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E-raamat: Mathematical Principles of the Internet, Volume 1: Engineering

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Nirdosh Bhatnagar

Formaat: 1076 pages
Sari: Chapman & Hall/CRC Computer and Information Science Series
Ilmumisaeg: 20-Nov-2018
Kirjastus: CRC Press
Keel: eng
ISBN-13: 9781351379151

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Formaat: 1076 pages
Sari: Chapman & Hall/CRC Computer and Information Science Series
Ilmumisaeg: 20-Nov-2018
Kirjastus: CRC Press
Keel: eng
ISBN-13: 9781351379151

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This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles.

Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed.

In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.

Preface

xix

List of Symbols

xxix

Greek Symbols

xxxvii

Prologue

xxxix

1 Information Theory

(100)

1.1 Introduction

(1)

1.2 Entropy

(3)

1.3 Mutual Information and Relative Entropy

(4)

1.3.1 Mutual Information

(2)

1.3.2 Relative Entropy

(2)

1.4 Noiseless Coding for Memoryless Source

(4)

1.4.1 Pair of Inequalities

(2)

1.4.2 Shannon-Fano Coding Theorem

(1)

1.5 Data Compression

(17)

1.5.1 Huffman's Coding

(5)

1.5.2 Arithmetic Coding

(5)

1.5.3 Lempel-Ziv Coding

(6)

1.6 Communication Channels

(12)

1.6.1 Discrete Memoryless Channel

(2)

1.6.2 Symmetric Channel

(1)

1.6.3 Extension of a Discrete Memoryless Channel

(1)

1.6.4 Basics of Coding and Decoding

(2)

1.6.5 Noiseless Communication Channel Coding Theorem

(3)

1.6.6 Noisy Communication Channel Coding Theorem

(3)

1.7 Differential Entropy and Capacity of Communication Channels

(8)

1.7.1 Differential Entropy

(4)

1.7.2 Information Capacity Theorem

(3)

1.7.3 Parallel Gaussian-Noise Communication Channels

(1)

1.8 Rate Distortion Theory

(14)

1.8.1 Quantization

(1)

1.8.2 Rate Distortion Function

(2)

1.8.3 Properties of Rate Distortion Function

(3)

1.8.4 Representation of Independent Gaussian Random Variables

(3)

1.8.5 Computation of Rate Distortion Function

(5)

1.9 Network Information Theory

(3)

1.9.1 Multi-access Gaussian Communication Channel

(1)

1.9.2 Gaussian Broadcast Channels

(2)

1.10 Maximum Entropy Principle

(4)

1.10.1 Maximum-Likelihood Estimation

(1)

1.10.2 Maximum Entropy Estimation

(3)

Reference Notes

(1)

Problems

(23)

References

(4)

2 Algebraic Coding Theory

101

(72)

2.1 Introduction

103

(2)

2.2 Basics of Coding Theory

105

(7)

2.2.1 Information Rate

105

(2)

2.2.2 Hamming Distance

107

(1)

2.2.3 Decoding Rules

108

(1)

2.2.4 Bounds on Codes

108

(2)

2.2.5 Perfect Codes

110

(1)

2.2.6 Error Probabilities

111

(1)

2.3 Vector Spaces over Binary Field

112

(1)

2.4 Linear Codes

113

(8)

2.4.1 Basics of Linear Codes

114

(4)

2.4.2 Minimum-Distance Decoding

118

(3)

2.5 Cyclic Codes

121

(5)

2.5.1 Basics of Cyclic Codes

121

(2)

2.5.2 Check Polynomial and Parity-Check Matrix

123

(1)

2.5.3 Encoding and Decoding Process

124

(2)

2.6 Hamming Codes

126

(4)

2.6.1 Basics of Hamming Codes

126

(2)

2.6.2 Hamming Codes via Cyclic Codes

128

(2)

2.7 Cyclic Redundancy Check Codes

130

(2)

2.8 Reed-Muller Codes

132

(5)

2.9 Bose-Chaudhuri-Hocquenghem Codes

137

(10)

2.9.1 Binary BCH Codes

139

(2)

2.9.2 Decoding of BCH Codes

141

(6)

2.10 Reed-Solomon Codes

147

(2)

2.11 Convolutional Codes

149

(15)

2.11.1 Polynomial Representation

150

(3)

2.11.2 Error-Correction and Distance Measures

153

(1)

2.11.3 Matrix Representation

154

(2)

2.11.4 Wyner-Ash Convolutional Codes

156

(2)

2.11.5 Shift Registers

158

(1)

2.11.6 Decoding

158

(6)

2.12 Turbo Codes

164

(1)

