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| coding theory and techniques: Coding Theory Andre Neubauer, Jurgen Freudenberger, Volker Kuhn, 2007-10-22 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 |
| coding theory and techniques: Source Coding Theory Robert M. Gray, 2012-12-06 Source coding theory has as its goal the characterization of the optimal performance achievable in idealized communication systems which must code an information source for transmission over a digital communication or storage channel for transmission to a user. The user must decode the information into a form that is a good approximation to the original. A code is optimal within some class if it achieves the best possible fidelity given whatever constraints are imposed on the code by the available channel. In theory, the primary constraint imposed on a code by the channel is its rate or resolution, the number of bits per second or per input symbol that it can transmit from sender to receiver. In the real world, complexity may be as important as rate. The origins and the basic form of much of the theory date from Shan non's classical development of noiseless source coding and source coding subject to a fidelity criterion (also called rate-distortion theory) [73] [74]. Shannon combined a probabilistic notion of information with limit theo rems from ergodic theory and a random coding technique to describe the optimal performance of systems with a constrained rate but with uncon strained complexity and delay. An alternative approach called asymptotic or high rate quantization theory based on different techniques and approx imations was introduced by Bennett at approximately the same time [4]. This approach constrained the delay but allowed the rate to grow large. |
| coding theory and techniques: Coding Theory Sudhakar Radhakrishnan, Muhammad Sarfraz, 2020-03-11 This book is intended to attract the attention of practitioners and researchers in academia and industry interested in challenging paradigms of coding theory and computer vision. The chapters in this comprehensive reference explore the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavours. This book is compiled with a view to provide researchers, academicians, and readers with an in-depth discussion of the latest advances in this field. It consists of twelve chapters from academicians, practitioners, and researchers from different disciplines of life. All the chapters are authored by various researchers around the world covering the field of coding theory and image and video processing. This book mainly focusses on researchers who can do quality research in the area of coding theory and image and video processing and related fields. Each chapter is an independent research study, which will motivate young researchers to think about. These twelve chapters are presented in three sections and will be an eye-opener for all who systematic researchers in these fields. |
| coding theory and techniques: Channel Coding: Theory, Algorithms, and Applications , 2014-07-29 This book gives a review of the principles, methods and techniques of important and emerging research topics and technologies in Channel Coding, including theory, algorithms, and applications. Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic. With this reference source you will: - Quickly grasp a new area of research - Understand the underlying principles of a topic and its applications - Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved - Quick tutorial reviews of important and emerging topics of research in Channel Coding - Presents core principles in Channel Coding theory and shows their applications - Reference content on core principles, technologies, algorithms and applications - Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge |
| coding theory and techniques: Essentials of Error-Control Coding Techniques Hideki Imai, 2014-06-28 Essentials of Error-Control Coding Techniques presents error-control coding techniques with an emphasis on the most recent applications. It is written for engineers who use or build error-control coding equipment. Many examples of practical applications are provided, enabling the reader to obtain valuable expertise for the development of a wide range of error-control coding systems. Necessary background knowledge of coding theory (the theory of error-correcting codes) is also included so that the reader is able to assimilate the concepts and the techniques. The book is divided into two parts. The first provides the reader with the fundamental knowledge of the coding theory that is necessary to understand the material in the latter part. Topics covered include the principles of error detection and correction, block codes, and convolutional codes. The second part is devoted to the practical applications of error-control coding in various fields. It explains how to design cost-effective error-control coding systems. Many examples of actual error-control coding systems are described and evaluated. This book is particularly suited for the engineer striving to master the practical applications of error-control coding. It is also suitable for use as a graduate text for an advanced course in coding theory. |
| coding theory and techniques: A Student's Guide to Coding and Information Theory Stefan M. Moser, Po-Ning Chen, 2012-01-26 This is a concise, easy-to-read guide, introducing beginners to coding theory and information theory. |
| coding theory and techniques: Channel Coding Techniques for Wireless Communications K. Deergha Rao, 2019-11-22 This book discusses the latest channel coding techniques, MIMO systems, and 5G channel coding evolution. It provides a comprehensive overview of channel coding, covering modern techniques such as turbo codes, low-density parity-check (LDPC) codes, space–time coding, polar codes, LT codes, and Raptor codes as well as the traditional codes such as cyclic codes, BCH, RS codes, and convolutional codes. It also explores MIMO communications, which is an effective method for high-speed or high-reliability wireless communications. It also examines the evolution of 5G channel coding techniques. Each of the 13 chapters features numerous illustrative examples for easy understanding of the coding techniques, and MATLAB-based programs are integrated in the text to enhance readers’ grasp of the underlying theories. Further, PC-based MATLAB m-files for illustrative examples are included for students and researchers involved in advanced and current concepts of coding theory. |
