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Algebraic and Stochastic Coding Theory

2017-07-28 Computers
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Release : 2017-07-28
Genre : Computers
Kind : eBook
Book Rating : 621/5 ( reviews)

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Book Synopsis Algebraic and Stochastic Coding Theory by : Dave K. Kythe

Download or read book Algebraic and Stochastic Coding Theory written by Dave K. Kythe. This book was released on 2017-07-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Geometry, Coding Theory and Cryptography

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 347/5 ( reviews)

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Book Synopsis Topics in Geometry, Coding Theory and Cryptography by : Arnaldo Garcia

Download or read book Topics in Geometry, Coding Theory and Cryptography written by Arnaldo Garcia. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

Concise Encyclopedia of Coding Theory

2021-03-26 Computers
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Release : 2021-03-26
Genre : Computers
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman

Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman. This book was released on 2021-03-26. Available in PDF, EPUB and Kindle. Book excerpt: Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Introduction to Coding Theory and Algebraic Geometry

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 861/5 ( reviews)

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Book Synopsis Introduction to Coding Theory and Algebraic Geometry by : J. van Lint

Download or read book Introduction to Coding Theory and Algebraic Geometry written by J. van Lint. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course

Algebraic coding theory

1978
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Release : 1978
Genre :
Kind : eBook
Book Rating : 031/5 ( reviews)

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Book Synopsis Algebraic coding theory by : Elwyn R. Berlekamp

Download or read book Algebraic coding theory written by Elwyn R. Berlekamp. This book was released on 1978. Available in PDF, EPUB and Kindle. Book excerpt:

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