Fundamentals of Codes, Graphs, and Iterative Decoding

Fundamentals of Codes, Graphs, and Iterative Decoding

Author: Stephen B. Wicker

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 241

ISBN-13: 0306477947

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Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.


List Decoding of Error-Correcting Codes

List Decoding of Error-Correcting Codes

Author: Venkatesan Guruswami

Publisher: Springer

Published: 2004-11-29

Total Pages: 354

ISBN-13: 3540301801

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How can one exchange information e?ectively when the medium of com- nication introduces errors? This question has been investigated extensively starting with the seminal works of Shannon (1948) and Hamming (1950), and has led to the 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 errors e?ciently. This thesis presents some spectacular new results in the area of decoding algorithms for error-correctingcodes. Speci?cally,itshowshowthenotionof“list-decoding” can be applied to recover from far more errors, for a wide variety of err- correcting codes, than achievable before. A brief bit of background: error-correcting codes are combinatorial str- tures that show how to represent (or “encode”) information so that it is - silient to a moderate number of errors. Speci?cally, an error-correcting code takes a short binary string, called the message, and shows how to transform it into a longer binary string, called the codeword, so that if a small number of bits of the codewordare ?ipped, the resulting string does not look like any other codeword. The maximum number of errorsthat the code is guaranteed to detect, denoted d, is a central parameter in its design. A basic property of such a code is that if the number of errors that occur is known to be smaller than d/2, the message is determined uniquely. This poses a computational problem,calledthedecodingproblem:computethemessagefromacorrupted codeword, when the number of errors is less than d/2.


Introduction to Coding Theory

Introduction to Coding Theory

Author: Ron Roth

Publisher: Cambridge University Press

Published: 2006-02-23

Total Pages: 592

ISBN-13: 9780521845045

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This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.


Codes and turbo codes

Codes and turbo codes

Author: Claude Berrou

Publisher: Springer Science & Business Media

Published: 2011-01-27

Total Pages: 400

ISBN-13: 2817800397

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This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. Its main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes.


Error-correcting Codes

Error-correcting Codes

Author: William Wesley Peterson

Publisher: MIT Press

Published: 1972

Total Pages: 584

ISBN-13: 9780262160391

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The coding problem; Introduction to algebra; Linear codes; Error correction capabilities of linear codes; Important linear block codes; Polynomial rings and galois fields; Linear switching circuits; Cyclic codes; Bose-chaudhuri-hocquenghem codes; Arithmetic codes.


Wireless Communications

Wireless Communications

Author: Keith Q. T. Zhang

Publisher: John Wiley & Sons

Published: 2015-10-13

Total Pages: 448

ISBN-13: 1119113288

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Understand the mechanics of wireless communication Wireless Communications: Principles, Theory and Methodology offers a detailed introduction to the technology. Comprehensive and well-rounded coverage includes signaling, transmission, and detection, including the mathematical and physics principles that underlie the technology's mechanics. Problems with modern wireless communication are discussed in the context of applied skills, and the various approaches to solving these issues offer students the opportunity to test their understanding in a practical manner. With in-depth explanations and a practical approach to complex material, this book provides students with a clear understanding of wireless communication technology.


Digital Communications with Emphasis on Data Modems

Digital Communications with Emphasis on Data Modems

Author: Richard W. Middlestead

Publisher: John Wiley & Sons

Published: 2017-04-03

Total Pages: 836

ISBN-13: 0470408529

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This book uses a practical approach in the application of theoretical concepts to digital communications in the design of software defined radio modems. This book discusses the design, implementation and performance verification of waveforms and algorithms appropriate for digital data modulation and demodulation in modern communication systems. Using a building-block approach, the author provides an introductory to the advanced understanding of acquisition and data detection using source and executable simulation code to validate the communication system performance with respect to theory and design specifications. The author focuses on theoretical analysis, algorithm design, firmware and software designs and subsystem and system testing. This book treats system designs with a variety of channel characteristics from very low to optical frequencies. This book offers system analysis and subsystem implementation options for acquisition and data detection appropriate to the channel conditions and system specifications, and provides test methods for demonstrating system performance. This book also: Outlines fundamental system requirements and related analysis that must be established prior to a detailed subsystem design Includes many examples that highlight various analytical solutions and case studies that characterize various system performance measures Discusses various aspects of atmospheric propagation using the spherical 4/3 effective earth radius model Examines Ionospheric propagation and uses the Rayleigh fading channel to evaluate link performance using several robust waveform modulations Contains end-of-chapter problems, allowing the reader to further engage with the text Digital Communications with Emphasis on Data Modems is a great resource for communication-system and digital signal processing engineers and students looking for in-depth theory as well as practical implementations.


Algebraic and Stochastic Coding Theory

Algebraic and Stochastic Coding Theory

Author: Dave K. Kythe

Publisher: CRC Press

Published: 2017-07-28

Total Pages: 515

ISBN-13: 135183245X

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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.