered a practical introductory approach to the techniques of error concealment, this book, now fully revised and updated, provides a comprehensive treatment of the subject and includes a wealth of additional features. The Art of Error Correcting Coding, Second Edition explores intermediate and advanced level concepts as well as those which will appeal to the novice. All key topics are discussed, including Reed-Solomon codes, Viterbi decoding, soft-output decoding algorithms, MAP, log-MAP and MAX-log-MAP. Reliability-based algorithms GMD and Chase are examined, as are turbo codes, both serially and parallel concatenated, as well as low-density parity-check (LDPC) codes and their iterative decoders. Features additional problems at the end of each chapter and an instructor’s solutions manual Updated companion website offers new C/C ++programs and MATLAB scripts, to help with the understanding and implementation of basic ECC techniques Easy to follow examples illustrate the fundamental concepts of error correcting codes Basic analysis tools are provided throughout to help in the assessment of the error performance block and convolutional codes of a particular error correcting coding (ECC) scheme for a selection of the basic channel models This edition provides an essential resource to engineers, computer scientists and graduate students alike for understanding and applying ECC techniques in the transmission and storage of digital information.

This new edition has been extensively revised to reflect the progress in error control coding over the past few years. Over 60% of the material has been completely reworked, and 30% of the material is original. Convolutional, turbo, and low density parity-check (LDPC) coding and polar codes in a unified framework Advanced research-related developments such as spatial coupling A focus on algorithmic and implementation aspects of error control coding

Discover the first unified treatment of today's most essential information technologies— Compressing, Encrypting, and Encoding With identity theft, cybercrime, and digital file sharing proliferating in today's wired world, providing safe and accurate information transfers has become a paramount concern. The issues and problems raised in this endeavor are encompassed within three disciplines: cryptography, information theory, and error-correction. As technology continues to develop, these fields have converged at a practical level, increasing the need for a unified treatment of these three cornerstones of the information age. Stressing the interconnections of the disciplines, Cryptography, Information Theory, and Error-Correction offers a complete, yet accessible account of the technologies shaping the 21st century. This book contains the most up-to-date, detailed, and balanced treatment available on these subjects. The authors draw on their experience both in the classroom and in industry, giving the book's material and presentation a unique real-world orientation. With its reader-friendly style and interdisciplinary emphasis, Cryptography, Information Theory, and Error-Correction serves as both an admirable teaching text and a tool for self-learning. The chapter structure allows for anyone with a high school mathematics education to gain a strong conceptual understanding, and provides higher-level students with more mathematically advanced topics. The authors clearly map out paths through the book for readers of all levels to maximize their learning. This book: Is suitable for courses in cryptography, information theory, or error-correction as well as courses discussing all three areas Provides over 300 example problems with solutions Presents new and exciting algorithms adopted by industry Discusses potential applications in cell biology Details a new characterization of perfect secrecy Features in-depth coverage of linear feedback shift registers (LFSR), a staple of modern computing Follows a layered approach to facilitate discussion, with summaries followed by more detailed explanations Provides a new perspective on the RSA algorithm Cryptography, Information Theory, and Error-Correction is an excellent in-depth text for both graduate and undergraduate students of mathematics, computer science, and engineering. It is also an authoritative overview for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, entrepreneurs, and the generally curious.

CRYPTOGRAPHY, INFORMATION THEORY, AND ERROR-CORRECTION A rich examination of the technologies supporting secure digital information transfers from respected leaders in the field As technology continues to evolve Cryptography, Information Theory, and Error-Correction: A Handbook for the 21ST Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book.This book is geared toward a broad audience. It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. It is also an authoritative overview for professionals working at financial institutions, law firms, and governments who need up-to-date information to make critical decisions. The book’s discussions will be of interest to those involved in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars. With its reader-friendly style and interdisciplinary emphasis this book serves as both an ideal teaching text and a tool for self-learning for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs.Six new chapters cover current topics like Internet of Things security, new identities in information theory, blockchains, cryptocurrency, compression, cloud computing and storage. Increased security and applicable research in elliptic curve cryptography are also featured. The book also:Shares vital, new research in the field of information theoryProvides quantum cryptography updatesIncludes over 350 worked examples and problems for greater understanding of ideas. Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.

Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other. In this fresh approach, the authors consider the data network as a superchannel (a multi-layered entity) which allows error correcting coding to be evaluated as it is applied to a number of network layers as a whole. By exposing the problems of applying error correcting coding in data networks, and by discussing coding theory and its applications, this original technique shows how to correct errors in the network through joint coding at different network layers. Discusses the problem of reconciling coding applied to different layers using a superchannel approach Includes thorough coverage of all the key codes: linear block codes, Hamming, BCH and Reed-Solomon codes, LDPC codes decoding, as well as convolutional, turbo and iterative coding Considers new areas of application of error correcting codes such as transport coding, code-based cryptosystems and coding for image compression Demonstrates how to use error correcting coding to control such important data characteristics as mean message delay Provides theoretical explanations backed up by numerous real-world examples and practical recommendations Features a companion website containing additional research results including new constructions of LDPC codes, joint error-control coding and synchronization, Reed-Muller codes and their list decoding By progressing from theory through to practical problem solving, this resource contains invaluable advice for researchers, postgraduate students, engineers and computer scientists interested in data communications and applications of coding theory.

