Wireless Communications

A vector quantizer is a system for mapping a sequence of continuous or discrete vectors into a digital sequence suitable for communication over or storage in a digital channel. The goal of such a system is data compression: to reduce the bit rate so as to minimize communication channel capacity or digital storage memory requirements while maintaining the necessary fidelity of the data. The mapping for each vector may or may not have memory in the sense of depending on past actions of the coder, just as in well established scalar techniques such as PCM, which has no memory, and predictive quantization, which does. Even though information theory implies that one can always obtain better performance by coding vectors instead of scalars, scalar quantizers have remained by far the most common data compression system because of their simplicity and good performance when the communication rate is sufficiently large. In addition, relatively few design techniques have existed for vector quantizers. During the past few years several design algorithms have been developed for a variety of vector quantizers and the performance of these codes has been studied for speech waveforms, speech linear predictive parameter vectors, images, and several simulated random processes. It is the purpose of this article to survey some of these design techniques and their applications.

Vector quantization

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

Introduction to data compression

This paper describes a self-organizing, multihop, mobile radio network which relies on a code-division access scheme for multimedia support. In the proposed network architecture, nodes are organized into nonoverlapping clusters. The clusters are independently controlled, and are dynamically reconfigured as the nodes move. This network architecture has three main advantages. First, it provides spatial reuse of the bandwidth due to node clustering. Second, bandwidth can be shared or reserved in a controlled fashion in each cluster. Finally, the cluster algorithm is robust in the face of topological changes caused by node motion, node failure, and node insertion/removal. Simulation shows that this architecture provides an efficient, stable infrastructure for the integration of different types of traffic in a dynamic radio network.

Adaptive clustering for mobile wireless networks

Quantization is a process that maps a continous or discrete set of values into approximations that belong to a smaller set. Quantization is a lossy: some information about the original data is lost in the process. The key to a successful quantization is therefore the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.

Quantization

Simulation work is reported indicating that packet reservation multiple access (PRMA) allows a variety of information sources to share the same wireless access channel. Some of the sources, such as speech terminals, are classified as periodic and others, such as signaling, are classified as random. Packets from all sources contend for access to channel time slots. When a periodic information terminal succeeds in gaining access, it reserves subsequent time slots for uncontested transmission. Both computer simulations and a listening test reveal that PRMA achieves a promising combination of voice quality and bandwidth efficiency. >

Packet reservation multiple access for local wireless communications

Vector quantization (VQ) provides many attractive features for image coding with high compression ratios. However, initial studies of image coding with VQ have revealed several difficulties, most notably edge degradation and high computational complexity. We address these two problems and propose a new coding method, classified vector quantization (CVQ), which is based on a composite source model. Blocks with distinct perceptual features, such as edges, are generated from different subsources, i.e., belong to different classes. In CVQ, a classifier determines the class for each block, and the block is then coded with a vector quantizer designed specifically for that class. We obtain better perceptual quality with significantly lower complexity with CVQ when compared to ordinary VQ. We demonstrate with CVQ visual quality which is comparable to that produced by existing coders of similar complexity, for rates in the range 0.6-1.0 bits/pixel.

Classified Vector Quantization of Images

Direct-sequence spread spectrum with differential phase shift-keying (DPSK) modulation and code-division multiple-access is a promising approach for wireless communications in an indoor environment, which is characterized in this paper by a Rayleigh-fading multipath channel. In this study, we consider two specific channel models having different path-delay distributions and average path power profiles. A star configuration, in which each user exercises average power control in transmitting to a central station, is the basic communication unit, which could be one cell in a cellular hierarchy. We obtain the performance of a single link between a user and its receiver in the central station, and consider two types of diversity, selection diversity and predetection combining to exploit the multipath. A similar system with coherent PSK (CPSK) modulation has been studied previously for one of the channel models considered here. For the same channel model, we show that the irreducible error probability with selection diversity is about half an order of magnitude higher when DPSK is used instead of CPSK. With predetection combining, the performance improves significantly in comparison with selection diversity as the diversity order increases. DPSK modulation with predetection combining is akin to coherent PSK with optimal maximal-ratio combining, but is simpler to implement. The performance with selection diversity for a second channel model, which is based on measurements in an office building, is not significantly different. This indicates that the spreadspectrum approach is rather robust to the path-delay distribution and average path-power profile.

Direct-Sequence Spread Spectrum with DPSK Modulation and Diversity for Indoor Wireless Communications

An image is partitioned into cells of pxp pixels. Each cell is regarded as a vector of dimension p2and is encoded by searching through a codebook for a nearest matching representative vector. A binary word identifying the selected representative vector is assigned as the codeword to describe the original cell. The decoder uses this codeword to address a codebook. Each entry of the codebook contains a full precision digital representation of one of the N representative vectors. The codebook design is based on a clustering technique for vector quantizer design preceded by a classification of training cells into edge or shade cells. Results for coding rates from 0.5 to 1.5 bits/pixel are discussed. Vector quantization appears to be a powerful and promising technique for image coding.

Image coding using vector quantization

A fundamental computational task that arises in several areas of signal processing is pattern matching, where a given test pattern is compared with a large set of stored templates, to find the best match that minimizes a given measure of dissimilarity. Three different geometrically-oriented methods are proposed for substantially reducing the computational complexity of the search process by reducing the number of multiplies in exchange for additional low complexity operations and, in two of the methods, additional memory for storing precomputed tables.

Bhaskar Ramamurthi

Papers

Packet reservation multiple access for local wireless communications

Classified Vector Quantization of Images

Direct-Sequence Spread Spectrum with DPSK Modulation and Diversity for Indoor Wireless Communications

Image coding using vector quantization

Fast search algorithms for vector quantization and pattern matching