Reference Notes

165

(1)

Problems

165

(6)

References

171

(2)

3 Cryptography

173

(76)

3.1 Introduction

175

(3)

3.2 Some Classical Ciphering Schemes

178

(6)

3.2.1 The Shift Cipher

178

(1)

3.2.2 The Affine Cryptosystem

179

(1)

3.2.3 A Polyalphabetic Cipher

180

(2)

3.2.4 The Hill Cipher

182

(1)

3.2.5 The Permutation Cipher

183

(1)

3.2.6 One-Time Pad

184

(1)

3.3 Cryptanalysis

184

(1)

3.4 Information-Theoretic Cryptanalysis

185

(7)

3.4.1 Probabilistic Cryptosystem

185

(2)

3.4.2 Perfect Secrecy

187

(1)

3.4.3 Entropy

188

(1)

3.4.4 Combination of Cryptosystems

188

(1)

3.4.5 Unicity Distance

189

(3)

3.5 Public-Key Cryptography

192

(7)

3.5.1 The RSA Cryptosystem

193

(4)

3.5.2 The El Gamal Cryptosystem

197

(2)

3.6 Probabilistic Encryption

199

(4)

3.7 Homomorphic Encryption

203

(4)

3.7.1 Applications

204

(1)

3.7.2 Algebraic Homomorphism

204

(1)

3.7.3 Homomorphic Cryptosystems

205

(2)

3.8 Digital Signatures

207

(4)

3.8.1 The RSA Signature Scheme

208

(1)

3.8.2 The El Gamal Signature Scheme

209

(2)

3.9 Key Distribution

211

(1)

3.10 Elliptic Curve Based Cryptosystems

212

(6)

3.10.1 Elliptic Curve Based El Gamal Cryptosystem

213

(2)

3.10.2 Menezes-Vanstone Elliptic Curve Cryptosystem

215

(2)

3.10.3 Elliptic Curve Based Key Exchange Algorithm

217

(1)

3.11 Hyperelliptic Curve Based Cryptosystem

218

(2)

3.12 Hash Functions

220

(1)

3.13 Authentication

221

(3)

3.13.1 Identification

221

(2)

3.13.2 Message Authentication

223

(1)

3.14 The Data Encryption Standard

224

(5)

3.14.1 The DES Algorithm

224

(3)

3.14.2 Modes of Operation of DES

227

(2)

3.15 The Advanced Encryption Standard

229

(7)

3.15.1 Arithmetic Used in AES

229

(2)

3.15.2 The AES Algorithm

231

(1)

3.15.3 Different Layers

232

(4)

3.16 Probabilistic Perspective on Cryptographic Security

236

(6)

3.16.1 Basics of Probabilistic Security

236

(3)

3.16.2 Security of a Symmetric-Key Cryptosystem

239

(2)

3.16.3 Security of an Asymmetric-Key Cryptosystem

241

(1)

Reference Notes

242

(1)

Problems

243

(2)

References

245

(4)

4 Internet Traffic

249

(52)

4.1 Introduction

251

(2)

4.2 Self-Similarity in the LAN and Internet Traffic

253

(1)

4.2.1 Self-Similarity in the LAN Traffic

253

(1)

4.2.2 Self-Similarity in the Internet Traffic

254

(1)

4.3 Power-Law Probability Distributions

254

(2)

4.3.1 Pareto Distribution

255

(1)

4.3.2 Zipf Distribution

255

(1)

4.4 Modeling Highly Variable Measurements

256

(3)

4.4.1 Heavy-Tailed Distributions

256

(2)

4.4.2 Properties of Power-Law-Tailed Distributions

258

(1)

4.5 Internet Traffic Modeling

259

(9)

4.5.1 Self-Similar Processes

259

(1)

4.5.2 Fractional Brownian Motion

260

(4)

4.5.3 Second Order Self-Similarity

264

(2)

4.5.4 Self-Similarity and the Hurst's Law

266

(1)

4.5.5 Estimation of the Hurst Parameter

266

(2)

4.6 Explanation of Self-Similarity in the Internet Traffic

268

(6)

4.6.1 Notation and Assumptions

268

(1)

4.6.2 Single Source Characterization

269

(3)

4.6.3 Multiple Source Characterization

272

(2)

4.7 Asymptotic Analysis of the R/S Statistic

274

(4)

4.8 Transform Analysis of Fractional Brownian Motion

278

(4)

4.8.1 Power Spectrum of the Increment of a FBMP

278

(1)

4.8.2 Wigner-Ville Transform Technique

279

(1)

4.8.3 Continuous Wavelet Transform Technique

279

(2)

