Csiszar I., Körner J. — Information Theory: Coding Theorems for Discrete Memoryless Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Csiszar I., Körner J. — Information Theory: Coding Theorems for Discrete Memoryless Systems

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Название: Information Theory: Coding Theorems for Discrete Memoryless Systems

Авторы: Csiszar I., Körner J.

Язык:

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1982

Количество страниц: 452

Добавлена в каталог: 03.04.2008

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Предметный указатель

Conditional distribution      10
Conditional entropy      20
Conditional informational divergence      31
Conditional mutual information      48
Conditional type      31
Connected by channel W, RV’s      99
Conservation of entropy      79 83
Conservation of entropy and ergodic theory      79—80
Constant composition codes      117 161
Constant composition codes, expurgated bound      185
Constant composition codes, Gilbert bound, general      179
Constant composition codes, random coding bound      165
Constant composition codes, random coding bound, universal attainability of      172
Constant composition codes, random coding bound, universal improvement of      182
Constant composition codes, reliability at zero rate      191
Constant composition codes, sphere packing bound      166
Constant composition codes, undetected error and erasure      175
Constraint upon the codewords      108 (see also “Input constraint”)
Continuity lemmas with respect to entropy metric      57
Continuity lemmas, entropy      33
Continuity lemmas, Fanos’s inequality      53
Continuity lemmas, random coding exponent function      169
Continuity lemmas, rate-distortion function      124
Converse result      110 (see also “Strong converse” “Weak “Exponential
Convex closure      11
Convex closure of a set of stochastic matrices      205
Convex closure of a set of stochastic matrices, row      205
Convexity of achievable rate regions and capacity regions      see “Time sharing principle”
Convexity of capacity-constraint function      109
Convexity of expurgated exponent function      187
Convexity of functions of distributions and channels      12
Convexity of information measures      50
Convexity of rate-distortion function      124
Convexity of sphere packing exponent function      168
Correlated random code      see “Random code”
Correlated source      see “Multiple source”
Cost      66 120
Cost function, general      83
Cost of transmission      2 4
Cover, T.M.      263 269 288 299 302 378 381 390 416 419
Covering of product graphs      160
Covering, type covering lemma      150
Cramer — Rao inequality      28
Cramer, H.      28
Critical rate      171 181
Critical rate for list codes      196
Critical rate of a BSC      195
Critical rate with feedback, BSC      200
Critical rate, $E_{x}(R)=E_{sp}(R)$ at      194
Cross-entropy      see “Informational divergence”
Crossover probability, BSC      114
Csibi, S.      VIII IX
Csiszar, I.      41 58 60 74 79 81—83 85 121 147 149 182 185 188 198 203 233 264 268 269 358 413 416 419 420
Cybakov, B.S.      136 420
Daroczy, Z.      26 27 420
Data compression      see “Source coding”
Data processing lemma      55
Data processing lemma, strong      95 350
data storage      3
Davisson, L.D.      83 85 158 420 424
Decision feedback      201
Decoder      2 4
Decoder, channel networks      279
Decoder, channels      99
Decoder, channels, maximum likelihood      111
Decoder, channels, maximum mutual information      164
Decoder, channels, minimum distance      114
Decoder, channels, standard minimum distance      206
Decoder, minimum entropy      265
Decoder, network      246
Decoder, sources      123
Decoder, stochastic      226
Decoding      2
Decoding set      see “Inverse image of a message under a decoder (channels)”
Degraded broadcast channel      379
Degraded broadcast channels, product of      384
Degraded broadcast channels, sum of      387
Degraded channels      115
Degraded channels, entropy and image size characterization      343
Delta-convention      34
Depth of a graph      246
Depth of a vertex      246
Destination      2
Deterministic broadcast channel      391
Deterministic broadcast channel, semi      392
Direct result      110
Directed graph      245
Discrete memoryless broadcast channel      see “Broadcast channel”
Discrete memoryless channel (DMC)      100 ff 161
Discrete memoryless channel (DMC), capacity      see “Capacity”
Discrete memoryless channel (DMC), coding theorem      104 108
Discrete memoryless channel (DMC), coding theorem, for codewords from a given set      106—108
Discrete memoryless channel (DMC), coding theorem, remainder terms in      119
Discrete memoryless channel (DMC), coding theorem, strong converse      110
Discrete memoryless channel (DMC), coding theorem, weak converse      112
Discrete memoryless channel (DMC), exponential probability bounds      see “Error”
Discrete memoryless channel (DMC), feedback      see “Feedback”
Discrete memoryless channel (DMC), image of a set over      see “Image (of a set over channel)”
Discrete memoryless channel (DMC), input constraint      see “Input constraint $(c</a></span> <span class=subjpages><a href=

