Huffman coding

About: Huffman coding is a research topic. Over the lifetime, 4988 publications have been published within this topic receiving 93635 citations.

Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding

Abstract: Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, we introduce "deep compression", a three stage pipeline: pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman coding. After the first two steps we retrain the network to fine tune the remaining connections and the quantized centroids. Pruning, reduces the number of connections by 9x to 13x; Quantization then reduces the number of bits that represent each connection from 32 to 5. On the ImageNet dataset, our method reduced the storage required by AlexNet by 35x, from 240MB to 6.9MB, without loss of accuracy. Our method reduced the size of VGG-16 by 49x from 552MB to 11.3MB, again with no loss of accuracy. This allows fitting the model into on-chip SRAM cache rather than off-chip DRAM memory. Our compression method also facilitates the use of complex neural networks in mobile applications where application size and download bandwidth are constrained. Benchmarked on CPU, GPU and mobile GPU, compressed network has 3x to 4x layerwise speedup and 3x to 7x better energy efficiency.

Vector Quantization and Signal Compression

Abstract: 1 Introduction- 11 Signals, Coding, and Compression- 12 Optimality- 13 How to Use this Book- 14 Related Reading- I Basic Tools- 2 Random Processes and Linear Systems- 21 Introduction- 22 Probability- 23 Random Variables and Vectors- 24 Random Processes- 25 Expectation- 26 Linear Systems- 27 Stationary and Ergodic Properties- 28 Useful Processes- 29 Problems- 3 Sampling- 31 Introduction- 32 Periodic Sampling- 33 Noise in Sampling- 34 Practical Sampling Schemes- 35 Sampling Jitter- 36 Multidimensional Sampling- 37 Problems- 4 Linear Prediction- 41 Introduction- 42 Elementary Estimation Theory- 43 Finite-Memory Linear Prediction- 44 Forward and Backward Prediction- 45 The Levinson-Durbin Algorithm- 46 Linear Predictor Design from Empirical Data- 47 Minimum Delay Property- 48 Predictability and Determinism- 49 Infinite Memory Linear Prediction- 410 Simulation of Random Processes- 411 Problems- II Scalar Coding- 5 Scalar Quantization I- 51 Introduction- 52 Structure of a Quantizer- 53 Measuring Quantizer Performance- 54 The Uniform Quantizer- 55 Nonuniform Quantization and Companding- 56 High Resolution: General Case- 57 Problems- 6 Scalar Quantization II- 61 Introduction- 62 Conditions for Optimality- 63 High Resolution Optimal Companding- 64 Quantizer Design Algorithms- 65 Implementation- 66 Problems- 7 Predictive Quantization- 71 Introduction- 72 Difference Quantization- 73 Closed-Loop Predictive Quantization- 74 Delta Modulation- 75 Problems- 8 Bit Allocation and Transform Coding- 81 Introduction- 82 The Problem of Bit Allocation- 83 Optimal Bit Allocation Results- 84 Integer Constrained Allocation Techniques- 85 Transform Coding- 86 Karhunen-Loeve Transform- 87 Performance Gain of Transform Coding- 88 Other Transforms- 89 Sub-band Coding- 810 Problems- 9 Entropy Coding- 91 Introduction- 92 Variable-Length Scalar Noiseless Coding- 93 Prefix Codes- 94 Huffman Coding- 95 Vector Entropy Coding- 96 Arithmetic Coding- 97 Universal and Adaptive Entropy Coding- 98 Ziv-Lempel Coding- 99 Quantization and Entropy Coding- 910 Problems- III Vector Coding- 10 Vector Quantization I- 101 Introduction- 102 Structural Properties and Characterization- 103 Measuring Vector Quantizer Performance- 104 Nearest Neighbor Quantizers- 105 Lattice Vector Quantizers- 106 High Resolution Distortion Approximations- 107 Problems- 11 Vector Quantization II- 111 Introduction- 112 Optimality Conditions for VQ- 113 Vector Quantizer Design- 114 Design Examples- 115 Problems- 12 Constrained Vector Quantization- 121 Introduction- 122 Complexity and Storage Limitations- 123 Structurally Constrained VQ- 124 Tree-Structured VQ- 125 Classified VQ- 126 Transform VQ- 127 Product Code Techniques- 128 Partitioned VQ- 129 Mean-Removed VQ- 1210 Shape-Gain VQ- 1211 Multistage VQ- 1212 Constrained Storage VQ- 1213 Hierarchical and Multiresolution VQ- 1214 Nonlinear Interpolative VQ- 1215 Lattice Codebook VQ- 1216 Fast Nearest Neighbor Encoding- 1217 Problems- 13 Predictive Vector Quantization- 131 Introduction- 132 Predictive Vector Quantization- 133 Vector Linear Prediction- 134 Predictor Design from Empirical Data- 135 Nonlinear Vector Prediction- 136 Design Examples- 137 Problems- 14 Finite-State Vector Quantization- 141 Recursive Vector Quantizers- 142 Finite-State Vector Quantizers- 143 Labeled-States and Labeled-Transitions- 144 Encoder/Decoder Design- 145 Next-State Function Design- 146 Design Examples- 147 Problems- 15 Tree and Trellis Encoding- 151 Delayed Decision Encoder- 152 Tree and Trellis Coding- 153 Decoder Design- 154 Predictive Trellis Encoders- 155 Other Design Techniques- 156 Problems- 16 Adaptive Vector Quantization- 161 Introduction- 162 Mean Adaptation- 163 Gain-Adaptive Vector Quantization- 164 Switched Codebook Adaptation- 165 Adaptive Bit Allocation- 166 Address VQ- 167 Progressive Code Vector Updating- 168 Adaptive Codebook Generation- 169 Vector Excitation Coding- 1610 Problems- 17 Variable Rate Vector Quantization- 171 Variable Rate Coding- 172 Variable Dimension VQ- 173 Alternative Approaches to Variable Rate VQ- 174 Pruned Tree-Structured VQ- 175 The Generalized BFOS Algorithm- 176 Pruned Tree-Structured VQ- 177 Entropy Coded VQ- 178 Greedy Tree Growing- 179 Design Examples- 1710 Bit Allocation Revisited- 1711 Design Algorithms- 1712 Problems

