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Cover T.M., Thomas J.A. Ч Elements of information theory
Cover T.M., Thomas J.A. Ч Elements of information theory

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Ќазвание: Elements of information theory

јвторы: Cover T.M., Thomas J.A.

јннотаци€:

Following a brief introduction and overview, early chapters cover the basic algebraic relationships of entropy, relative entropy and mutual information, AEP, entropy rates of stochastics processes and data compression, duality of data compression and the growth rate of wealth. Later chapters explore Kolmogorov complexity, channel capacity, differential entropy, the capacity of the fundamental Gaussian channel, the relationship between information theory and statistics, rate distortion and network information theories. The final two chapters examine the stock market and inequalities in information theory. In many cases the authors actually describe the properties of the solutions before the presented problems.


язык: en

–убрика: Computer science/“еори€ информации/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1991

 оличество страниц: 542

ƒобавлена в каталог: 15.11.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\chi^{2}$ (Chi-squared) distribution      333 486
$\omega$      164 165Ч167 179 181
Abramson, N.M.      xi 510
Acceptance region      305 306 309Ч311
Achievable rate      195 404 406 454
Achievable rate distortion pair      341
Achievable rate region      389 408 421
Aczel, J.      511
Adams, K.      xi
Adaptive source coding      107
Additive channel      220 221
Additive white Gaussian noise (AWGN) channel      see УGaussian channelФ
Adler, R.L.      124 510
AEP (asymptotic equipartition property)      ix x 6 11 51
AEP, continuous random variables      226 227
AEP, discrete random variables      51 50Ч59 65 133 216Ч218
AEP, joint      195 201Ч204 384
AEP, stationary ergodic processes      474Ч480
AEP, stock market      471
Ahlswede, R.      10 457 458 510
Algoet, P.      xi 59 481 510
Algorithm, arithmetic coding      104Ч107 124 136Ч138
Algorithm, Blahut Ч Arimoto      191 223 366 367 373
Algorithm, Durbin      276
Algorithm, Frank Ч Wolfe      191
Algorithm, generation of random variables      110Ч117
Algorithm, Huffman coding      92Ч110
Algorithm, Lempel Ч Ziv      319Ч326
Algorithm, Levinson      275
Algorithm, universal data compression      107 288Ч291 319Ч326
algorithmic complexity      1 3 144 146 147 162 182
Algorithmically random      156 157 166 179 181Ч182
Alphabet, continuous      224 239
Alphabet, discrete      13
Alphabet, effective size      46 237
Alphabet, input      184
Alphabet, output      184
Alphabetic code      96
Amari, S.      49 510
Approximation, Stirling's      151 181 269 282 284
Approximations to English      133Ч135
Arimoto, S.      191 223 366 367 373 510 511
Arithmetic coding      104Ч107 124 136Ч138
Arithmetic mean geometric mean inequality      492
ASCII      147 326
Ash, R.B.      511
Asymmetric distortion      368
Asymptotic equipartition property (AEP)      see УAEPФ
Asymptotic optimality of log-optimal portfolio      466
Atmosphere      270
atom      114Ч116 238
Autocorrelation      272 276 277
Autoregressive process      273
Auxiliary random variable      422 426
Average codeword length      85
Average distortion      340 356 358 361
Average power      239 246
Average probability of error      194
AWGN (additive white Gaussian noise)      see УGaussian channelФ
Axiomatic definition of entropy      13 14 42 43
Bahl, L.R.      xi 523
Band      248 349 407
Band-limited channel      247Ч250 262 407
Bandpass filter      247
Bandwidth      249 250 262 379 406
Barron, A.      xi 59 276 496 511
Base of logarithm      13
BASEBALL      316
Bayesian hypothesis testing      314Ч316 332
BCH (Bose Ч Chaudhuri Ч Hocquenghem) codes      212
Beckner, W.      511
Bell, R.      143 481 511
Bell, T.C.      320 335 517
Bellman, R.      511
Bennett, C.H.      49 511
Benzel, R.      458 511
Berger, T.      xi 358 371 373 457 458 511 525
Bergmans, P.      457 512
Berlekamp, E.R.      512 523
Bernoulli random variable      14 43 56 106 154 157 159 164 166 175 177 236 291 392 454
Bernoulli random variable, entropy      14
Bernoulli random variable, rate distortion function      342 367Ч369
Bernoulli, J.      143
Berry's paradox      163
Betting      126Ч133 137Ч138 166 474