| coding theory and techniques: Coding and Information Theory Steven Roman, 1992-06-04 This book is an introduction to information and coding theory at the graduate or advanced undergraduate level. It assumes a basic knowledge of probability and modern algebra, but is otherwise self- contained. The intent is to describe as clearly as possible the fundamental issues involved in these subjects, rather than covering all aspects in an encyclopedic fashion. The first quarter of the book is devoted to information theory, including a proof of Shannon's famous Noisy Coding Theorem. The remainder of the book is devoted to coding theory and is independent of the information theory portion of the book. After a brief discussion of general families of codes, the author discusses linear codes (including the Hamming, Golary, the Reed-Muller codes), finite fields, and cyclic codes (including the BCH, Reed-Solomon, Justesen, Goppa, and Quadratic Residue codes). An appendix reviews relevant topics from modern algebra. |
| coding theory and techniques: Coding Theory Sudhakar Radhakrishnan, Sudev Naduvath, 2022-05-25 This book explores the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavors. It consists of seven chapters that address such topics as applications of coding theory in networking and cryptography, wireless sensor nodes in wireless body area networks, the construction of linear codes, and more. |
| coding theory and techniques: Modulation and Coding Techniques in Wireless Communications Evgenii Krouk, Sergei Semenov, 2011-01-19 The high level of technical detail included in standards specifications can make it difficult to find the correlation between the standard specifications and the theoretical results. This book aims to cover both of these elements to give accessible information and support to readers. It explains the current and future trends on communication theory and shows how these developments are implemented in contemporary wireless communication standards. Examining modulation, coding and multiple access techniques, the book is divided into two major sections to cover these functions. The two-stage approach first treats the basics of modulation and coding theory before highlighting how these concepts are defined and implemented in modern wireless communication systems. Part 1 is devoted to the presentation of main L1 procedures and methods including modulation, coding, channel equalization and multiple access techniques. In Part 2, the uses of these procedures and methods in the wide range of wireless communication standards including WLAN, WiMax, WCDMA, HSPA, LTE and cdma2000 are considered. An essential study of the implementation of modulation and coding techniques in modern standards of wireless communication Bridges the gap between the modulation coding theory and the wireless communications standards material Divided into two parts to systematically tackle the topic - the first part develops techniques which are then applied and tailored to real world systems in the second part Covers special aspects of coding theory and how these can be effectively applied to improve the performance of wireless communications systems |
| coding theory and techniques: Coding Techniques and Coding Theory , 1988 |
| coding theory and techniques: Information and Coding Theory Gareth A. Jones, J.Mary Jones, 2000-06-26 This text is an elementary introduction to information and coding theory. The first part focuses on information theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon’s Fundamental Theorem. In the second part, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes. Contains proofs, worked examples, and exercises. |
| coding theory and techniques: Selected Topics In Information And Coding Theory Isaac Woungang, Sudip Misra, Subhas Chandra Misra, 2010-02-26 The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text. |
| coding theory and techniques: Algebraic Coding Theory and Applications Carlos R. P. Hartmann, Giuseppe Longo, 2013-12-19 |
| coding theory and techniques: Algebraic and Stochastic Coding Theory Dave K. Kythe, Prem K. Kythe, 2017-07-28 Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing. |
| coding theory and techniques: An Introduction to Coding and Information Theory Steven Roman, 1996 |
| coding theory and techniques: Optical Communication Theory and Techniques Enrico Forestieri, 2004-10-21 Since the advent of optical communications, a greattechnological effort has been devoted to the exploitation of the huge bandwidth of optical fibers. Sta- ing from a few Mb/s single channel systems, a fast and constant technological development has led to the actual 10 Gb/s per channel dense wavelength - vision multiplexing (DWDM) systems, with dozens of channels on a single fiber. Transmitters and receivers are now ready for 40 Gb/s, whereas hundreds of channels can be simultaneously amplified by optical amplifiers. Nevertheless, despite such a pace in technological progress, optical c- munications are still in a primitive stage if compared, for instance, to radio communications: the widely spread on-off keying (OOK) modulation format is equivalent to the rough amplitude modulation (AM) format, whereas the DWDM technique is nothing more than the optical version of the frequency - vision multiplexing (FDM) technique. Moreover, adaptive equalization, ch- nel coding or maximum likelihood detection are still considered something “exotic” in the optical world. This is mainly due to the favourable char- teristics of the fiber optic channel (large bandwidth, low attenuation, channel stability, ...), which so far allowed us to use very simple transmission and detection techniques. |