Comprehensive introduction to non-binary error-correction coding techniques Non-Binary Error Control Coding for Wireless Communication and Data Storage explores non-binary coding schemes that have been developed to provide an alternative to the Reed – Solomon codes, which are expected to become unsuitable for use in future data storage and communication devices as the demand for higher data rates increases. This book will look at the other significant non-binary coding schemes, including non-binary block and ring trellis-coded modulation (TCM) codes that perform well in fading conditions without any expansion in bandwidth use, and algebraic-geometric codes which are an extension of Reed-Solomon codes but with better parameters. Key Features: Comprehensive and self-contained reference to non-binary error control coding starting from binary codes and progressing up to the latest non-binary codes Explains the design and construction of good non-binary codes with descriptions of efficient non-binary decoding algorithms with applications for wireless communication and high-density data storage Discusses the application to specific cellular and wireless channels, and also magnetic storage channels that model the reading of data from the magnetic disc of a hard drive. Includes detailed worked examples for each coding scheme to supplement the concepts described in this book Focuses on the encoding, decoding and performance of both block and convolutional non-binary codes, and covers the K?tter-Vardy algorithm and Non-binary LDPC codes This book will be an excellent reference for researchers in the wireless communication and data storage communities, as well as development/research engineers in telecoms and storage companies. Postgraduate students in these fields will also find this book of interest.

Network coding, a relatively new area of research, has evolved from the theoretical level to become a tool used to optimize the performance of communication networks – wired, cellular, ad hoc, etc. The idea consists of mixing “packets” of data together when routing them from source to destination. Since network coding increases the network performance, it becomes a tool to enhance the existing protocols and algorithms in a network or for applications such as peer-to-peer and TCP. This book delivers an understanding of network coding and provides a set of studies showing the improvements in security, capacity and performance of fixed and mobile networks. This is increasingly topical as industry is increasingly becoming more reliant upon and applying network coding in multiple applications. Many cases where network coding is used in routing, physical layer, security, flooding, error correction, optimization and relaying are given – all of which are key areas of interest. Network Coding is the ideal resource for university students studying coding, and researchers and practitioners in sectors of all industries where digital communication and its application needs to be correctly understood and implemented. Contents 1. Network Coding: From Theory to Practice, Youghourta Benfattoum, Steven Martin and Khaldoun Al Agha. 2. Fountain Codes and Network Coding for WSNs, Anya Apavatjrut, Claire Goursaud, Katia Jaffr?s-Runser and Jean-Marie Gorce. 3. Switched Code for Ad Hoc Networks: Optimizing the Diffusion by Using Network Coding, Nour Kadi and Khaldoun Al Agha. 4. Security by Network Coding, Katia Jaffr?s-Runser and C?dric Lauradoux. 5. Security for Network Coding, Marine Minier, Yuanyuan Zhang and Wassim Zna?di. 6. Random Network Coding and Matroids, Maximilien Gadouleau. 7. Joint Network-Channel Coding for the Semi-Orthogonal MARC: Theoretical Bounds and Practical Design, Atoosa Hatefi, Antoine O. Berthet and Raphael Visoz. 8. Robust Network Coding, Lana Iwaza, Marco Di Renzo and Michel Kieffer. 9. Flow Models and Optimization for Network Coding, Eric Gourdin and Jeremiah Edwards.

Offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations This book offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations. This text focuses on the ways to structure information so that its transmission will be in the safest, quickest, and most efficient and error-free manner possible. All coding operations are covered in a single framework, with initial chapters addressing early mathematical models and algorithmic developments which led to the structure of code. After discussing the general foundations of code, chapters proceed to cover individual topics such as notions of compression, cryptography, detection, and correction codes. Both classical coding theories and the most cutting-edge models are addressed, along with helpful exercises of varying complexities to enhance comprehension. Explains how to structure coding information so that its transmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in their preferential programming language Features descriptive diagrams and illustrations, and almost 150 exercises, with corrections, of varying complexity to enhance comprehension Foundations of Coding: Compression, Encryption, Error-Correction is an invaluable resource for understanding the various ways information is structured for its secure and reliable transmission in the 21st-century world.

One of the most important key technologies for digital communication systems as well as storage media is coding theory. It provides a means to transmit information across time and space over noisy and unreliable communication channels. Coding Theory: Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space-time codes. Coding Theory provides algorithms and architectures used for implementing coding and decoding strategies as well as coding schemes used in practice especially in communication systems. Feature of the book include: Unique presentation-like style for summarising main aspects Practical issues for implementation of coding techniques Sound theoretical approach to practical, relevant coding methodologies Covers standard coding schemes such as block and convolutional codes, coding schemes such as Turbo and LDPC codes, and space time codes currently in research, all covered in a common framework with respect to their applications. This book is ideal for postgraduate and undergraduate students of communication and information engineering, as well as computer science students. It will also be of use to engineers working in the industry who want to know more about the theoretical basics of coding theory and their application in currently relevant communication systems