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Hamming R.W. — Coding and Information Theory
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Название: Coding and Information TheoryАвтор: Hamming R.W. Аннотация: The second edition is mainly an expansion of the material in the first edition. The changes were made to (1) increase the clarity of the presentation, (2) extend some of the basic ideas, and (3) indicate further practical details. 1 have resisted the urgings (both from others and myself) to include more difficult codes, such as Reed-Muller, Vitcrbi, Fire, and cyclic. They seem to be more suitable for a second course, and in any case require a firmer mathematical background than 1 have assumed, if they are to be "understood." I still believe that it is better, in this subject, to master the fundamentals than it is to rush through, with little real understanding, a large body of material. There are now many excellent texts devoted to algebraic coding theory.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Second EditionГод издания: 1986Количество страниц: 259Добавлена в каталог: 23.11.2009Операции: Положить на полку |
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Abramson, N. 253 Abstract theory 1 Adjoint system 133 Algebraic coding theory 209 AM signaling 242 AND 30 Anti-Gray code 99 ASCII code 8 10 11 27 ASCII code, table of 13 Average code length 2 63 Average error probability 201 Average random code 201 Backward conditional probabilities 142 Bandwidth 237 Bandwidth example 238 Bandwidth generally 246 Bandwidth vs. change 242 Bayes' formula (theorem) 141 Berlekamp, E.R. 253 Bernoulli trials 183 Binary encoding 7 Binary symmetric channel 18 142 159 195 Binary symmetric channel, capacity of 160—161 Binomial coefficient bound 170—173 Binomial coefficients 13 Bit 7 Bit of information 106 Blake, I. 253 Block code 68 Burst error—detecting codes 26 BYTE 10 Cain, F.B. 253 Carrier frequency 224 Cauchy functional equation 104 Channel 138 Channel capacity 103 201 Channel capacity of binary symmetric channel 160—161 Channel capacity, definition of 153 Channel capacity, encoding 5 Channel relationships 140 Channel uniform 154—155 Channel, definition of 139 Channel, encoding 2 Channel, properties of 140 Chebyshev's inequality 181—182 Clark, G. 253 Code compression 18 Codes 2-out-of-5 14 23 Codes anti-Gray 99 Codes comma 54 59 69 Codes delta modulation 100 Codes Gray 80 97 Codes hash 94 Codes Huffman 51 Codes instantaneous 53—55 Codes miscellaneous 79 Codes Morse 12—13 Codes radix r 15 Codes random 79 Codes Shannon — Fano 121—122 126 Codes van Duuren (3-out-of-7) 23 Codes variable—length 12 51 Codes, burst—detecting 26 Codes, error—correcting 34 Codes, error—detecting 20 Codes, extensions of 72 Codes, hexadecimal 10 Codes, octal 9 Codes, predictive 79 Codes, resynchronization of 101 Codes, unique 52 Codes, weighted 27 Coding Huffman 51 Coding Shannon — Fano 121 Combinations 13 Comma codes 54 69 Conditional mutual information 150 161 Conditional probability 80 Continuous signals 247 Costello, D.J. 254 Davidson, L.D. 253 Decision rule 192 Decision tree 53 Decoding tree 54 56—57 60 62 Delta modulation 100 Digital signaling 6 237 Direct product 53 Double-error-correcting code 228—234 Double-error-detecting code 47 Efficient codes 51 56 64 Efficient codes Markov 86 Eigenfunctions 237 England, J. 254 entropy 103 107 Entropy function 1 107 Entropy function fundamental inequality 115 Entropy function, maximum of 117 Entropy function, properties of 114—119 Entropy function, table of 250 Entropy joint 146 Entropy of Markov processes 129 Entropy of source 18 Entropy received symbols 145 Entropy robustness 136 Entropy source alphabet 145 Entropy, conditional 130 146 Equilibrium probabilities 133 Equivalent codes 42 Equivocation 148 Ergodic Markov processes 85 Error correction 34 Error integral 174 Error-correcting codes 35—36 158 Error-correcting codes, perfect 158 Errors of interchange of symbols 28 Error—detecting codes 20 22 147 210 Error—detecting codes probability 24 Error—detecting codes why 20 escape characters 15 Evolution 3 Excess redundancy 22 Extensions of a code 53 72 124 Extensions of a code examples 126 Extensions of a code Markov process 87 Fano bound 205 Finite automation 