# Search Results for "algebraic-codes-for-data-transmission"

## Algebraic Codes for Data Transmission

• Author: Richard E. Blahut
• Publisher: Cambridge University Press
• ISBN: 1139435078
• Category: Technology & Engineering
• Page: N.A
• View: 7343
The need to transmit and store massive amounts of data reliably and without error is a vital part of modern communications systems. Error-correcting codes play a fundamental role in minimising data corruption caused by defects such as noise, interference, crosstalk and packet loss. This book provides an accessible introduction to the basic elements of algebraic codes, and discusses their use in a variety of applications. The author describes a range of important coding techniques, including Reed-Solomon codes, BCH codes, trellis codes, and turbocodes. Throughout the book, mathematical theory is illustrated by reference to many practical examples. The book was first published in 2003 and is aimed at graduate students of electrical and computer engineering, and at practising engineers whose work involves communications or signal processing.

## Algebraic Codes on Lines, Planes, and Curves

An Engineering Approach

• Author: Richard E. Blahut
• Publisher: Cambridge University Press
• ISBN: 1139469460
• Category: Technology & Engineering
• Page: N.A
• View: 2317
The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.

## Theory and Practice of Error Control Codes

• Author: Richard E. Blahut
• Publisher: Addison Wesley Publishing Company
• ISBN: N.A
• Category: Reference
• Page: 500
• View: 9141

## Applied Algebra

Codes, Ciphers and Discrete Algorithms, Second Edition

• Author: Darel W. Hardy,Fred Richman,Carol L. Walker
• Publisher: CRC Press
• ISBN: 1420071432
• Category: Mathematics
• Page: 410
• View: 8047
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.

## Codes, Cryptology and Curves with Computer Algebra:

• Author: Ruud Pellikaan,Xin-Wen Wu,Stanislav Bulygin,Relinde Jurrius
• Publisher: Cambridge University Press
• ISBN: 1108547826
• Category: Mathematics
• Page: N.A
• View: 5828
This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

## Coding for Data and Computer Communications

• Author: David Salomon
• Publisher: Springer Science & Business Media
• ISBN: 0387238042
• Category: Computers
• Page: 548
• View: 5576
Details the most important techniques used to make the storage and transmission of data fast, secure, and reliable. Accessible to both specialists and nonspecialists: Avoids complex mathematics

## Algebraic and Stochastic Coding Theory

• Author: Dave K. Kythe,Prem K. Kythe
• Publisher: CRC Press
• ISBN: 135183245X
• Category: Computers
• Page: 512
• View: 9006
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.

## Space-Time Block Coding for Wireless Communications

• Author: Erik G. Larsson,Petre Stoica
• Publisher: Cambridge University Press
• ISBN: 9780521065337
• Category: Technology & Engineering
• Page: 304
• View: 8682
Detailed coverage of a technology that is embedded in the UMTS and WCDMA mobile standards.

## Introduction to Coding Theory

• Author: Ron Roth
• Publisher: Cambridge University Press
• ISBN: 9780521845045
• Category: Computers
• Page: 566
• View: 4944
This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

## Algebraic Coding Theory

• Author: Elwyn R. Berlekamp
• Publisher: N.A
• ISBN: 9780894120633
• Category: Mathematics
• Page: 474
• View: 4661

## Algebraic Methods for Signal Processing and Communications Coding

• Author: Richard E. Blahut
• Publisher: Springer Science & Business Media
• ISBN: 1461228263
• Category: Technology & Engineering
• Page: 143
• View: 5625
Algorithms for computation are a central part of both digital signal pro cessing and decoders for error-control codes and the central algorithms of the two subjects share many similarities. Each subject makes extensive use of the discrete Fourier transform, of convolutions, and of algorithms for the inversion of Toeplitz systems of equations. Digital signal processing is now an established subject in its own right; it no longer needs to be viewed as a digitized version of analog signal process ing. Algebraic structures are becoming more important to its development. Many of the techniques of digital signal processing are valid in any algebraic field, although in most cases at least part of the problem will naturally lie either in the real field or the complex field because that is where the data originate. In other cases the choice of field for computations may be up to the algorithm designer, who usually chooses the real field or the complex field because of familiarity with it or because it is suitable for the particular application. Still, it is appropriate to catalog the many algebraic fields in a way that is accessible to students of digital signal processing, in hopes of stimulating new applications to engineering tasks.