4.8.4 Discrete Wavelet Transform Technique

281

(1)

4.9 Internet Traffic Modeling via Chaotic Maps

282

(9)

4.9.1 Nonlinear Maps

284

(4)

4.9.2 Sojourn Time Probability

288

(1)

4.9.3 Asymptotic Spectral Analysis

289

(2)

Reference Notes

291

(1)

Problems

291

(7)

References

298

(3)

5 Dynamics, Control, and Management of Internet Congestion

301

(94)

5.1 Introduction

303

(2)

5.2 Congestion Control and Resource Allocation

305

(2)

5.3 Network Basics

307

(1)

5.4 The Transmission Control and Internet Protocols

308

(4)

5.4.1 Transmission Control Protocol

308

(3)

5.4.2 User Datagram Protocol

311

(1)

5.4.3 Internet Protocol

311

(1)

5.5 A Simple Periodic TCP Model

312

(2)

5.6 Queue Management

314

(8)

5.6.1 Passive Queue Management

314

(1)

5.6.2 Active Queue Management

315

(1)

5.6.3 Random Early Detection

315

(7)

5.7 A Mean-Field Model of Multiple TCP/IP Connections

322

(5)

5.7.1 Window-Size Evolution

323

(1)

5.7.2 Differential Equation of the Queue Size

324

(1)

5.7.3 Window-Size Probability Density Function

325

(1)

5.7.4 Analysis of Stable System

325

(2)

5.8 Traffic Rate, Congestion Management, and Stability

327

(11)

5.8.1 Traffic Rate Control and Fairness

328

(4)

5.8.2 Congestion Control via Feedback and Its Stability

332

(3)

5.8.3 Max-Min Fair Algorithms

335

(3)

5.9 Traffic Management via Packet Scheduling and Regulation

338

(4)

5.9.1 Generalized Processor Sharing

339

(1)

5.9.2 Packetized Generalized Processor Sharing Scheme

340

(1)

5.9.3 Leaky Bucket for Traffic Regulation

341

(1)

5.10 Network Calculus

342

(6)

5.10.1 Mathematical Preliminaries

343

(2)

5.10.2 Basic Concepts

345

(1)

5.10.3 Fundamental Bounds

346

(2)

5.11 Multiple Access of Communicating Medium

348

(9)

5.11.1 Medium Access Control Techniques

348

(6)

5.11.2 CSMA/CD Model

354

(2)

5.11.3 CSMA/CA Model

356

(1)

5.12 Stochastic Geometry of Wireless Networks

357

(15)

5.12.1 Basics of Wireless Technology

357

(3)

5.12.2 Preliminaries on Stochastic Modeling

360

(2)

5.12.3 Interference Model

362

(4)

5.12.4 A Combination Model for Path Loss and Fading

366

(2)

5.12.5 Outage Probability

368

(1)

5.12.6 Transmission Capacity

369

(3)

Reference Notes

372

(1)

Problems

373

(18)

References

391

(4)

6 Queueing Theory

395

(74)

6.1 Introduction

397

(1)

6.2 Terminology and Notation

398

(3)

6.3 Little's Law

401

(1)

6.4 Steady-State Probabilities

402

(2)

6.5 Birth-and-Death Process Based Queueing Systems

404

(11)

6.5.1 Exponentially Distributed Random Variable

404

(1)

6.5.2 Birth-and-Death Process Description of a Queue

405

(1)

6.5.3 M/M/infinity Queue

406

(1)

6.5.4 M/M/c/c Queue

407

(1)

6.5.5 M/M/1 Queue

408

(2)

6.5.6 M/M/1/K Queue

410

(2)

6.5.7 M/M/c Queue

412

(2)

6.5.8 M/M/1/K/K Queue

414

(1)

6.6 Non-Poisson Queues

415

(20)

6.6.1 D/D/1 Queue

416

(1)

6.6.2 M/G/1 Queue

416

(5)

6.6.3 G/M/1 Queue

421

(6)

6.6.4 G/M/c Queue

427

(3)

6.6.5 G/G/1 Queue

430

(5)

6.7 Priority Queueing Systems

435

(3)

6.7.1 Single Server Nonpreemptive Priorities

436

(2)

6.7.2 Multiserver Nonpreemptive Priorities

438

(1)

6.8 Queueing Networks

438

(6)

6.8.1 Open Queueing Networks

439

(1)

6.8.2 Closed Queueing Networks

440

(4)

6.9 Bounds and Approximations

444

(6)

6.9.1 Heavy Traffic Approximations

444

(2)

6.9.2 Approximations for Multiserver Queues

446

(1)

