## Vector Quantization and Signal CompressionHerb Caen, a popular columnist for the San Francisco Chronicle, recently quoted a Voice of America press release as saying that it was reorganizing in order to "eliminate duplication and redundancy. " This quote both states a goal of data compression and illustrates its common need: the removal of duplication (or redundancy) can provide a more efficient representation of data and the quoted phrase is itself a candidate for such surgery. Not only can the number of words in the quote be reduced without losing informa tion, but the statement would actually be enhanced by such compression since it will no longer exemplify the wrong that the policy is supposed to correct. Here compression can streamline the phrase and minimize the em barassment while improving the English style. Compression in general is intended to provide efficient representations of data while preserving the essential information contained in the data. This book is devoted to the theory and practice of signal compression, i. e. , data compression applied to signals such as speech, audio, images, and video signals (excluding other data types such as financial data or general purpose computer data). The emphasis is on the conversion of analog waveforms into efficient digital representations and on the compression of digital information into the fewest possible bits. Both operations should yield the highest possible reconstruction fidelity subject to constraints on the bit rate and implementation complexity. |

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### Contents

Introduction | 1 |

12 Optimality | 8 |

13 How to Use this Book | 12 |

14 Related Reading | 13 |

Basic Tools | 15 |

Random Processes and Linear Systems | 17 |

22 Probability | 18 |

23 Random Variables and Vectors | 23 |

103 Measuring Vector Quantizer Performance | 323 |

104 Nearest Neighbor Quantizers | 327 |

105 Lattice Vector Quantizers | 335 |

106 High Resolution Distortion Approximations | 338 |

107 Problems | 340 |

Vector Quantization II Optimality and Design | 345 |

112 Optimally Conditions for VQ | 349 |

113 Vector Quantizer Design | 358 |

24 Random Processes | 26 |

25 Expectation | 29 |

26 Linear Systems | 32 |

27 Stationary and Ergodic Properties | 35 |

28 Useful Processes | 39 |

29 Problems | 42 |

Sampling | 49 |

32 Periodic Sampling | 50 |

33 Noise in Sampling | 57 |

34 Practical Sampling Schemes | 60 |

35 Sampling Jitter | 65 |

36 Multidimensional Sampling | 67 |

37 Problems | 78 |

Linear Prediction | 83 |

42 Elementary Estimation Theory | 84 |

43 FiniteMemory Linear Prediction | 93 |

44 Forward and Backward Prediction | 98 |

45 The LevinsonDurbin Algorithm | 104 |

46 Linear Predictor Design from Empirical Data | 108 |

47 Minimum Delay Property | 112 |

48 Predictability and Determinism | 115 |

49 Infinite Memory Linear Prediction | 117 |

410 Simulation of Random Processes | 125 |

Scalar Coding | 131 |

Scalar Quantization I Structure and Performance | 133 |

52 Structure of a Quantizer | 138 |

53 Measuring Quantizer Performance | 142 |

54 The Uniform Quantizer | 151 |

55 Nonuniform Quantization and Companding | 156 |

General Case | 161 |

57 Problems | 168 |

Scalar Quantization II Optimality and Design | 173 |

63 High Resolution Optimal Companding | 185 |

64 Quantizer Design Algorithms | 187 |

65 Implementation | 194 |

66 Problems | 198 |

Predictive Quantization | 203 |

72 Difference Quantization | 204 |

73 ClosedLoop Predictive Quantization | 206 |

74 Delta Modulation | 214 |

75 Problems | 220 |

Bit Allocation and Transform Coding | 225 |

82 The Problem of Bit Allocation | 226 |

83 Optimal Bit Allocation Results | 228 |

84 Integer Constrained Allocation Techniques | 233 |

85 Transform Coding | 235 |

86 KarhunenLoeve Transform | 240 |

87 Performance Gain of Transform Coding | 243 |

88 Other Transforms | 245 |

89 Subband Coding | 246 |

810 Problems | 252 |

Entropy Coding | 259 |

92 VariableLength Scalar Noiseless Coding | 261 |

93 Prefix Codes | 269 |

94 Huffman Coding | 271 |

95 Vector Entropy Coding | 276 |

96 Arithmetic Coding | 277 |

97 Universal and Adaptive Entropy Coding | 284 |

98 ZivLempel Coding | 288 |