A Method for the Construction of Minimum-Redundancy Codes

Abstract: An optimum method of coding an ensemble of messages consisting of a finite number of members is developed. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

Arithmetic coding for data compression

Abstract: The state of the art in data compression is arithmetic coding, not the better-known Huffman method. Arithmetic coding gives greater compression, is faster for adaptive models, and clearly separates the model from the channel encoding.

Introduction to data compression

Abstract: Preface 1 Introduction 1.1 Compression Techniques 1.1.1 Lossless Compression 1.1.2 Lossy Compression 1.1.3 Measures of Performance 1.2 Modeling and Coding 1.3 Organization of This Book 1.4 Summary 1.5 Projects and Problems 2 Mathematical Preliminaries 2.1 Overview 2.2 A Brief Introduction to Information Theory 2.3 Models 2.3.1 Physical Models 2.3.2 Probability Models 2.3.3. Markov Models 2.3.4 Summary 2.5 Projects and Problems 3 Huffman Coding 3.1 Overview 3.2 "Good" Codes 3.3. The Huffman Coding Algorithm 3.3.1 Minimum Variance Huffman Codes 3.3.2 Length of Huffman Codes 3.3.3 Extended Huffman Codes 3.4 Nonbinary Huffman Codes 3.5 Adaptive Huffman Coding 3.5.1 Update Procedure 3.5.2 Encoding Procedure 3.5.3 Decoding Procedure 3.6 Applications of Huffman Coding 3.6.1 Lossless Image Compression 3.6.2 Text Compression 3.6.3 Audio Compression 3.7 Summary 3.8 Projects and Problems 4 Arithmetic Coding 4.1 Overview 4.2 Introduction 4.3 Coding a Sequence 4.3.1 Generating a Tag 4.3.2 Deciphering the Tag 4.4 Generating a Binary Code 4.4.1 Uniqueness and Efficiency of the Arithmetic Code 4.4.2 Algorithm Implementation 4.4.3 Integer Implementation 4.5 Comparison of Huffman and Arithmetic Coding 4.6 Applications 4.6.1 Bi-Level Image Compression-The JBIG Standard 4.6.2 Image Compression 4.7 Summary 4.8 Projects and Problems 5 Dictionary Techniques 5.1 Overview 5.2 Introduction 5.3 Static Dictionary 5.3.1 Diagram Coding 5.4 Adaptive Dictionary 5.4.1 The LZ77 Approach 5.4.2 The LZ78 Approach 5.5 Applications 5.5.1 File Compression-UNIX COMPRESS 5.5.2 Image Compression-the Graphics Interchange Format (GIF) 5.5.3 Compression over Modems-V.42 bis 5.6 Summary 5.7 Projects and Problems 6 Lossless Image Compression 6.1 Overview 6.2 Introduction 6.3 Facsimile Encoding 6.3.1 Run-Length Coding 6.3.2 CCITT Group 3 and 4-Recommendations T.4 and T.6 6.3.3 Comparison of MH, MR, MMR, and JBIG 6.4 Progressive Image Transmission 6.5 Other Image Compression Approaches 6.5.1 Linear Prediction Models 6.5.2 Context Models 6.5.3 Multiresolution Models 6.5.4 Modeling Prediction Errors 6.6 Summary 6.7 Projects and Problems 7 Mathematical Preliminaries 7.1 Overview 7.2 Introduction 7.3 Distortion Criteria 7.3.1 The Human Visual System 7.3.2 Auditory Perception 7.4 Information Theory Revisted 7.4.1 Conditional Entropy 7.4.2 Average Mutual Information 7.4.3 Differential Entropy 7.5 Rate Distortion Theory 7.6 Models 7.6.1 Probability Models 7.6.2 Linear System Models 7.6.3 Physical Models 7.7 Summary 7.8 Projects and Problems 8 Scalar Quantization 8.1 Overview 8.2 Introduction 8.3 The Quantization Problem 8.4 Uniform Quantizer 8.5 Adaptive Quantization 8.5.1 Forward Adaptive Quantization 8.5.2 Backward Adaptive Quantization 8.6 Nonuniform Quantization 8.6.1 pdf-Optimized Quantization 8.6.2 Companded Quantization 