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

$(n,\varepsilon)$ -code      101
$\Delta$ -distortion rate      124 (see also “Distortion measure” “Rate
$\Delta$ -distortion rate computing algorithm      144
$\Delta$ -distortion rate, alternative definitions      124 128 158
$\Delta$ -distortion rate, zero error      133 152
$\Delta$ -distortion rate, zero error, computation of      159
a-capacity and m-capacity, difference, AVC      224
a-capacity and m-capacity, equality, AVC, stochastic encoder      217
a-capacity and m-capacity, equality, DMC      111
a-capacity region      see “Capacity region”
a-capacity region and m-capacity region, difference, MAC      284
a-capacity region and m-capacity region, equality, broadcast channels      291
a-capacity region and m-capacity region, equality, stochastic encoders      284 291
a-capacity, AVC      205
a-capacity, AVC, coding theorem      214
a-capacity, AVC, positivity      224
ABC coding theorem      366 (see also “Asymmetric broadcast channel”)
ABC coding theorem with input constraint      392
ABC coding theorem, alternative form      378
ABC coding theorem, converse part      364
ABC coding theorem, direct part      359
Achievable ( $\varepsilon$ -achievable) rate pair, MAC      271
Achievable ( $\varepsilon$ -achievable) rate region      see “Source network coding theorems”
Achievable ( $\varepsilon$ -achievable) rate region, channel network      see “Capacity region”
Achievable ( $\varepsilon$ -achievable) rate region, fork network      see “Fork network achievable
Achievable ( $\varepsilon$ -achievable) rate region, optimal points of      242
Achievable ( $\varepsilon$ -achievable) rate region, source network      247
Achievable ( $\varepsilon$ -achievable) rate region, source network, particular points      402
Achievable ( $\varepsilon$ -achievable) rate region, source network, product space characterization      255
Achievable ( $\varepsilon$ -achievable) rate triple, fork network      241
Achievable ( $\varepsilon$ -achievable) rate vector, channel network      281
Achievable ( $\varepsilon$ -achievable) rate vector, source network      247 249
Achievable ( $\varepsilon$ -achievable) rate, channel      101
Achievable ( $\varepsilon$ -achievable) rate, source, at distortion level $\Delta$       123
Achievable ( $\varepsilon$ -achievable) rate-distortion pair      124
Achievable entropy triples      304 (see also “Entropy characterization problem”)
Achievable exponent triples      304 (see also “Image size problem”)
Active feedback      202 224
Aczel, J.      26 27 417
Additive noise      114
Additivity of information measures      26 49 51
Addressing      279
Ahlswede, R.      VIII 95 96 120 122 182 223 224 230 231 233 269 284 289 296 302 347—352 357 358 381 383 404 416—418
Algebraic codes      see “Linear codes”
Alphabet, channel input, output      4 100 270
Alphabet, code      51
Alphabet, reproduction      123
Alphabet, source      15
Alphabetic code      77
Amount of information      6 17 20—22
Amount of information, unit of      7
Arbitrarily varying channel (AVC)      204 ff
Arbitrarily varying channel (AVC), capacity, a- and m-capacity      205
Arbitrarily varying channel (AVC), capacity, positivity      222 224
Arbitrarily varying channel (AVC), capacity, random code      212 224
Arbitrarily varying channel (AVC), capacity, stochastic encoder      217
Arbitrarily varying channel (AVC), coding theorem, a-capacity      214
Arbitrarily varying channel (AVC), coding theorem, m-capacity, binary output      208
Arbitrarily varying channel (AVC), coding theorem, stochastic encoder      217
Arbitrarily varying channel (AVC), feedback      224 230
Arbitrarily varying channel (AVC), game-theoretic approach      219 226
Arbitrarily varying channel (AVC), source-channel transmission      225
Arbitrarily varying channel (AVC), states depending on inputs      221 232 233
Arbitrarily varying channel (AVC), states known at input or output      220 227—229
Arbitrarily varying channel (AVC), stochastic decoder      226
Arbitrarily varying channel (AVC), zero-error capacity of DMC and      223
Arbitrarily varying source (AVS)      153 159
Arbitrarily “star” varying channel (A*VC)      221 232
Arimoto, S.      149 184 192 418
Arutunjan      see “Haroutunian”
Asymmetric broadcast channel (ABC)      359 ff
Asymmetric broadcast channel (ABC) with confidential messages      413
Asymmetric broadcast channel (ABC), a- and m-capacity regions equal      362
Asymmetric broadcast channel (ABC), coding theorem      see “ABC coding theorem”
Asymptotics, refined, in the noisy channel coding theorem      119
Asymptotics, refined, of average distortion      159
Asymptotics, refined, of error probability, sources      46
Asymptotics, refined, of minimax redundancy      83
Asymptotics, refined, of size of $T_{P}$       39
Asymptotics, refined, of size of high probability set      24
Attainable error exponent      170 173
Attainable error exponent with feedback      199—202
Attainable error exponent, universally      see “Universally attainable error exponent”
Augustin, U.      185 296 418
Automata as noiseless channels      82
Average cost theorem      66
Average cost theorem, alternative proof of converse      74 76
Average fidelity criterion      123 129
