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

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 452

Добавлена в каталог: 03.04.2008

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Предметный указатель

Peak distortion measure      134
Pearson, E.S.      23
Perfect graph      118
Pile, R.      159 425
Pinsker, M.S.      58 199 392 406 422 425
Plotkin, M.      190 425
Poltyrev, G. §.      385 387 425
Polynomial coefficient, bounds on      30 39
Posner, E.C.      160 425
Postulational characterization of entropy      25—27
Pragmatic approach      22
Pre-channel      300
Prefix code      62 74
Prefix code and search strategies      76
Prefix code, alphabetic      77
Prefix code, Kraft inequality      72 73
Prefix code, optimal      see “Huffmann code”
Prefix code, Shannon — Fano code      85
Prefix code, synchronizing      75
Prefix code, tree representation      62
prefix property      61
Prelov, V.V.      416 422
Probability distributions, preliminaries on      12
Probability of correct decoding, non-achievable rates      see “Exponential probability bounds”
Probability of erasure      174
Probability of error      3 15 99 248
Probability of error at output c      248 281 282
Probability of error fidelity criterion      3 15 132
Probability of error fidelity criterion for source networks      248
Probability of error, average      99 173
Probability of error, family of channels      172 173
Probability of error, hypothesis testing      19
Probability of error, maximum      99 172
Probability of undetected error      174
Product graph      see “Graph”
Product of channels      115 118
Product of degraded broadcast channels      384
Product of sources      134
Product space characterization      259
Product space characterization of achievable rate region, NSN      255
Product space characterization of capacity region, channel networks      302
Progressive encoder      79
Quasi-image      350
Questionnaire      see “Code tree with probabilities assigned to the terminal vertices”
Rajski, C.      57 425
Random code      209 223
Random code capacity of an AVC      224
Random code reduction lemma      210
Random codes, readability of      209 224
Random coding      see “Random selection of codes”
Random coding bound      165 170
Random coding bound for undetected error and erasure      175 183
Random coding bound for undetected error and erasure, universal attainability of      175
Random coding bound without remainder term      196
Random coding bound, alternative derivation      198
Random coding bound, alternative form      192
Random coding bound, BSC      194
Random coding bound, BSC, linear codes      198
Random coding bound, compound DMC      173
Random coding bound, constant composition codes      165
Random coding bound, improvement for small rates      185
Random coding bound, improvement for small rates, universal      182
Random coding bound, list codes      196
Random coding bound, tightness for, large rates      168 171
Random coding bound, tightness for, randomly selected codes      196
Random coding bound, universal attainability of      172
Random coding exponent function $E_{r}(R,P,W)$       165
Random coding exponent function $E_{r}(R,W)$       180
Random coding exponent function, alternative form      192
Random coding exponent function, modified, $E_{r,\lambda}(R,P,W)$       174
Random coding exponent function, properties      168 169
Random coding exponent function, relation to sphere packing exponent function      168
Random selection of channel codes      113
Random selection of codes (sources)      23
Random selection of fork network codes      252
Random selection of MA codes      287—289
Random selection of rate-slicing codes      263
Random selection, method of      150
Random variables, connected by a channel      99
Random variables, preliminaries on      12
Randomized, decoder      see “Stochastic decoder”
Randomized, encoder      see “Stochastic encoder”
Randomized, test      22
Range constraint on auxiliary RV’s      310 ff
Range constraint on auxiliary RV’s in computable characterizations      259 343
Rao, C.R.      28
Rate distortion theorem      125 (see also “Exponential probability bounds”)
Rate distortion theorem, application to coverings of product graphs      160
Rate distortion theorem, arbitrarily varying source      153 159
Rate distortion theorem, compound source      158 159
Rate distortion theorem, multi-terminal generalizations      373 377 401
Rate distortion theorem, non-finite distortion measures      134
Rate distortion theorem, peak distortion measures      134
Rate distortion theorem, remote sources      136
Rate distortion theorem, several distortion measures      134
Rate distortion theorem, two-step source coding      401
Rate distortion theorem, variable length codes      135
Rate distortion theorem, zero-error      152
Rate of channel block code      100
Rate of source block code      123
Rate of variable length code, channel      119
Rate pair (MA code)      271
Rate slicing corollary      239
Rate slicing, limitations on      383 399
Rate triple (fork network code)      241
Rate vector (channel network code)      279
Rate, $\Delta$ -distortion      see “ $\Delta$ -distortion rate”
Rate, achievable      see “Achievable rate”
Rate, critical      see “Critical rate”
Rate, entropy, of a source      65
Rate, equivocation      407
Rate-Distortion function      137 (see also “ $\Delta$ -distortion rate” “Rate
Rate-distortion function, alternative formula      146
Rate-distortion function, channel achieving      147
Rate-distortion function, computation of      144 148
Rate-distortion function, convexity      124
Rate-distortion function, differentiability      148
Rate-distortion function, joint continuity      124
Rates, exponential probability bounds at non-achievable      see “Exponential probability bounds at non-achievable rates”
Reduction of channel network problems      300—302
Reduction of source network problems      249—250
Redundancy, asymptotics of minimax      83
Reliability function, compound DMC      173
Reliability function, DMC      170 171 181 DMC”)
Reliability function, DMC, bounds on      197
Reliability function, DMC, generalized capacity as inverse of      180 183
Reliability function, DMC, list codes      196
Reliability function, DMC, R=0      189
Reliability function, DMC, R=0, constant composition codes      191
Reliability function, DMC, rates above capacity      184
Reliability function, DMC, under input constraint      182 192
Reliability function, DMC, with feedback      199—202
Reliable transmission      3 4
Reliable transmission, non-terminating      6 132
Remainder terms      see “Asymptotics refined”
Remote sources      136
Renyi, A.      26 27 28 425
Renyi’s entropy of order a      27
Reproduction alphabet      123
Reza, F.M.      60 425
Robbins, H.      40
Rodemich, E.R.      196 424
Row-convex closure      205
Rumsey, H. Jr.      196 424
Sanov, I.N.      43 425
Sardinas, A.A.      74 425
Saturated code tree      72
Sauer, N.      96 425
Schmetterer, L.      28 425
Schneider, K.      78 423