8.7 Entropy-Coded Quantization 8.7.1 Entropy Coding of Lloyd-Max Quantizer Outputs 8.7.2 Entropy-Constrained Quantization 8.7.3 High-Rate Optimum Quantization 8.8 Summary 8.9 Projects and Problems 9 Vector Quantization 9.1 Overview 9.2 Introduction 9.3 Advantages of Vector Quantization over Scalar Quantization 9.4 The Linde-Buzo-Gray Algorithm 9.4.1 Initializing the LBG Algorithm 9.4.2 The Empty Cell Problem 9.4.3 Use of LBG for Image Compression 9.5 Tree-Structured Vector Quantizers 9.5.1 Design of Tree-Structured Vector Quantizers 9.6 Structured Vector Quantizers 9.6.1 Pyramid Vector Quantization 9.6.2 Polar and Spherical Vector Quantizers 9.6.3 Lattice Vector Quantizers 9.7 Variations on the Theme 9.7.1 Gain-Shape Vector Quantization 9.7.2 Mean-Removed Vector Quantization 9.7.3 Classified Vector Quantization 9.7.4 Multistage Vector Quantization 9.7.5 Adaptive Vector Quantization 9.8 Summary 9.9 Projects and Problems 10 Differential Encoding 10.1 Overview 10.2 Introduction 10.3 The Basic Algorithm 10.4 Prediction in DPCM 10.5 Adaptive DPCM (ADPCM) 10.5.1 Adaptive Quantization in DPCM 10.5.2 Adaptive Prediction in DPCM 10.6 Delta Modulation 10.6.1 Constant Factor Adaptive Delta Modulation (CFDM) 10.6.2 Continuously Variable Slope Delta Modulation 10.7 Speech Coding 10.7.1 G.726 10.8 Summary 10.9 Projects and Problems 11 Subband Coding 11.1 Overview 11.2 Introduction 11.3 The Frequency Domain and Filtering 11.3.1 Filters 11.4 The Basic Subband Coding Algorithm 11.4.1 Bit Allocation 11.5 Application to Speech Coding-G.722 11.6 Application to Audio Coding-MPEG Audio 11.7 Application to Image Compression 11.7.1 Decomposing an Image 11.7.2 Coding the Subbands 11.8 Wavelets 11.8.1 Families of Wavelets 11.8.2 Wavelets and Image Compression 11.9 Summary 11.10 Projects and Problems 12 Transform Coding 12.1 Overview 12.2 Introduction 12.3 The Transform 12.4 Transforms of Interest 12.4.1 Karhunen-Loeve Transform 12.4.2 Discrete Cosine Transform 12.4.3 Discrete Sine Transform 12.4.4 Discrete Walsh-Hadamard Transform 12.5 Quantization and Coding of Transform Coefficients 12.6 Application to Image Compression-JPEG 12.6.1 The Transform 12.6.2 Quantization 12.6.3 Coding 12.7 Application to Audio Compression 12.8 Summary 12.9 Projects and Problems 13 Analysis/Synthesis Schemes 13.1 Overview 13.2 Introduction 13.3 Speech Compression 13.3.1 The Channel Vocoder 13.3.2 The Linear Predictive Coder (Gov.Std.LPC-10) 13.3.3 Code Excited Linear Prediction (CELP) 13.3.4 Sinusoidal Coders 13.4 Image Compression 13.4.1 Fractal Compression 13.5 Summary 13.6 Projects and Problems 14 Video Compression 14.1 Overview 14.2 Introduction 14.3 Motion Compensation 14.4 Video Signal Representation 14.5 Algorithms for Videoconferencing and Videophones 14.5.1 ITU_T Recommendation H.261 14.5.2 Model-Based Coding 14.6 Asymmetric Applications 14.6.1 The MPEG Video Standard 14.7 Packet Video 14.7.1 ATM Networks 14.7.2 Compression Issues in ATM Networks 14.7.3 Compression Algorithms for Packet Video 14.8 Summary 14.9 Projects and Problems A Probability and Random Processes A.1 Probability A.2 Random Variables A.3 Distribution Functions A.4 Expectation A.5 Types of Distribution A.6 Stochastic Process A.7 Projects and Problems B A Brief Review of Matrix Concepts B.1 A Matrix B.2 Matrix Operations C Codes for Facsimile Encoding D The Root Lattices Bibliography Index