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| Авторизация |
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| Поиск по указателям |
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| Ash R.B. — Information theory |
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| Предметный указатель |
Probability of error, for general binary codes 113 ff.
Probability of error, maximum 66
Random coding 66 67 74 110
Random process 275 ff.
Random process, covariance function of 250 256 275
Random process, Gaussian 250 256 279
Random process, second order 250 275
Random process, spectral density of 250 256 282
Random process, stationary 185
Random variables(s), conditionally independent 25
Random variables(s), Gaussian 231
Random variables(s), Gaussian, uncertainty of 240
Random variables(s), independent see “Independent random variables”
Random variables(s), independent, noiseless coding problem for 27
Random variables(s), independent, uncertainty of 5 ff.
Random vectors 19 25 39 240 243
Rate of transmission 1 3 63
Rate of transmission,  -permissible 224
Rate of transmission, critical, for the binary symmetric channel 117
Rate of transmission, permissible 223 234 251
Sampling theorem 258
Schwarz inequality 78 255 262
Sequence, input 65
Sequence, output 65
Sequence, typical 14 24 83 196
Sequence, typical in Shannon’s original proof of the fundamental theorem 66
Sequence, “meaningful”, produced by an information source 195 196 206
Sequential circuit, linear 163
Shannon — McMillan theorem see “Asymptotic equipartition property”
Shift register see “Feedback shift register”
Source of information 1 63 169 184
Source of information, alphabet of 172 185
Source of information, approximation of, by a source of finite order 189 ff.
Source of information, asymptotic equipartition property 197 223
Source of information, ergodic 197 202 207 208 223
Source of information, Markov 172 185
Source of information, Markov, indecomposable 185
Source of information, Markov, regular 185 202 223
Source of information, Markov, uncertainty of 186 219
Source of information, Markov, unifilar 187
Source of information, Markov, unifilar, connection matrix of 209
Source of information, Markov, unifilar, maximum uncertainty of 209
Source of information, Markov, unifilar, order of 189 ff.
Source of information, Markov, unifilar, uncertainty of 188
Source-channel matrix 215—217
Spectral density, of a random process 250 256 282
States, of a channel 46 215 230
States, of a Markov chain 171
| Stationary distribution, of a finite Markov chain 174 181 184
Stationary Gaussian random process 250
Stationary sequence of random variables 1
Steady state probabilities of a finite Markov chain 174 176
Steady state probabilities of a finite Markov chain, effective determination of existence of 180 208
Stirling’s formula 113
Storage requirements, of a decoder 92 161
Strong converse to the fundamental theorem 83 223 224
Strong converse to the fundamental theorem, failure of 225
Strong converse to the fundamental theorem, for the binary symmetric channel 124
Strong converse to the fundamental theorem, for the time-discrete Gaussian channel 246
Syndrome ( = corrector) 94
Uncertainty 4 8
Uncertainty, average 5
Uncertainty, axioms for 5 ff. 24 26
Uncertainty, axioms for, grouping axiom 8 80 81
Uncertainty, axioms for, grouping axiom, generated 26
Uncertainty, conditional 19 219 229 238 241
Uncertainty, convexity of 54 81
Uncertainty, input and output 50
Uncertainty, interpretations of 12 ff.
Uncertainty, joint 18—21 238—240
Uncertainty, maximization of 17
Uncertainty, maximization of, for a unifilar Markov source 209
Uncertainty, n-gram, unigram, digram, and trigram 191
Uncertainty, of a discrete random variable 5 ff.
Uncertainty, of a discrete random variable given an absolutely continuous random variable, and vice versa 241
Uncertainty, of a function of a random variable 26
Uncertainty, of a Gaussian random variable 240
Uncertainty, of a language 206
Uncertainty, of a unifilar Markov source 188
Uncertainty, of an absolutely continuous random variable 236
Uncertainty, of an information source 186 219
Uncertainty, properties of 16 ff.
Unifilar Markov source see “Source”
Uniform error bound 62 66
Varsharmov — Gilbert — Sacks condition 108 122 130 131 163 225
Vector space 126 147
Weak converse to the fundamental theorem, for the discrete memoryless channel 82 307
Weak converse to the fundamental theorem, for the finite state regular channel 223
Weak converse to the fundamental theorem, for the time-continuous Gaussian channel 252
Weak converse to the fundamental theorem, for the time-discrete Gaussian channel 234 245
Weak law of large numbers 3 130
Weak law of large numbers, exponential convergence in 83
Weak law of large numbers, for regular Markov chains 203
Weight, of a binary sequence 102
“Yes or no” questions 13 14
“Yes or no” questions, relation to instantaneous binary codes 40
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