6.9.3 G/G/1 Queue Bounds

447

(1)

6.9.4 Diffusion Approximation

448

(2)

6.10 Application of Large Deviation Techniques

450

(8)

6.10.1 Theory of Effective Bandwidths

451

(4)

6.10.2 Queue with Large Buffer

455

(3)

Reference Notes

458

(1)

Problems

458

(9)

References

467

(2)

7 Stochastic Structure of the Internet and the World Wide Web

469

(98)

7.1 Introduction

471

(1)

7.2 Metrics to Characterize Random Graphs

472

(1)

7.3 Experimental Evidence

473

(4)

7.3.1 Macroscopic Structure of the World Wide Web

475

(1)

7.3.2 A Kappa-shell Decomposition of the Internet Topology

475

(2)

7.4 Some Important Metrics Revisited

477

(5)

7.4.1 Degree Distribution

477

(3)

7.4.2 Clustering Coefficient

480

(2)

7.4.3 Betweenness

482

(1)

7.5 Classical Random Graph Theory

482

(4)

7.6 Study of Random Graphs via z-Transforms

486

(7)

7.6.1 Phase Transition

486

(1)

7.6.2 Average Path Length

487

(1)

7.6.3 Clustering Coefficient of the Random Graph

488

(1)

7.6.4 Distribution of Component Sizes

488

(2)

7.6.5 Examples

490

(3)

7.7 The Kappa-core of a Random Graph

493

(6)

7.8 Graph Spectra

499

(2)

7.8.1 Graph with Poissonian Degree Distribution

499

(1)

7.8.2 Graph with Power-Law Degree Distribution

500

(1)

7.9 Small-World Networks

501

(3)

7.10 Network Evolution Models

504

(10)

7.10.1 Barabasi and Albert Model

505

(2)

7.10.2 A Variant of the Barabasi and Albert Model

507

(1)

7.10.3 A Generalization of Barabasi and Albert Model

508

(2)

7.10.4 Intrinsic Vertex Weight Model

510

(3)

7.10.5 Web Graph Evolution Model

513

(1)

7.11 Hyperbolic Geometry of Networks

514

(8)

7.11.1 Relevant Hyperbolic Geometry

514

(1)

7.11.2 Modeling Complex Networks

515

(4)

7.11.3 Popularity-Similarity Network Dynamics

519

(3)

7.12 Search Techniques on Networks

522

(9)

7.12.1 Application of SVD Techniques

523

(1)

7.12.2 Detailed Network Search

524

(5)

7.12.3 Random and Guided Search on the Network

529

(2)

7.13 Virus Epidemics and Immunization in the Internet

531

(5)

7.13.1 A Model of Spread of Epidemic

531

(4)

7.13.2 Immunization Process

535

(1)

7.14 Error and Attack Tolerance of Networks

536

(4)

7.14.1 Error Tolerance

537

(1)

7.14.2 Attack Tolerance

538

(2)

7.15 Congestion in a Stochastic Network

540

(2)

7.15.1 Network with Equally-Busy Nodes

541

(1)

7.15.2 Scale-Free Networks

541

(1)

7.16 Exponential Random Graph Models

542

(4)

Reference Notes

546

(1)

Problems

547

(14)

References

561

(6)

8 Graph-Theoretic Algorithms

567

(100)

8.1 Introduction

569

(1)

8.2 Shortest Path Algorithms

569

(9)

8.2.1 Bellman-Ford Shortest Path Algorithm

570

(1)

8.2.2 Dijkstra's Shortest Path Algorithm

571

(3)

8.2.3 All-Pairs Shortest Path Algorithms

574

(4)

8.3 Special Path Algorithms

578

(11)

8.3.1 K Shortest Paths Algorithm

578

(2)

8.3.2 Routing with Transit-Times and Constraints

580

(4)

8.3.3 Disjoint Paths Algorithm

584

(5)

8.4 Algebraic Path Techniques

589

(8)

8.4.1 Semirings and Dioids

589

(3)

8.4.2 Applications

592

(2)

8.4.3 Prebimonoids

594

(3)

8.5 Geographic Routing in Hyperbolic Space

597

(5)

8.5.1 Greedy Embeddings

597

(1)

8.5.2 Applicable Hyperbolic Geometry

598

(3)

8.5.3 Greedy Embedding in Hyperbolic Space

601

(1)

8.6 Minimum Spanning Tree Algorithms

602

(5)

8.6.1 Jarnik's Algorithm

604

(1)

8.6.2 Kruskal's Algorithm

605

(2)

8.7 Connectivity of a Graph

607

(2)

