Introduction to error control codes

Introduction to error control codes /

This textbook provides a firm foundation for those studying the field of error control codes. giving step-by-step instruction on this complex topic beginning with single parity code checks and repetition codes. Through these basic error-control mechanisms the fundamental principles of error detectio...

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Bibliographic Details
Main Author: Gravano, Salvatore
Format: Book
Language:English
Published: Oxford ; New York : Oxford University Press, 2001.
Series:Textbooks in electrical and electronic engineering ; 9.
Subjects:
Error-correcting codes (Information theory)
Fehlerkorrekturcode
ERROR CORRECTING CODES.
CODING.
INFORMATION THEORY.
Fehlerkorrekturcode.
Table of Contents:
  • 1 Block codes
  • 1.1 Digital communication channel 1
  • 1.2 Introduction to block codes 4
  • 1.3 Single-parity-check codes 8
  • 1.4 Product codes 15
  • 1.5 Repetition codes 16
  • 1.6 Hamming codes 22
  • 1.7 Minimum distance of block codes 28
  • 1.8 Soft-decision decoding 35
  • 1.9 Automatic-repeat-request schemes 38
  • 2 Linear codes
  • 2.1 Definition of linear codes 42
  • 2.2 Generator matrices 45
  • 2.3 Standard array 52
  • 2.4 Parity-check matrices 56
  • 2.5 Error syndromes 61
  • 2.6 Error detection and correction 64
  • 2.7 Shortened and extended linear codes 67
  • 3 Cyclic codes
  • 3.1 Definition of cyclic codes 73
  • 3.2 Polynomials 74
  • 3.3 Generator polynomials 79
  • 3.4 Encoding cyclic codes 81
  • 3.5 Decoding cyclic codes 85
  • 3.6 Factors of x[superscript n] + 1 87
  • 3.7 Parity-check polynomials 90
  • 3.8 Dual cyclic codes 92
  • 3.9 Generator and parity-check matrices of cyclic codes 94
  • 4 Linear-feedback shift registers for encoding and decoding cyclic codes
  • 4.1 Linear-feedback shift registers 98
  • 4.2 Polynomial-division register 101
  • 4.3 Registers for encoding 106
  • 4.4 Registers for error detection and correction 114
  • 4.5 Meggitt decoder 117
  • 5 Linear algebra
  • 5.1 Sets 129
  • 5.2 Groups 129
  • 5.3 Fields 134
  • 5.4 Vector spaces 136
  • 5.5 Matrices 144
  • 5.6 Linear codes as vector spaces 146
  • 5.7 Dual codes 150
  • 6 Galois fields
  • 6.1 Roots of equations 154
  • 6.2 Galors field GF(2[superscript 3]) 157
  • 6.3 Fields GF(2[superscript 4]) and GF(2[superscript 5]) 162
  • 6.4 Primitive field elements 167
  • 6.5 Irreducible and primitive polynomials 169
  • 6.6 Minimal polynomials 172
  • 6.7 Solution of equations in GF(2[superscript 4]) and GF(2[superscript 3]) 175
  • 7 Bose-Chaudhuri-Hocquenghem codes
  • 7.1 Cyclic codes revisited 184
  • 7.2 Definition and construction of binary BCH codes 186
  • 7.3 Error syndromes in finite fields 188
  • 7.4 Decoding SEC and DEC binary BCH codes 192
  • 7.5 Error-location polynomial 197
  • 7.6 Peterson-Gorenstein-Zierler decoder 202
  • 7.7 Reed-Solomon codes 207
  • 7.8 Berlekamp algorithm 218
  • 7.9 Error-evaluator polynomial 225
  • 8 Convolution codes
  • 8.2 Encoding convolutional codes 235
  • 8.3 Generator matrices for convolutional codes 240
  • 8.4 Generator polynomials for convolutional codes 242
  • 8.5 Graphical representation of convolutional codes 246
  • 8.6 Viterbi decoder 250.

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