$(c</a></span> <span class=subjpages><a href=

Discrete memoryless channel (DMC), linear codes      114 198
Discrete memoryless channel (DMC), maximal code lemma      101
Discrete memoryless channel (DMC), maximal code lemma, for two channels      316
Discrete memoryless channel (DMC), multi-terminal      see “Channel network”
Discrete memoryless channel (DMC), reliability function      see “Reliability function DMC”
Discrete memoryless channel (DMC), transmission of a source over      129 ff 197
Discrete memoryless channel (DMC), universal coding      172 175 182
Discrete memoryless channel (DMC), zero-error capacity      see “Zero error capacity”
Discrete memoryless multiple source (DMMS)      237 240
Discrete memoryless multiple sources (DMMS), coding theorems involving      see “Source network coding theorems”
Discrete memoryless multiple-access channel      see “Multiple-access channel”
Discrete memoryless source (DMS)      15
Discrete memoryless sources (DMS), coding theorems for      see “Source coding theorems”
Discrimination, information for      see “Informational divergence”
Distance, distributions, variational      58
Distance, distributions, variational, and entropy      33
Distance, distributions, variational, and informational divergence      58
Distance, random variables, entropy      53 57
Distance, sequences, Hamming      see “Hamming minimum
Distortion measure      4 123
Distortion measure, associated with a channel      185
Distortion measure, averaging      124
Distortion measure, non-finite      134 148
Distortion measure, peak      134
Distortion measure, single-letter      see “Averaging distortion measure”
Distortion measures, several      134
Distortion-rate function      156
Divergence      see “Informational divergence”
Divergence contraction      see “Data processing lemma”
Divergence geometry      59
Divergence projection      59 60
Divergence, symmetrized      58
Djackov, A.G.      199 200 420
Dobrusin, R.L.      46 121 136 160 199 203 233 420 421
Double Markovity      402
Doubly stochastic matrix      58
Dueck, G.      122 181 184 277 284 300 421
Eggleston, H.G.      310 421
El Gamal, A.A.      381 385 387 421
Elias, P.      24 114 121 196 198 203 421
Empirical distribution      29
Empirical distribution, large deviation probabilities for      43
Encoder      2 4
Encoder with feedback      120
Encoder, channel networks      279
Encoder, channels      99
Encoder, networks      246
Encoder, progressive      79
Encoder, source networks      see “Encoder networks”
Encoder, sources      123
Encoder, stochastic      217 284 291

