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Algebraic Codes for Data Transmission

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ISBN-10: 0521553741

ISBN-13: 9780521553742

Edition: 2nd 2002

Authors: Richard E. Blahut

List price: $143.00
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An accessible introduction to the basic elements of algebraic codes including Reed-Solomon, trellis, turbocodes, etc. Throughout the book, mathematical theory is illustrated by reference to many practical examples.
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Book details

List price: $143.00
Edition: 2nd
Copyright year: 2002
Publisher: Cambridge University Press
Publication date: 2/6/2003
Binding: Hardcover
Pages: 498
Size: 7.25" wide x 10.00" long x 1.00" tall
Weight: 2.596
Language: English

Richard E. Blahut is Head of the Department of Electrical and Computer Engineering at the University of Illinois, Urbana Champaign, where he is also a professor. He is a Fellow of the IEEE and the recipient of many awards including the IEEE Alexander Graham Bell Medal (1998), the Tau Beta Pi Daniel C. Drucker Eminent Faculty Award, and the IEEE Millennium Medal. He was named Fellow of the IBM Corporation in 1980, where he worked for over 30 years, and was elected to the National Academy of Engineering in 1990.

The discrete communication channel
The history of data-transmission codes
Elementary concepts
Elementary codes
Introduction to Algebra
Fields of characteristic two
Vector spaces
Linear algebra
Linear Block Codes
Structure of linear block codes
Matrix description of linear block codes
Hamming codes
The standard array
Hamming spheres and perfect codes
Simple modifications to a linear code
The Arithmetic of Galois Fields
The integer ring
Finite fields based on the integer ring
Polynomial rings
Finite fields based on polynomial rings
Primitive elements
The structure of finite fields
Cyclic Codes
Viewing a code from an extension field
Polynomial description of cyclic codes
Minimal polynomials and conjugates
Matrix description of cyclic codes
Hamming codes as cyclic codes
Cyclic codes for correcting double errors
Quasi-cyclic codes and shortened cyclic codes
The Golay code as a cyclic code
Cyclic codes for correcting burst errors
The Fire codes as cyclic codes
Cyclic codes for error detection
Codes Based on the Fourier Transform
The Fourier transform
Reed-Solomon codes
Conjugacy constraints and idempotents
Spectral description of cyclic codes
BCH codes
The Peterson-Gorenstein-Zierler decoder
The Reed-Muller codes as cyclic codes
Extended Reed-Solomon codes
Extended BCH codes
Algorithms Based on the Fourier Transform
Spectral estimation in a finite field
Synthesis of linear recursions
Decoding of binary BCH codes
Decoding of nonbinary BCH codes
Decoding with erasures and errors
Decoding in the time domain
Decoding within the BCH bound
Decoding beyond the BCH bound
Decoding of extended Reed-Solomon codes
Decoding with the euclidean algorithm
Logic circuits for finite-field arithmetic
Shift-register encoders and decoders
The Meggitt decoder
Error trapping
Modified error trapping
Architecture of Reed-Solomon decoders
Multipliers and inverters
Bit-serial multipliers
Convolutional Codes
Codes without a block structure
Trellis description of convolutional codes
Polynomial description of convolutional codes
Check matrices and inverse matrices
Error correction and distance notions
Matrix description of convolutional codes
The Wyner-Ash codes as convolutional codes
Syndrome decoding algorithms
Convolutional codes for correcting error bursts
Algebraic structure of convolutional codes
Beyond BCH Codes
Product codes and interleaved codes
Bicyclic codes
Concatenated codes
Cross-interleaved codes
Turbo codes
Justesen codes
Codes and Algorithms Based on Graphs
Distance, probability, and likelihood
The Viterbi algorithm
Sequential algorithms to search a trellis
Trellis description of linear block codes
Gallager codes
Tanner graphs and factor graphs
Posterior probabilities
The two-way algorithm
Iterative decoding of turbo codes
Tail-biting representations of block codes
The Golay code as a tail-biting code
Performance of Error-Control Codes
Weight distributions of block codes
Performance of block codes
Bounds on minimum distance of block codes
Binary expansions of Reed-Solomon codes
Symbol error rates on a gaussian-noise channel
Sequence error rates on a gaussian-noise channel
Coding gain
Capacity of a gaussian-noise channel
Codes and Algorithms for Majority Decoding
Reed-Muller codes
Decoding by majority vote
Circuits for majority decoding
Affine permutations for cyclic codes
Cyclic codes based on permutations
Convolutional codes for majority decoding
Generalized Reed-Muller codes
Euclidean-geometry codes
Projective-geometry codes