Schuetzenberger, M.P.      74 75 85 425
Search strategies and codes      76
Secrecy capacity      408
Secrecy problems      see “Unfriendly participants”
Secret and public messages      411
Self-information      see “Information provided by an event”
Self-synchronizing code      see “Synchronizing code”
Separable codes      62
Separable codes and prefix codes      74
Separable codes, composition of      74
Separable codes, composition of, Kraft inequality, generalized      70 73
Separable range (of a code)      61
Separable range (of a code), algorithm to test      74
Separation of source and channel coding      131 132
Separation of source and channel coding, multi-terminal case      286 287 292
Severdjaev, A. Ju.      185 199 425
Sgarro, A.      VIII 46 398 424 425
Shannon theory      VII
Shannon — Fano code      85
Shannon, C.E.      VII 1 3 6 38 40 46 60 73 81 82 85 112—115 118 121 122 134 136 149 160 180 188 189 192 196 197 203 231 290 300 302 425 426
Shannon’s block diagram      2
Shannon’s entropy      see “Entropy”
Shannon’s formula      17
Shannon’s partial ordering of channels      see “Better in the Shannon sense”
Shell (V-shell)      31
Side information source      237 367
Side information, channels      see “Compound DMC with encoder or decoder informed” “AVC states
Side information, code with, (source)      238
Side information, fork network with      405
Side information, source coding with      see “Source coding with side information”
Simon, J.      76 424
Sinai, J.G.      80 426
Single-letter characterization      259 260
Single-letter distortion measure      see “Averaging distortion measure”
Single-letterization lemma      313
Size constraint      see “Range constraint”
Slepian — Wolf network      see “Fork network”
Slepian — Wolf theorem      see “Fork network coding theorem”
Slepian, D.      269 293 302 426
Sliding block code      79
Smorodinsky, M.      81 426
Sobel, M.      77 426
Source      2 15
Source coding theorem      see “Exponential probability bounds” “Universal “Asymptotics refined”
Source coding theorem, block codes      15 23
Source coding theorem, block codes, with prescribed distortion level      see “Rate distortion theorem”
Source coding theorem, multi-terminal      see “Source coding with side information” “Source
Source coding theorem, variable length codes      62—63 66—67 135
Source coding theorem, variable-to-fixed length codes      78
Source coding with side information      238
Source coding with side information with prescribed distortion level      370 ff
Source coding with side information, partial side information      367
Source coding with side information, partial side information, alternative proof      381
Source coding with side information, partial side information, several decoders      398
Source coding with side information, partial side information, unfriendly participants      414
source network      246 ff (see also “Normal source network”)
Source network coding theorems      see “Normal source network” “Source
Source network coding theorems and entropy characterization problem      261 266
Source network coding theorems, error exponent      267 269
Source network coding theorems, fork network      see “Fork network”
Source network coding theorems, NSN without helpers      253 254
Source network coding theorems, strong converse and image size problem      see “Strong converse and image size problem”
Source network coding theorems, unfriendly participants      414
Source network coding theorems, various      383 393 405
Source network of depth 2      249 ff
Source network of depth >2      406
Source network with 2 helpers      398 399
Source network with 3 inputs and 1 helper      393—397
Source network with probability of error fidelity criterion, graphical representation      248
Source network with probability of error fidelity criterion, reduction to NSN      249 250