Bias      326 334 335
Biased      305 334
Bierbaum, M.      454 512
Binary entropy function      14 44 150
Binary entropy function, graph of      15
Binary erasure channel      187Ч189 218
Binary erasure channel, multiple access      391
Binary erasure channel, with feedback      189 214
Binary multiplying channel      457
Binary random variable      see УBernoulli random variableФ
Binary rate distortion function      342
Binary symmetric channel (BSC)      8 186 209 212 218 220 240 343 425Ч427 456
Binning      410 411 442 457
Birkhoff's Ergodic Theorem      474
Bit      13 14
Blachman, N.      497 509 512
Blackwell, D.      512
Blahut Ч Arimoto algorithm      191 223 366 367 373
Blahut, R.E.      191 223 367 373 512
Block code, channel coding      193 209 211 221
Block code, source coding      53Ч55 288
Block length      8 104 211 212 221 222 291 356 399 445
Boltzmann, L.      49 (see also УMaxwell Ч Boltzmann distributionФ)
Bookie      128
Borel Ч Cantelli lemma      287 467 478
Bose, R.C.      212 512
Bottleneck      47
Bounded convergence theorem      329 477 496
Bounded distortion      342 354
Brain      146
Brascamp, H.J.      512
Breiman, L.      59 512
Brillouin, L.      49 512
Broadcast channel      10 374 377 379 382 396 420 418Ч428 449 451 454Ч458
Broadcast channel, common information      421
Broadcast channel, definitions      420Ч422
Broadcast channel, degraded, achievability      422Ч424
Broadcast channel, degraded, capacity region      422
Broadcast channel, degraded, converse      455
Broadcast channel, degraded, physically degraded      422
Broadcast channel, degraded, stochastically degraded      422
Broadcast channel, examples      418Ч420 425Ч427
Broadcast channel, Gaussian      379Ч380 427Ч428
Brunn Ч Minkowski inequality      viii x 482 497 498 500 501 509
BSC (binary symmetric channel)      186 208 220
Burg's theorem      viii 274 278
Burg, J.P.      273 278 512
Burst error correcting code      212
Buzo, A.      519
Calculus      78 85 86 191 267
Capacity      ix 2 7Ч10 184Ч223 239Ч265 377Ч458 508
Capacity region      10 374 379 380 384 389 390Ч458
Capacity region, broadcast channel      421 422
Capacity region, multiple access channel      389 396
Capital assets pricing model      460
Caratheodory      398
Cardinality      226 397 398 402 422 426
cards      36 132 133 141
Carleial, A.B.      458 512
Cascade of channels      221 377 425
Castelli, V.      xi
Cauchy distribution      486
Cauchy Ч Schwarz inequality      327 329
Causal      257 258 380
Causal, portfolio strategy      465 466
Central limit theorem      240 291
central processing unit (CPU)      146
Centroid      338 346
Cesaro mean      64 470 505
Chain rule      16 21Ч24 28 32 34 39 47 65 70 204Ч206 232 275 351 400 401 414 435 441 447 469 470 480 483 485 490 491 493
Chain rule, differential entropy      232
Chain rule, entropy      21
Chain rule, growth rate      469
Chain rule, mutual information      22
Chain rule, relative entropy      23
Chaitin, G.J.      3 4 182 512 513
Channel      ix 3 7Ч10 183 184 185Ч223 237 239Ч265 374Ч458 508 УBroadcast УGaussian УInterference УMultiple УRelay УTwo-way
Channel code      194 215Ч217
Channel coding theorem      198
Channel transition matrix      184 189 374
Channel, capacity, computation      191 367
Channel, capacity, examples      7 8 184Ч190
Channel, capacity, information capacity      184
Channel, capacity, operational definition      194
Channel, capacity, zero-error      222 223
Channel, cascade      221 377 425
Channel, discrete memoryless, capacity theorem      198Ч206
Channel, discrete memoryless, converse      206Ч212
Channel, discrete memoryless, definitions      192
Channel, discrete memoryless, feedback      212Ч214
Channel, symmetric      189
Channels with memory      220 253 256 449
Chebyshev's inequality      57
Chernoff bound      309 312Ч316 318
Chernoff information      312 314 315 332
Chernoff, H.      312 318 513
Chessboard      68 75
Choi, B.S.      278 513 514
Chung, K.L.      59 513
Church's thesis      146
Cipher      136
Cleary, J.G.      124 320 335 511 524
Closed system      10
Cloud of codewords      422 423
Cocktail party      379
Code      3 6 8 10 18 53Ч55 78Ч124 136Ч137 194Ч222 242Ч258 337Ч358 374Ч458
Code, alphabetic      96
Code, arithmetic      104Ч107 136Ч137
Code, convolutional      212
Code, Morse      78 80
Code, rate distortion      341
Code, Reed Ч Solomon      212