| coding theory and techniques: Space-Time Coding Hamid Jafarkhani, 2005-09-22 This book covers the fundamental principles of space-time coding for wireless communications over multiple-input multiple-output (MIMO) channels, and sets out practical coding methods for achieving the performance improvements predicted by the theory. Starting with background material on wireless communications and the capacity of MIMO channels, the book then reviews design criteria for space-time codes. A detailed treatment of the theory behind space-time block codes then leads on to an in-depth discussion of space-time trellis codes. The book continues with discussion of differential space-time modulation, BLAST and some other space-time processing methods and the final chapter addresses additional topics in space-time coding. The theory and practice sections can be used independently of each other. Written by one of the inventors of space-time block coding, this book is ideal for a graduate student familiar with the basics of digital communications, and for engineers implementing the theory in real systems. |
| coding theory and techniques: Concise Encyclopedia of Coding Theory W. Cary Huffman, Jon-Lark Kim, Patrick Solé, 2023-05-31 Coding theory has grown into a discipline with many practical applications requiring various mathematical techniques in the last few decades. Most topics covered in this book are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. |
| coding theory and techniques: Error Correction Coding Todd K. Moon, 2005-06-06 An unparalleled learning tool and guide to error correction coding Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy. Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes. This text offers both classical coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems. Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists. |
| coding theory and techniques: Essentials of Error-Control Coding Jorge Castiñeira Moreira, Patrick Guy Farrell, 2006-08-04 Rapid advances in electronic and optical technology have enabled the implementation of powerful error-control codes, which are now used in almost the entire range of information systems with close to optimal performance. These codes and decoding methods are required for the detection and correction of the errors and erasures which inevitably occur in digital information during transmission, storage and processing because of noise, interference and other imperfections. Error-control coding is a complex, novel and unfamiliar area, not yet widely understood and appreciated. This book sets out to provide a clear description of the essentials of the subject, with comprehensive and up-to-date coverage of the most useful codes and their decoding algorithms. A practical engineering and information technology emphasis, as well as relevant background material and fundamental theoretical aspects, provides an in-depth guide to the essentials of Error-Control Coding. Provides extensive and detailed coverage of Block, Cyclic, BCH, Reed-Solomon, Convolutional, Turbo, and Low Density Parity Check (LDPC) codes, together with relevant aspects of Information Theory EXIT chart performance analysis for iteratively decoded error-control techniques Heavily illustrated with tables, diagrams, graphs, worked examples, and exercises Invaluable companion website features slides of figures, algorithm software, updates and solutions to problems Offering a complete overview of Error Control Coding, this book is an indispensable resource for students, engineers and researchers in the areas of telecommunications engineering, communication networks, electronic engineering, computer science, information systems and technology, digital signal processing and applied mathematics. |
| coding theory and techniques: Fundamentals of Error-Correcting Codes W. Cary Huffman, Vera Pless, 2010-02-18 Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background. |
| coding theory and techniques: Essays on Coding Theory Ian F. Blake, 2024-03-14 Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, yet they are rarely covered in the graduate curricula. This book provides new researchers in academia and industry with informal introductions to the basic ideas of these topics, including pointers to further reading. |
| coding theory and techniques: The Mathematical Theory of Coding Ian F. Blake, Ronald C. Mullin, 2014-05-10 The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding. |
| coding theory and techniques: A First Course in Coding Theory Raymond Hill, 1986 Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study. |
| coding theory and techniques: Information Theory and Coding - Solved Problems Predrag Ivaniš, Dušan Drajić, 2016-11-29 This book is offers a comprehensive overview of information theory and error control coding, using a different approach then in existed literature. The chapters are organized according to the Shannon system model, where one block affects the others. A relatively brief theoretical introduction is provided at the beginning of every chapter, including a few additional examples and explanations, but without any proofs. And a short overview of some aspects of abstract algebra is given at the end of the corresponding chapters. The characteristic complex examples with a lot of illustrations and tables are chosen to provide detailed insights into the nature of the problem. Some limiting cases are presented to illustrate the connections with the theoretical bounds. The numerical values are carefully selected to provide in-depth explanations of the described algorithms. Although the examples in the different chapters can be considered separately, they are mutually connected and the conclusions for one considered problem relate to the others in the book. |