Encoding      2
entropy      7 17 22
Entropy characterization problem      261 303
Entropy characterization problem and source networks      261 262
Entropy characterization problem, partial results      352 ff
Entropy characterization problem, relation to image size problem      325 342 346
Entropy characterization problem, solution for 3-sources      see “Entropy characterization theorem”
Entropy characterization theorem      342 (see also “Entropy characterization problem”)
Entropy characterization theorem, converse part      313
Entropy characterization theorem, direct part      339
Entropy in ergodic theory      80
Entropy in physics      28 46
Entropy metrics      53 57
Entropy of an individual sequence      48
Entropy rate of a source      65
Entropy, $\varepsilon$ - (in Soviet literature)      see “ $\Delta$ -distortion rate”
Entropy, conditional      20
Entropy, conservation of      79 83
Entropy, cross-      see “Informational divergence”
Entropy, formal properties      47 ff
Entropy, intuitive concept      7
Entropy, postulational characterizations      25—27
Entropy, relation to polynomial coefficients      30 39
Entropy, Renyi’s, of order $\alpha$       27
Entropy, upper bounds on      56
Entropy-typical sequences      40
Equidistant channel      194
Equivocation rate      407
erasure      174
Erasure, binary, channel      114
Erasure, probability of      174
Erasure, probability of, joint bounds on, and undetected error      175
Erdoes, P.      26 421
Ergodic theory, isomorphy problem of      80
Error exponent      see “Exponential probability bounds”
Error exponent, compound DMC      173
Error exponent, DMC      161 ff (see also “Reliability function” “Random “Sphere “Expurgated
Error exponent, DMC, constant composition codes      165—168 185 191
Error exponent, DMC, feedback      199—202
Error exponent, DMC, list codes      196
Error exponent, DMC, rates above capacity      184
Error exponent, DMC, two messages      188
Error exponent, DMC, undetected error and erasure      175
Error exponent, DMC, universally attainable      172 182
Error exponent, hypothesis testing      19 44
Error exponent, source networks      264 265 267 268
Error exponent, source-channel      197
Error exponent, sources      37 42 44
Error exponent, sources in rate distortion theorem      156
Error frequency fidelity criterion      63 132 133
Error probability      see “Probability of error” “Error
Error probability for two messages      188
Expected common length of codes      403
Exponential probability bounds at achievable rates      see “Error exponent”
Exponential probability bounds at non-achievable rates, channel      184
Exponential probability bounds at non-achievable rates, source      41 158
Exponential probability bounds, hypothesis testing      19 44
Expurgated bound      185 (see also “Expurgated exponent function”)
Expurgated bound and Gilbert bound      195
Expurgated bound and zero-error capacity      187
Expurgated bound under input constraint      192
Expurgated bound, alternative formula      192
Expurgated bound, BSC      194
Expurgated bound, equidistant channels      194
Expurgated bound, product space      187
Expurgated bound, tightness at zero rate      189
Expurgated exponent function ( $E_{x}(R,P,W)$ and $E_{x}(R,W)$ )      185
Expurgated exponent function ( $E_{x}(R,P,W)$ and $E_{x}(R,W)$ ), alternative formula      193
Expurgated exponent function ( $E_{x}(R,P,W)$ and $E_{x}(R,W)$ ), and distortion-rate functions      194
Expurgated exponent function ( $E_{x}(R,P,W)$ and $E_{x}(R,W)$ ), properties of      187
Expurgated exponent function ( $E_{x}(R,P,W)$ and $E_{x}(R,W)$ ), relation to random coding exponent function      185 194
Extension of a code      101
Faddeev, D.K.      26 421
Family of channels      see “Compound channel” “Arbitrarily
Family of channels, average probability of error      173
Family of channels, maximum probability of error      172
Fano, R.M.      60 85 112 113 203 421
Fano’s inequality      53
Feedback      8 120
Feedback, active      202
Feedback, arbitrarily varying channel with      see “Arbitrarily varying channel (AVC) feedback”
Feedback, complete      120
Feedback, decision      201
Feedback, does not increase the capacity of a DMC      120
Feedback, error exponent      199—202
Feedback, multiple-access channel with      298
Feedback, passive and active      202
Feedback, probability of error for R>C      184
Feedback, variable-length codes for channes with      121 202
Feedback, zero-error capacity with      121
Feinstein, A.      122 421
Feller, W.      40 81 88 421
Fenchel — Eggleston — Carat heodory theorem      310
Fenchel, W.      310
Fibonacci sequence      75
Fidelity criterion      2 4
Fidelity criterion, $\varepsilon$ , $(d,\Delta)$       123
Fidelity criterion, $\varepsilon$ , $(d,\Delta)$ , arbitrary varying source      153
Fidelity criterion, $\varepsilon$ , $(d,\Delta)$ , source networks      247
Fidelity criterion, $\varepsilon$ , $(d,\Delta)$ , source networks, relation to average      372 373
Fidelity criterion, average distortion      see “Average fidelity criterion $(d</a></span> <span class=subjpages><a href=

$(d</a></span> <span class=subjpages><a href=

Fidelity criterion, average, $(d,\Delta)$       123
Fidelity criterion, average, $(d,\Delta)$ , for source-channel transmission      129
Fidelity criterion, average, $(d,\Delta)$ , relation to $\varepsilon$ , $(d,\Delta)$       133 158
Fidelity criterion, error frequency      63 132 133
Fidelity criterion, probability of error      3 15 132
Fidelity criterion, probability of error, source networks      248
Fidelity criterion, several distortion measures      134
Fidelity criterion, zero-error      see “ $\varepsilon$ fidelity criterion with $\varepsilon=0$ ”
Finite state noiseless channel      82
Fisher, R.A.      28 421
Fisher’s information      27
Fitingof weight      see “Entropy of an individual sequence”
Fitingof, B.M.      85 421
Fixed-length-to-fixed-length code      5
Fixed-to-variable length code      61
Fork network      241
Fork network with side information      405
Fork network, achievable rate region      242
Fork network, coding theorem      243 254
Fork network, exponential error bounds      264 265 267 268
Fork network, universal coding      264
Fork network, zero-error rate region      262
Forney, G.D.      196 201 203 421
Forte, B.      27 417 421
Gaarder, N.T.      299 421
Gabidulin, E.M.      115 421
Gacs, P.      VIII 96 120 122 269 347 350 351 357 358 381 383 403 416 418 421
Gallager, R.G.      60 134 148 149 180 181 185—189 192—198 203 264 266 357 421 422 426
Gallai, T.      118 422
Galois field      24
Game-theoretic approach      219 226
Gelfand, S.I.      VIII 391 392 406 416 422
Generated sequence (W-, Y|X-)      34
Generic distribution      15
Generic variables      237 240
Gerrish, A.M.      148 422
Gilbert bound      179
Gilbert bound and expurgated bound      195
Gilbert bound, general      179
Gilbert, E.N.      77 179 180 195 422
Goppa, V.D.      117 203 422
Graph representation of codes      see “Tree representation”
Graph representation of source and channel network problems      see “Source network” “Channel
Graph, associated with a channel      118
Graph, directed      245 (see also “Network”)
Graph, interval      118
Graph, perfect      118
Graph, product      118
Graph, product, chromatic number and zero-error rate region      262

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