Source network with unfriendly participants      414
Source network, achievable ( $\varepsilon$ -achievable) rate region      247
Source network, achievable ( $\varepsilon$ -achievable) rate region, probability of error fidelity criterion      249
Source network, coding theorems      see “Source network coding theorems”
Source network, fork      see “Fork network”
Source network, normal, (NSN)      see “Normal source network (NSN)”
Source network, one side information source      381
Source network, zigzag      393 394
Source, arbitrarily varying      153 159
Source, component, of a DMMS      240
Source, compound      158
Source, discrete memoryless (DMS)      15
Source, discrete memoryless (DMS), multiple (DMMS)      237 240
Source, stationary      65
Source-channel, block code      see “k-to-n block code”
Source-channel, coding theorem      see “Source-channel transmission
Source-channel, error exponent      197
Source-channel, network      281
Source-channel, network, independent component sources      292
Source-channel, transmission theorem      130 133
Source-channel, transmission theorem, arbitrarily varying channels      225
Source-channel, transmission theorem, remote sources      136
Source-channel, transmission theorem, variable length codes      135
Source-channel, transmission theorem, wire-tap channel      412
Sphere packing bound      166 170
Sphere packing bound under input constraint      182
Sphere packing bound with feedback      199
Sphere packing bound, alternative derivations      180
Sphere packing bound, alternative formula      192
Sphere packing bound, BSC      195
Sphere packing bound, compound DMC      173
Sphere packing bound, constant composition codes      16
Sphere packing bound, improvement for small rates      19/
Sphere packing bound, list codes      196
Sphere packing bound, tightness for large rates      168 171
Sphere packing exponent function $E_{sp}(R,P,W)$       166
Sphere packing exponent function $E_{sp}(R,W)$       170
Sphere packing exponent function $E_{sp}(R,W)$ , alternative form      192
Sphere packing exponent function $E_{sp}(R,W)$ , compound DMC      173
Sphere packing exponent function $E_{sp}(R,W)$ , properties      168 180
Sphere packing exponent function $E_{sp}(R,W)$ , relation to random coding exponent function      168
Stambler, S.Z.      227 233 421 426
Standard minimum distance (SMD) decoder      206
State of a channel      82 204
State of a channel, depending on inputs      232 233
State of a channel, known at the input or output      227 229
State selector      219
Stationary source      65
Stationary source, isomorphy problem      80
Stein, C.      28 426
Stein’s lemma      28
Stiglitz, I.G.      233 426
Stochastic decoding      226
Stochastic encoder      217
Stochastic encoder in secrecy problems      407 ff
Stochastic encoder, effect on a- and m-capacity region, general channel network      291
Stochastic encoder, effect on a- and m-capacity region, MAC      284
Stochastic encoder, effect on a- and m-capacity, AVC      217
Stochastic matrix      10 12
Stochastic matrix, doubly      58
Stopping time      11
Straight line bound      197
Strassen, V.      25 28 119 426
Strong converse      110 (see also under “Specific coding theorems”)
Strong converse and image size problem      369 377 394—397
Strong converse for channel codes from arbitrary sets      107
Strong converse with exponential bound      see “Exponential probability bounds”
Strong converse, invalidity of      113 182
Strong data processing lemma      59 350
Strongly typical sequences      see “Typical sequences”
Sub-achievable entropy vectors      352
Subcode      101
Suffix code      74
Super-achievable entropy vectors      354
Support (of a distribution)      10
Support lemma      310
Suranyi, J.      422
Symmetric, channel      114
Symmetric, joint distribution      398
Synchronizing codes      15

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