| coding theory and techniques: Algebraic Coding Theory (Revised Edition) Elwyn R Berlekamp, 2015-03-26 This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value. |
| coding theory and techniques: Introduction to Coding Theory J.H. van Lint, 2012-12-06 It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4• There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2,a section on Coding Gain ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10. |
| coding theory and techniques: Foundations of Coding Jiri Adamek, 2011-02-14 Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible. |
| coding theory and techniques: Different Aspects of Coding Theory Robert Calderbank, 1995 The symposia in applied mathematics have been held under the auspices of the American Mathematical Society and others since 1967. This books connects coding theory with actual applications in consumer electronics and with other areas of mathematics. It covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science. |
| coding theory and techniques: Special Issue on Coding Techniques and Coding Theory Jack van Lint, Daniel J. Costello, Institute of Electrical and Electronics Engineers, 1988 |
| coding theory and techniques: Coding Theory San Ling, Chaoping Xing, 2004-02-12 Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material. |
| coding theory and techniques: Modern Coding Theory Tom Richardson, Rüdiger Urbanke, 2008-03-17 Having trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system? This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager's original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor's solutions and figures, available online: www.cambridge.org/9780521852296. |
| coding theory and techniques: Advances In Algebraic Geometry Codes Edgar Martinez-moro, Carlos Munuera, Diego Ruano, 2008-10-08 Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory. |
| coding theory and techniques: Source and Channel Coding John B. Anderson, Seshadri Mohan, 2012-12-06 oW should coded communication be approached? Is it about prob H ability theorems and bounds, or about algorithms and structures? The traditional course in information theory and coding teaches these together in one course in which the Shannon theory, a probabilistic the ory of information, dominates. The theory's predictions and bounds to performance are valuable to the coding engineer, but coding today is mostly about structures and algorithms and their size, speed and error performance. While coding has a theoretical basis, it has a practical side as well, an engineering side in which costs and benefits matter. It is safe to say that most of the recent advances in information theory and coding are in the engineering of coding. These thoughts motivate the present text book: A coded communication book based on methods and algorithms, with information theory in a necessary but supporting role. There has been muchrecent progress in coding, both inthe theory and the practice, and these pages report many new advances. Chapter 2 cov ers traditional source coding, but also the coding ofreal one-dimensional sources like speech and new techniques like vector quantization. Chapter 4 is a unified treatment of trellis codes, beginning with binary convolu tional codes and passing to the new trellis modulation codes. |
| coding theory and techniques: Information Theory Imre Csiszár, János Körner, 2014-07-10 Information Theory: Coding Theorems for Discrete Memoryless Systems presents mathematical models that involve independent random variables with finite range. This three-chapter text specifically describes the characteristic phenomena of information theory. Chapter 1 deals with information measures in simple coding problems, with emphasis on some formal properties of Shannon's information and the non-block source coding. Chapter 2 describes the properties and practical aspects of the two-terminal systems. This chapter also examines the noisy channel coding problem, the computation of channel capacity, and the arbitrarily varying channels. Chapter 3 looks into the theory and practicality of multi-terminal systems. This book is intended primarily for graduate students and research workers in mathematics, electrical engineering, and computer science. |
| coding theory and techniques: Error Control Coding Peter Sweeney, 2002-04-29 Error Control Coding: From Theory to Practice provides a concise introduction to basic coding techniques and their application. The fundamental concepts of coding theory are explained using simple examples with minimum use of complex mathematical tools. The selection of appropriate codes and the design of decoders are discussed. Bridging the gap between digital communications and information theory, this accessible approach will appeal to students and practising engineers alike. The clear presentation and practical emphasis make this book an excellent tool for both communications and electronic engineering students. Practitioners new to the field will find this text an essential guide to coding. Features include: * End of chapter problems to test and develop the readers understanding of the most popular codes and decoding methods * Finite field arithematic and algebraic decoding methods for BCH and Reed-Solomon codes * Detailed coverage of Viterbi decoding and related implementation issues * Turbo codes and related code types, including Gallager codes and turbo product codes * Practical examples of MAP and SOVA decoding for turbo codes |
| coding theory and techniques: Coding Theory and Applications Ángela I. Barbero, Vitaly Skachek, Øyvind Ytrehus, 2017-08-22 This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017. The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including codes and combinatorial structures, algebraic geometric codes, group codes, convolutional codes, network coding, other applications to communications, and applications of coding theory in cryptography. |
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