algebraic codes for data transmission

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Algebraic Codes For Data Transmission

Author : Richard E. Blahut
ISBN : 9781139435079
Genre : Technology & Engineering
File Size : 85. 23 MB
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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

Author : Richard E. Blahut
ISBN : 9781139469463
Genre : Technology & Engineering
File Size : 50. 63 MB
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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
ISBN : UOM:39015040304217
Genre : Reference
File Size : 49. 66 MB
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Channel Codes

Author : William Ryan
ISBN : 9781139483018
Genre : Technology & Engineering
File Size : 22. 97 MB
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Channel coding lies at the heart of digital communication and data storage, and this detailed introduction describes the core theory as well as decoding algorithms, implementation details, and performance analyses. In this book, Professors Ryan and Lin provide clear information on modern channel codes, including turbo and low-density parity-check (LDPC) codes. They also present detailed coverage of BCH codes, Reed-Solomon codes, convolutional codes, finite geometry codes, and product codes, providing a one-stop resource for both classical and modern coding techniques. Assuming no prior knowledge in the field of channel coding, the opening chapters begin with basic theory to introduce newcomers to the subject. Later chapters then extend to advanced topics such as code ensemble performance analyses and algebraic code design. 250 varied and stimulating end-of-chapter problems are also included to test and enhance learning, making this an essential resource for students and practitioners alike.

Introduction To Coding Theory

Author : Ron Roth
ISBN : 0521845041
Genre : Computers
File Size : 51. 1 MB
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This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

Algebraic And Stochastic Coding Theory

Author : Dave K. Kythe
ISBN : 9781466505629
Genre : Computers
File Size : 25. 44 MB
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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.

Algebraic Coding Theory

Author : Elwyn R Berlekamp
ISBN : 9789814635912
Genre :
File Size : 82. 24 MB
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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. Contents:Basic Binary CodesArithmetic Operations Modulo An Irreducible Binary PolynomialThe Number of Irreducible q-ary Polynomials of Given DegreeThe Structure of Finite FieldsCyclic Binary CodesThe Factorization of Polynomials Over Finite FieldsBinary BCH Codes for Correcting Multiple ErrorsNonbinary CodingNegacyclic Codes for the Lee MetricGorenstein-Zierler Generalized Nonbinary BCH Codes for the Hamming MetricLinearized Polynomials and Affine PolynomialsThe Enumeration of Information Symbols in BCH CodesThe Information Rate of the Optimum CodesCodes Derived by Modifying or Combining Other CodesOther Important Coding and Decoding MethodsWeight EnumeratorsAppendices and References Readership: Researchers in coding theory and cryptography, algebra and number theory, and software engineering. Key Features:A classic monograph and reference book on Coding Theory and Cryptography written by a revered scholar long known for his work in coding theoryContains several theorems created by the author that have been respected for 40 yearsKeywords:Coding Theory;Binary Codes;Irreducible Q-ary Polynomial;Error-Correcting Codes;BCH Codes;Berlekamp's Algorithm;Finite Fields

Algebraic Function Fields And Codes

Author : Henning Stichtenoth
ISBN : 9783540768784
Genre : Mathematics
File Size : 34. 69 MB
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This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

Algebraic Geometric Codes

Author : M. Tsfasman
ISBN : 9789401138109
Genre : Mathematics
File Size : 69. 95 MB
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Modem Theory

Author : Richard E. Blahut
ISBN : 9780521780148
Genre : Technology & Engineering
File Size : 71. 80 MB
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This detailed introduction presents the theory of digital modulation and coding underpinning the modern design of modems for telecommunications. From baseband and passband modulation and demodulation to sequence estimation, turbo codes, and the Viterbi algorithm, a wide range of key topics is covered, whilst end-of-chapter exercises test students' understanding throughout.

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