## Data Compression

The Complete Reference

• Author: David Salomon
• Publisher: Springer Science & Business Media
• ISBN: 1846286034
• Category: Computers
• Page: 1092
• View: 2870
This book provides a comprehensive reference for the many different types and methods of compression. Included are a detailed and helpful taxonomy, analysis of most common methods, and discussions on the use and comparative benefits of methods and description of "how to" use them. Detailed descriptions and explanations of the most well-known and frequently used compression methods are covered in a self-contained fashion, with an accessible style and technical level for specialists and nonspecialists. Comments and suggestions of many readers have been included as a benefit to future readers, and a website is maintained and updated by the author.

## Selected Unsolved Problems in Coding Theory

• Author: David Joyner,Jon-Lark Kim
• Publisher: Springer Science & Business Media
• ISBN: 9780817682569
• Category: Mathematics
• Page: 248
• View: 4524
Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.

## List Decoding of Error-Correcting Codes

Winning Thesis of the 2002 ACM Doctoral Dissertation Competition

• Author: Venkatesan Guruswami
• Publisher: Springer Science & Business Media
• ISBN: 3540240519
• Category: Computers
• Page: 350
• View: 4267
This monograph is a thoroughly revised and extended version of the author's PhD thesis, which was selected as the winning thesis of the 2002 ACM Doctoral Dissertation Competition. Venkatesan Guruswami did his PhD work at the MIT with Madhu Sudan as thesis adviser. Starting with the seminal work of Shannon and Hamming, coding theory has generated a rich theory of error-correcting codes. This theory has traditionally gone hand in hand with the algorithmic theory of decoding that tackles the problem of recovering from the transmission errors efficiently. This book presents some spectacular new results in the area of decoding algorithms for error-correcting codes. Specificially, it shows how the notion of list-decoding can be applied to recover from far more errors, for a wide variety of error-correcting codes, than achievable before The style of the exposition is crisp and the enormous amount of information on combinatorial results, polynomial time list decoding algorithms, and applications is presented in well structured form.

## Introduction to Digital Mobile Communication

• Author: Yoshihiko Akaiwa
• Publisher: John Wiley & Sons
• ISBN: 1119041120
• Category: Technology & Engineering
• Page: 648
• View: 4999
Introduces digital mobile communications with an emphasis on digital transmission methods This book presents mathematical analyses of signals, mobile radio channels, and digital modulation methods. The new edition covers the evolution of wireless communications technologies and systems. The major new topics are OFDM (orthogonal frequency domain multiplexing), MIMO (multi-input multi-output) systems, frequency-domain equalization, the turbo codes, LDPC (low density parity check code), ACELP (algebraic code excited linear predictive) voice coding, dynamic scheduling for wireless packet data transmission and nonlinearity compensating digital pre-distorter amplifiers. The new systems using the above mentioned technologies include the second generation evolution systems, the third generation systems with their evolution systems, LTE and LTE-advanced systems, and advanced wireless local area network systems. The second edition of Digital Mobile Communication: Presents basic concepts and applications to a variety of mobile communication systems Discusses current applications of modern digital mobile communication systems Covers the evolution of wireless communications technologies and systems in conjunction with their background The second edition of Digital Mobile Communication is an important textbook for university students, researchers, and engineers involved in wireless communications.

## Algebraic-Geometric Codes

• Publisher: Springer Science & Business Media
• ISBN: 9401138109
• Category: Mathematics
• Page: 667
• View: 6863

## Codes and Curves

• Author: Judy L. Walker
• Publisher: American Mathematical Soc.
• ISBN: 082182628X
• Category: Mathematics
• Page: 66
• View: 7296
When information is transmitted, errors are likely to occur. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes, one can see how to define new codes based on divisors on algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously known codes. This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above is discussed.

## Principles of Digital Communication

• Author: Robert G. Gallager
• Publisher: Cambridge University Press
• ISBN: 113946860X
• Category: Technology & Engineering
• Page: N.A
• View: 3442
The renowned communications theorist Robert Gallager brings his lucid writing style to the study of the fundamental system aspects of digital communication for a one-semester course for graduate students. With the clarity and insight that have characterized his teaching and earlier textbooks, he develops a simple framework and then combines this with careful proofs to help the reader understand modern systems and simplified models in an intuitive yet precise way. A strong narrative and links between theory and practice reinforce this concise, practical presentation. The book begins with data compression for arbitrary sources. Gallager then describes how to modulate the resulting binary data for transmission over wires, cables, optical fibers, and wireless channels. Analysis and intuitive interpretations are developed for channel noise models, followed by coverage of the principles of detection, coding, and decoding. The various concepts covered are brought together in a description of wireless communication, using CDMA as a case study.

## Information Theory, Inference and Learning Algorithms

• Author: David J. C. MacKay
• Publisher: Cambridge University Press
• ISBN: 9780521642989
• Category: Computers
• Page: 628
• View: 8950