Codebook, channel coding      193
Codebook, rate distortion      341
Codelength      86Ч89 94 96 107 119
Codepoints      337
Codeword      8 10 54 57 78Ч124 193Ч222 239Ч256 355Ч362 378Ч456
Coin tosses      13 110
Coin weighing      45
Common information      421
Communication channel      1 6 7 183 186 215 219 239 488
Communication system      8 49 184 193 215
Communication theory      vii viii 1 4 145
compact discs      3 212
Compact set      398
Competitive optimality, log-optimal portfolio      471Ч474
Competitive optimality, Shannon code      107Ч110
Compression      see УData compressionФ
Computable      147 161 163 164 170 179
Computable probability distribution      161
Computable statistical tests      159
Computation, channel capacity      191 367
Computation, halting      147
Computation, models of      146
Computation, rate distortion function      366Ч367
Computer science      vii 1 3 145 162
Computers      4Ч6 144Ч181 374
Concatenation      80 90
Concavity      14 23 24Ч27 29 31 40 155 191 219 237 247 267 323 369 461Ч463 479 483 488 501 505 506
Concavity of entropy      14 31
Conditional differential entropy      230
Conditional entropy      16
Conditional limit theorem      297Ч304 316 317 332
Conditional mutual information      22 44 48 396
Conditional relative entropy      23
Conditional type      371
Conditionally typical set      359 370 371
Conditioning reduces entropy      28 483
Consistent estimation      3 161 165 167 327
Constrained sequences      76 77
Continuous random variable      224 226 229 235 237 273 336 337 370 УQuantizationФ УRate
Continuous random variable, AEP      226
Converse, broadcast channel      355
Converse, discrete memory less channel      206Ч212
Converse, discrete memory less channel, with feedback      212Ч214
Converse, Gaussian channel      245Ч247
Converse, general multiterminal network      445Ч447
Converse, multiple access channel      399Ч402
Converse, rate distortion theorem      349Ч351
Converse, rate distortion with side information      440Ч442
Converse, Slepian Ч Wolf coding      413Ч415
Converse, source coding with side information      433Ч436
Convex hull      389 393 395 396 403 448 450
Convex sets      191 267 297 299 330 362 416 454
Convex sets, distance between      464
Convexification      454
Convexity      23 24Ч26 29Ч31 41 49 72 309 353 362 364 396Ч398 440Ч442 454 461 462 479 482Ч484
Convexity, capacity region, broadcast channel      454
Convexity, capacity region, multiple access channel      396
Convexity, conditional rate distortion function      439
Convexity, entropy and relative entropy      30Ч32
Convexity, rate distortion function      349
Convolution      498
Convolutional code      212
Coppersmith, D.      124 510
Correlated random variables      38 238 256 264
Correlated random variables, encoding of      see УSlepian Ч Wolf codingФ
Correlation      38 46 449
Costa, M.H.M.      449 513 517
Costello, D.J.      519
Covariance matrix      230 254Ч256 501Ч505
Cover, T.M.      x 59 124 143 182 222 265 278 432 449 450 457 458 481 509 510 511 513Ч515 523
CPU (central processing unit)      146
Cramer Ч Rao bound      325Ч329 332 335 494
Cramer, H.      514
Crosstalk      250 375
Cryptography      136
Csiszar, I.      42 49 279 288 335 358 364Ч367 371 454 458 514 518
Cumulative distribution function      101 102 104 106 224
D-adic      87
Daroczy, Z.      511
Data compression      vii ix 3Ч5 9 53 60 78 117 129 136 137 215Ч217 319 331 336 374 377 407 454 459 508
Data compression, universal      287 319
Davisson, L.D.      515
de Bruijn's identity      494
Decision theory      see УHypothesis testingФ
Decoder      104 137 138 184 192 203Ч220 288 291 339 354 405Ч451 488
Decoding delay      121
Decoding function      193
decryption      136
Degradation      430
degraded      see УBroadcast channel degradedФ УRelay degradedФ
Dembo, A.      xi 498 509 514
Demodulation      3
Dempster, A.P.      514
density      xii 224 225Ч231 267Ч271 486Ч507
Determinant      230 233 237 238 255 260
Determinant, inequalities      501Ч508
Deterministic      32 137 138 193 202 375 432 457
Deterministic function      370 454
Deterministic function, entropy      43
Dice      268 269 282 295 304 305
Differential entropy      ix 224 225Ч238 485Ч497
Differential entropy, table of      486Ч487
Digital      146 215
1 2 3 4
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