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ОбложкаZamir R. Lattice coding for signals and networks : a structured coding approach to quantization, modulation and multi-user information theory / with contributions by B.Nazer, Y.Kochman. - Cambridge: Cambridge university press, 2014. - xx, 437 p.: ill., tab. - Bibliogr.: p.408-424. - Ind.: p.425-437. - ISBN 978-0-521-76698-2
Шифр: (И/З.81-Z21) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ...................................................... xiii
Acknowledgements ............................................... xv
List of notation ............................................ xviii

1  Introduction ................................................. 1
   1.1  Source and channel coding ............................... 4
   1.2  The information theoretic view .......................... 6
   1.3  Structured codes ........................................ 7
   1.4  Preview ................................................. 8
2  Lattices .................................................... 11
   2.1  Representation ......................................... 11
   2.2  Partition .............................................. 17
   2.3  Equivalent cells and coset leaders ..................... 21
   2.4  Transformation and tiling .............................. 25
   2.5  Algebraic constructions ................................ 29
   Summary ..................................................... 34
   Problems .................................................... 35
   Interesting facts about lattices ............................ 37
3  Figures of merit ............................................ 39
   3.1  Sphere packing and covering ............................ 39
   3.2  Quantization: normalized second moment ................. 46
   3.3  Modulation: volume to noise ratio ...................... 49
   Summary ..................................................... 56
   Problems .................................................... 56
   Historical notes ............................................ 57
4  Dithering and estimation .................................... 59
   4.1  Crypto lemma ........................................... 61
   4.2  Generalized dither ..................................... 66
   4.3  White dither spectrum .................................. 71
   4.4  Wiener estimation ...................................... 74
   4.5  Filtered dithered quantization ......................... 78
   Summary ..................................................... 80
   Problems .................................................... 80
   Historical notes ............................................ 82
5  Entropy-coded quantization .................................. 84
   5.1  The Shannon entropy .................................... 84
   5.2  Quantizer entropy ...................................... 85
   5.3  Joint and sequential entropy coding* ................... 89
   5.4  Entropy-distortion trade-off ........................... 92
   5.5  Redundancy over Shannon ................................ 94
   5.6  Optimum test-channel simulation ........................ 98
   5.7  Comparison with Lloyd's conditions .................... 101
   5.8  Is random dither really necessary? .................... 102
   3.1  Universal quantization* ............................... 103
   Summary .................................................... 106
   Problems ................................................... 106
   Historical notes ........................................... 108
6  Infinite constellation for modulation ...................... 110
   6.1  Rate per unit volume .................................. 110
   6.2  ML decoding and error probability ..................... 112
   6.3  Gap to capacity ....................................... 114
   6.4  Non-AWGN and mismatch ................................. 117
   6.5  Non-equiprobable signaling ............................ 119
   6.6  Maximum a posteriori decoding* ........................ 128
   Summary .................................................... 131
   Problems ................................................... 132
   Historical notes ........................................... 133
7  Asymptotic goodness ........................................ 134
   7.1  Sphere bound s ........................................ 137
   7.2  Sphere-Gaussian equivalence ........................... 142
   7.3  Good covering and quantization ........................ 147
   7.4  Does packing imply modulation? ........................ 150
   7.5  The Minkowski-Hlawka theorem .......................... 152
   7.6  Good packing .......................................... 154
   7.7  Good modulation ....................................... 156
   7.8  Non-AWGN .............................................. 162
   7.9  Simultaneous goodness ................................. 164
   Summary .................................................... 173
   Problems ................................................... 174
   Historical notes ........................................... 176
8  Nested lattices ............................................ 178
   8.1  Definition and properties ............................. 179
   8.2  Cosets and Voronoi codebooks .......................... 181
   8.3  Nested linear, lattice and trellis codes .............. 185
   8.4  Dithered codebook ..................................... 189
   8.5  Good nested lattices .................................. 192
   Summary .................................................... 194
   Problems ................................................... 195
   Historical notes ........................................... 196
9  Lattice shaping ............................................ 197
   9.1  Voronoi modulation .................................... 199
   9.2  Syndrome dilution scheme .............................. 204
   9.3  The high SNR case ..................................... 206
   9.4  Shannon meets Wiener (at medium SNR) .................. 212
   9.5  The mod Λ channel ..................................... 219
   9.6  Achieving Cawgn for all SNR ........................... 226
   9.7  Geometric interpretation .............................. 233
   9.8  Noise-matched decoding ................................ 234
   9.9  Is the dither really necessary? ....................... 237
   9.10  Voronoi quantization ................................. 240
   Summary .................................................... 242
   Problems ................................................... 243
   Historical notes ........................................... 245
10 Side-information problems .................................. 247
   10.1 Syndrome coding ....................................... 250
   10.2 Gaussian multi-terminal problems ...................... 259
   10.3 Rate distortion with side information ................. 262
   10.4 Lattice Wyner-Ziv coding .............................. 267
   10.5 Channels with side information ........................ 279
   10.6 Lattice dirty-paper coding ............................ 283
   Summary .................................................... 289
   Problems ................................................... 290
   Historical notes ........................................... 292
11 Modulo-lattice modulation .................................. 295
   11.1 Separation versus JSCC ................................ 296
   11.2 Figures of merit for JSCC ............................. 298
   11.3 Joint Wyner-Ziv/dirty-paper coding .................... 299
   11.4 Bandwidth conversion .................................. 305
   Summary .................................................... 309
   Problems ................................................... 310
   Historical notes ........................................... 311
12 Gaussian networks .......................................... 313
   12.1 The two-help-one problem .............................. 314
   12.2 Dirty multiple-access channel ......................... 326
   12.3 Lattice network coding ................................ 335
   12.4 Interference alignment ................................ 355
   12.5 Summary and outlook ................................... 362
   Summary .................................................... 364
   Problems ................................................... 366
   Historical notes ........................................... 368
13 Error exponents ............................................ 372
   13.1 Sphere packing exponent ............................... 373
   13.2 Measures of lattice to noise density .................. 376
   13.3 Threshold-decoding exponent ........................... 377
   13.4 Nearest-neighbor decoding exponent .................... 380
   13.5 Distance spectrum and pairwise errors ................. 383
   13.6 Minimum-distance exponent ............................. 385
   13.7 The expurgated MHS ensemble ........................... 386
   13.8 Error exponents of Voronoi codes ...................... 388
   Summary .................................................... 396
   Problems ................................................... 396
   Historical notes ........................................... 398

Appendix ...................................................... 400
   A.l  Entropy and mutual information ........................ 400
   A.2  Success-threshold exponent ............................ 402
   A.3  Coset density and entropy ............................. 403
   A.4  Convolution of log-concave functions .................. 404
   A.5  Mixture versus Gaussian noise ......................... 405
   A.6  Lattice-distributed noise ............................. 406

References .................................................... 408
Index ......................................................... 425

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