Average length theorem      62 (see also “Average cost theorem”)
Average probability of error      99 173
Average probability of error at output c, channel network      281
Average probability of error, capacity for      see “a-capacity”
Average probability of error, family of channels      173
Averaging distortion measure      124
Axiomatic approach      22 25—27
Bartfai, P.      VIII
Beck, J.      VIII
Berge, C.      119 418
Berger, T.      136 148 159 160 416 418
Berger’s lemma      see “Type covering lemma”
Bergmans, P.P.      381 416 418
Berlekamp, E.R.      180 188 189 192 196 197 201 203 418 426
Better in the Shannon sense      116
Bierbaum, M.      287 418
Binary adder      398—400
Binary block code      15
Binary block code, expected common length      403
Binary channel      206
Binary channel, erasure      114
Binary channel, images for      348
Binary channel, noiseless      6
Binary channel, symmetric      see “Binary symmetric channel”
Binary entropy function      11
Binary symmetric channel (BSC)      114
Binary symmetric channel (BSC), capacity      114
Binary symmetric channel (BSC), exponential error bounds      195
Binary symmetric channel (BSC), exponential error bounds, with feedback      199
Binary symmetric channel (BSC), images over      347
Binary symmetric channel (BSC), linear codes      114 198
Bit      7
Blackwell, D.      203 223 224 227 232 233 391 419
Blahut, R.E.      46 149 160 179 180 188 194 195 203 268 419
Block code      6 (see also “Linear code”)
Block code, channel networks      279
Block code, channels      100
Block code, channels, feedback      120
Block code, channels, multiple-access (MA)      271
Block code, channels, stochastic encoder, decoder      217 226
Block code, fork network      241
Block code, k-to-n      129
Block code, k-to-n, binary      15
Block code, k-to-n, source-channel networks      282
Block code, source networks      247
Block code, sources      15 123
Block code, sources, side information at the decoder      238
Blockwise coding      5
Bloh, E.L.      85 419
Blowing up lemma      92
Boee, J.M.      75 419
Boltzmann, L.      28 46 419
Branching property      26
Breiman, L.      203 223 224 227 232 233 419
Broadcast channel (BC)      359 (see also “ABC coding theorem”)
Broadcast channel (BC) with comparable components      381
Broadcast channel (BC) with confidential messages      413
Broadcast channel (BC) with degraded message sets      see “Asymmetric broadcast channel (ABC)”
Broadcast channel (BC), a- and m-capacity regions are equal      291
Broadcast channel (BC), asymmetric two-output (ABC)      see “Asymmetric broadcast channel (ABC)”
Broadcast channel (BC), bounds on capacity region      379 390
Broadcast channel (BC), degraded      379

Broadcast channel (BC), deterministic      391
Broadcast channel (BC), deterministic, zero-error      392
Broadcast channel (BC), semi-deterministic      392
Broadcast channels (BC), product of degraded      384
Broadcast channels (BC), sum of degraded      387
Burnasev, M.V.      121 202 419
Capacity ( $\varepsilon$ -capacity)      6 101 “Compound “Noiseless
Capacity ( $\varepsilon$ -capacity) as information radius      142 147
Capacity ( $\varepsilon$ -capacity) for a communication model      219
Capacity ( $\varepsilon$ -capacity) of a set      106
Capacity ( $\varepsilon$ -capacity) of a set, asymptotic independence of $\varepsilon$       107
Capacity ( $\varepsilon$ -capacity) region      see “Capacity region ( $\varepsilon$ -capacity region)”
Capacity ( $\varepsilon$ -capacity) under input constraint      108 112 117 142
Capacity ( $\varepsilon$ -capacity) under input constraint, output constraint      117
Capacity ( $\varepsilon$ -capacity) with feedback      see “Feedback zero-error
Capacity ( $\varepsilon$ -capacity), a- and m-      see “a-capacity and m-capacity”
Capacity ( $\varepsilon$ -capacity), alternative definitions      111
Capacity ( $\varepsilon$ -capacity), alternative formulas, DMC      104 142 147
Capacity ( $\varepsilon$ -capacity), computation of      see “Computation of”
Capacity ( $\varepsilon$ -capacity), explicit formulas      114
Capacity ( $\varepsilon$ -capacity), generalized (for given order of magnitude of error probability)      178 183
Capacity ( $\varepsilon$ -capacity), independence of $\varepsilon$       see “Strong converse”
Capacity ( $\varepsilon$ -capacity), input distribution achieving      147
Capacity ( $\varepsilon$ -capacity), per unit cost, DMC      120
Capacity ( $\varepsilon$ -capacity), secrecy      408
Capacity ( $\varepsilon$ -capacity), zero-error      see “Zero error capacity”
Capacity computing algorithm      140
Capacity region ( $\varepsilon$ -capacity region)      111 281
Capacity region ( $\varepsilon$ -capacity region), a- and m-      see “a-capacity region and m-capacity region”
Capacity region ( $\varepsilon$ -capacity region), alternative definitions      283 301
Capacity region ( $\varepsilon$ -capacity region), characterization, computable      see “Coding theorem for channel networks” “Broadcast “Multiple-access “Two-way
Capacity region ( $\varepsilon$ -capacity region), characterization, product-space, general      301—302
Capacity region ( $\varepsilon$ -capacity region), feedback may increase      298