99 Quantization and Entropy Coding | 295 |

910 Problems | 302 |

Vector Coding | 307 |

Vector Quantization I Structure and Performance | 309 |

Basic Definitions | 310 |

102 Structural Properties and Characterization | 317 |

114 Design Examples | 372 |

115 Problems | 401 |

Constrained Vector Quantization | 407 |

122 Complexity and Storage Limitations | 408 |

123 Structurally Constrained VQ | 409 |

124 TreeStructured VQ | 410 |

125 Classified VQ | 423 |

126 Transform VQ | 424 |

127 Product Code Techniques | 430 |

128 Partitioned VQ | 434 |

129 MeanRemoved VQ | 435 |

1210 ShapeGain VQ | 441 |

1211 Multistage VQ | 451 |

1212 Constrained Storage VQ | 459 |

1213 Hierarchical and Multiresolution VQ | 461 |

1214 Nonlinear Interpolative VQ | 466 |

1215 Lattice Codebook VQ | 470 |

1216 Fast Nearest Neighbor Encoding | 479 |

1217 Problems | 482 |

Predictive Vector Quantization | 487 |

132 Predictive Vector Quantization | 491 |

133 Vector Linear Prediction | 496 |

134 Predictor Design from Empirical Data | 504 |

135 Nonlinear Vector Prediction | 506 |

136 Design Examples | 509 |

137 Problems | 517 |

FiniteState Vector Quantization | 519 |

142 FiniteState Vector Quantizers | 524 |

143 LabeledStates and LabeledTransitions | 528 |

144 EncoderDecoder Design | 533 |

145 NextState Function Design | 537 |

146 Design Examples | 545 |

147 Problems | 552 |

Tree and Trellis Encoding | 555 |

152 Tree and Trellis Coding | 557 |

153 Decoder Design | 568 |

154 Predictive Trellis Encoders | 573 |

155 Other Design Techniques | 584 |

156 Problems | 585 |

Adaptive Vector Quantization | 587 |

162 Mean Adaptation | 590 |

163 GainAdaptive Vector Quantization | 594 |

164 Switched Codebook Adaptation | 602 |

165 Adaptive Bit Allocation for Multiple Vectors | 605 |

166 Address VQ | 611 |

167 Progressive Code Vector Updating | 618 |

168 Adaptive Codebook Generation | 620 |

169 Vector Excitation Coding | 621 |

1610 Problems | 628 |

Variable Rate Vector Quantization | 631 |

172 Variable Dimension VQ | 634 |

173 Alternative Approaches to Variable Rate VQ | 638 |

174 Pruned TreeStructured VQ | 640 |

175 The Generalized BFOS Algorithm | 645 |

176 Pruned TreeStructured VQ | 652 |

177 Entropy Coded VQ | 653 |

178 Greedy Tree Growing | 654 |

179 Design Examples | 656 |

1710 Bit Allocation Revisited | 677 |

1711 Design Algorithms | 682 |

1712 Problems | 688 |

691 | |

720 | |

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### Common terms and phrases

adaptive applications approximation autocorrelation average distortion binary bit allocation bit rate block cell centroid Chapter code vector codebook codebook design coder codewords coding system coefficients complexity components compression compute condition consider corresponding data compression decoder defined density design algorithm dimension distortion measure entropy coding example Figure filter FSVQ gain Gaussian given hence high resolution Huffman code input vector integer iteration lattice levels linear prediction Lloyd algorithm matrix mean squared error memoryless minimize nearest neighbor node noise noiseless coding nonlinear number of bits optimal output parameters partition performance periodicity matrix pixels prediction error predictor probability problem pruned quantization error random process random variable random vector recursive reproduction vectors result samples scalar quantization simple spectral speech Step structure sub-band subtree technique Theorem tizer training sequence training set transform coding tree TSVQ uniform quantizer variable rate variance vector quantizer waveform

### Popular passages

Page 720 - Compression of individual sequences via variablerate coding," IEEE Transactions on Information Theory, vol.

Page 718 - PH Westerink, J. Biemond and DE Boekee "An Optimal Bit Allocation Algorithm for Subband Coding", Proc.

Page 714 - EA Riskin, T. Lookabaugh, PA Chou, and RM Gray, "Variable rate vector quantization for medical image compression," IEEE Trans, on Medical Imaging, Vol.

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Page 705 - RM Gray. A. Buzo. AH Gray, Jr., and Y. Matsuyama, "Distortion measures for speech processing,