53 77 Finite fields 210 FM signaling 244 FORTRAN 16 49 95 FORTRAN, compile 17 Forward conditional probabilities 141 Fourier integral 238 Fundamental error formula 199 Gallager, R.G. 253 Galois fields 4 195 Gamma function 173 Gatlin, L.L. 253 Geometric approach 44 Gibbs inequality 117 Gray codes 80 97 Gray codes, decoding 99 Gray codes, details of 98 Gray, R.M. 253 Gray, R.M. code 97 Guiasu, S. 254 Hamming error-correcting codes 210—211 213 220 Hamming error-correcting codes example 41 Hamming error-correcting codes parity checks 39 210 Hamming error-correcting codes, table of 40 Hamming — Huffman coding 78 Hamming, distance 45 189 Hamming, meaning of 46 Hartley 106 Hash coding 94 Hash coding collisions 95 Hash coding removals 96 Hexadecimal code 10 history 2 Huffman codes 51 63 71 114 Huffman codes, examples of 65 67—68 Huffman codes, noise in 74 Huffman codes, radix r 73 Huffman codes, use of 77 Huffman codes, variability of 68 Independent errors 23 Information source 1 5 Information source, definition of 104 Instantaneous codes 53 Instantaneous codes, construction of 55 Interchange of symbols 28 ISBN book numbers 32 Jacobs, I.M. 254 Jayant, N.S. 254 Knuth, D.E. 254 Kraft inequality 57 62 121 Kraft inequality theorem 57 Law of Large Numbers 183 Law of large numbers theorem 184 Lin, S. 254 Logical add (XOR) 23 31 MacWilliams, J. 254 Markov process 80 129 131 135 Markov process, ergodic 84 Martin, N. 254 Maximum likelihood rule 192 196 McEliece, R.J. 254 McMillan inequality 62 Memory source 80 Metalanguage 16 Midpoint formula 166 Minimum distance 45 Minimum variance codes 68 75 Model of signaling system 4 Modular arithmetic 30 Modulation 242 Modulo 2 arithmetic 21 Monic polynomial 215 Morse code 12 13 51 63 Morse code, table of 13 Mutual information 148 Mutual information, definition of 148 Mutual information, properties of 149—151 nat (unit of information) 106 Noise 23 Noise entropy 148 Noise in Huffman codes 74 Noise power 248 Noiseless coding theorem 104 125 NORC computer 34 n—dimensional codes 37 45 n—dimensional paradox 179 n—dimensional space 176 n—dimensional space Euclidean distance 176 n—dimensional space, Euclidean 176 n—dimensional spheres 177 n—dimensional spheres coefficients 177 n—dimensional spheres, formula for 177 n—dimensional spheres, table of 177 Octal code 9 Omura, J.K. 254 Parity check 21 40 Parity check even 21 Parity check odd 21 Parity check, computing 22 Peterson, W.W. 254 Pless, V. 254 Polynomials 214 Polynomials primitive root 219 Polynomials, prime 215 Predictive encoding 79 88 Predictive encoding decoder 90 Predictive encoding encoder 89 Predictive encoding run length 91 Predictive encoding summary 94 Prime polynomials 215 Primitive roots 219 Probabilities of symbols 1 63 Pulse signaling 245 Radix r codes 15 72 Random code 196 203 Random code, average of 201 Random encoding 79 196 Random type fonts 118 Rectangular codes 35 Redundancy 22 36 reliable 20 Restrictions on codes 21 Resynchronization 101 Retransmission 25 Sampling theorem 240 Shannon 2 Shannon's theorems, main 191 Shannon's theorems, main converse 207 Shannon's theorems, main general case of 204 Shannon's theorems, noiseless 125 Shift registers 224 Shortened block codes 60 Side lobes 240 Single-error-detecting plus double-error-correcting codes 46 228 Slepian, D. 254 Sloane, N.J.A. 254 Source alphabet 2 6 Source encoding 2 5 Stirling's approximation 165—170 Stirling's approximation, table of 170 Stretch computer 35 Symbol 1 Symmetric channel 18 Syndrome 38 39 212 Thompson, T.M. 254 Transition graph 81 Transition graph equilibrium 83 Transition graph limiting matrix 83 Transition graph matrix 82 Transition graph probability 82 Trapezoid Rule 165 Triangular codes 37 Two state devices 6 Two-out-of-five codes 14 23 Two-out-of-five codes table 14 Uniform channel 154—155 Uniform channel definition 155 Uniform input 156 Unique decoding 52 62 van Duuren code (3 out of 7) 23 Variable length codes 13 51 Variance 181 Variance minimum 75 Variance of sums 184 Viterbi, A.J. 254 Wakerly, J. 254 Wallis integrals 168 Weighted codes 27 Weldon, E.J., Jr. 254 White noise 23 39 Wozencraft, J.M. 254 XOR (instruction) 30 Zipf distribution 71 Zipf distribution, entropy of 112
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