Capacity region ( $\varepsilon$ -capacity region), relevance for source-channel transmission      282 284 286 292
Capacity region ( $\varepsilon$ -capacity region), stochastic encoders      284 291
Capacity-constraint function      108 137
Capacity-constraint function, alternative formula      142
Capacity-constraint function, concavity      109
Capacity-constraint function, differentiability      148
Capacity-constraint function, distribution achieving      147
Caratheodory theorem      see “Fenchel — Eggleston — Caratheodory theorem”
Caratheodory, C.      310
Carleial, A.B.      299 419
Cesari, Y.      74 419
Chain rules      50
Channel      2 4 “Arbitrarily “Compound “Channel
Channel as a matrix      99
Channel as a sequence of matrices      100
Channel network      279 ff
Channel network with one intermediate vertex      see “Broadcast channel”
Channel network with one output vertex      293
Channel network, capacity region      see “Capacity region”
Channel network, coding theorems      see “Multiple-access channel” “Broadcast “Two-way
Channel network, normal      see “Normal channel network”
Channel network, reduction of, problems      300—302
Channel, binary      see “Binary channel”
Channel, coding theorem      see “Coding theorem for channels”
Channel, equidistant      194
Channel, multiterminal      see “Channel network”
Channel, noiseless      see “Noiseless channel”
Channel, symmetric      114
Channels, comparison of      115 116 349
Channels, product of      115
Channels, sum of      115
Chaundy, T.W.      26 419
Chemoff, H.      128 419
Chromatic number of graphs and zero-error rate region      262
Code      3 4
Code alphabet      63
Code for channels with input set X and output set Y      99
Code for k-length messages      61
Code selector      219
Code stuffing lemma      334
Code tree      62 (see also “Tree representation”)
Code tree, entropy decomposition      77
Code with feedback      120
Code with stochastic encoder      217 284 291
Code, $(n,\varepsilon)$ -      101
Code, alphabetic      77
Code, associated with a network      246
Code, block      see “Block code”
Code, constant composition      117 161
Code, fixed-length-to-fixed-length      5
Code, fixed-to-variable length      61
Code, Gilbert — Moore      75
Code, Huffman      73
Code, infinite      80
Code, linear      see “Linear code”
Code, list      196
Code, multiple-access (MA)      280
Code, prefix      see “Prefix code”
Code, random      209
Code, separable      see “Separable code”
Code, Shannon — Fano      85
Code, sliding block      79
Code, synchronizing      75
Code, Tunstall      78
Code, universally optimal      see “Universally optimal codes”
Code, variable length      see “Variable length codes”
Code-stuffed sets      330 345
Coder      246
Codeword      4 61 99
Codeword length and information of an event      75
Coding theorem      110 (see also “Exponential probability bounds”)
Coding theorem for channel networks      see “Multiple-access channel” “Broadcast “Two-way
Coding theorem for channels      see “Discrete memoryless channel” “Compound “Arbitrarily
Coding theorem for source networks      see “Source network coding theorems”
Coding theorem for source-channel transmission      see “Source-channel transmission theorem”
Coding theorem for sources      see “Source coding theorems”
Coding theorem, converse part      see “Converse result”
Coding theorem, direct part      see “Direct result”
Coding theorem, noiseless      see “Average length theorem” “Average
Coding theorem, noisy channel      104
Coding theorem, practical significance      105
Coding theorem, remainder terms in      see “Asymptotics refined”
Combinatorial lemmas      29 ff 86
Combinatorial lemmas, packing      162
Combinatorial lemmas, type covering      150
Common information      402—405
Common length (of binary block codes)      403
Communication model (involving a channel with varying states)      219
Communication model (involving a channel with varying states), capacity for a      219
Communication system, Shannon’s model of      1 ff
Comparison of channels      115 116 349
Component channel (of a channel network)      279
Component source (of a DMMS)      240
Composed code      74
Composite source      see “Compound source”
Composition class      29
Compound channel      172
Compound channel, discrete memoryless      see “Compound DMC”
Compound channel, multiple-access      288
Compound DMC      173
Compound DMC with encoder or decoder informed      183
Compound DMC, coding theorem      173
Compound DMC, invalidity of strong converse      182
Compound DMC, maximal codes for      183 316
Compound DMC, reliability function      173
Compound source      158 159
Computable characterization      259
Computation of $\Delta$ -distortion rate      144 148
Computation of capacity of a DMC      140
Computation of capacity of a DMC, Muroga’s method      148
Computation of capacity of a DMC, simple channels      114
Computation of capacity-constraint function      140
Computation of error exponent in channel coding      192 195
Computation of error exponent in hypothesis testing      44
Computation of error exponent in source coding      44
Computation of rate-distortion function      144 148
Conclusive result      376

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