8.8 Network Reliability

609

(8)

8.8.1 Access Network Reliability

610

(2)

8.8.2 Mesh Network Reliability

612

(5)

8.9 Maximum Flows and Minimum Cost Flows

617

(20)

8.9.1 Maximum Flows

618

(10)

8.9.2 Minimum Cost Flows

628

(9)

8.10 Network Coding

637

(14)

8.10.1 A Communication Network Model

640

(1)

8.10.2 Linear Network Coding

641

(3)

8.10.3 Properties of Linear Network Coding

644

(2)

8.10.4 Throughput Improvement

646

(5)

8.11 Design of Communication Networks

651

(3)

Reference Notes

654

(1)

Problems

654

(9)

References

663

(4)

9 Game Theory and the Internet

667

(68)

9.1 Introduction

669

(1)

9.2 Game Theory

670

(31)

9.2.1 Preliminaries

671

(1)

9.2.2 Strategic-Form Games

672

(18)

9.2.3 Extensive-Form Games

690

(7)

9.2.4 Repeated Games

697

(4)

9.3 Selfish Routing

701

(10)

9.3.1 Braess' Paradox

701

(2)

9.3.2 Routing Model

703

(6)

9.3.3 Technique to Reduce the Price of Anarchy

709

(2)

9.4 A Selfish Task Allocation Model

711

(5)

9.5 A Repeated Game

716

(1)

9.6 Algorithmic Mechanism Design

717

(6)

9.6.1 Preliminaries

718

(2)

9.6.2 Vickrey-Groves-Clarke Mechanism

720

(1)

9.6.3 Examples

721

(2)

Reference Notes

723

(1)

Problems

724

(7)

References

731

(4)

10 Internet Economics

735

(44)

10.1 Introduction

737

(1)

10.2 Scope of Economics

738

(1)

10.3 Internet Technology, Costs, and Pricing

738

(2)

10.4 A Qualitative Economic Model of the Internet

740

(1)

10.5 Network Resources, Congestion, and Pricing

741

(4)

10.5.1 Social Welfare and Capacity

741

(1)

10.5.2 Competitive Market Pricing

742

(3)

10.5.3 Pricing without Usage Fees

745

(1)

10.6 Service Differentiation

745

(3)

10.7 Time-Dependent Pricing and Bandwidth Trade-Off

748

(3)

10.7.1 Basic Model

748

(1)

10.7.2 Nash Equilibrium of the Game

749

(1)

10.7.3 Social Welfare Function

750

(1)

10.7.4 Revenue Maximization

751

(1)

10.8 Auctions

751

(5)

10.8.1 Vickrey Auction

752

(1)

10.8.2 Generalized Vickrey Auction

753

(3)

10.9 Application of Coalitional Game Theory

756

(8)

10.9.1 Basics of Coalitional Game Theory

756

(5)

10.9.2 ISP Settlement

761

(3)

10.10 Bargaining Games

764

(3)

Reference Notes

767

(1)

Problems

767

(9)

References

776

(3)

11 Data Mining and Knowledge Discovery

779

(148)

11.1 Introduction

781

(1)

11.2 Basics of Knowledge Discovery Process and Data Mining

782

(6)

11.2.1 Knowledge Discovery Process

782

(1)

11.2.2 Elements of Data Mining

783

(3)

11.2.3 Data Mining as a Learning Process

786

(2)

11.3 Clustering

788

(16)

11.3.1 Proximity Measures

790

(2)

11.3.2 m-Means Clustering

792

(2)

11.3.3 Hierarchical Clustering

794

(1)

11.3.4 Model-Based Clustering

795

(5)

11.3.5 Fuzzy Clustering

800

(2)

11.3.6 Cluster Validity Measures

802

(2)

11.4 Association Rules and Sequential Pattern Mining

804

(15)

11.4.1 Basic Concepts of Association Rules

805

(2)

11.4.2 Necessity of an Efficient Algorithm

807

(1)

11.4.3 The Apriori Algorithm

808

(8)

11.4.4 Sequential Pattern Mining

816

(3)

11.5 Metric Classification

819

(21)

11.5.1 Bayesian Classifier

820

(3)

11.5.2 Support Vector Machines

823

(7)

11.5.3 Nearest-Neighbor Classification

830

(1)

11.5.4 Artificial Neural Network

831

(9)

11.6 Nonmetric Classification

840

(10)

11.6.1 Decision Tree Induction

841

(4)

11.6.2 Rule-Based Induction

845

(5)

11.7 Classification via Ensemble Methods

850

(6)

11.7.1 Bagging

851

(1)

11.7.2 Boosting

852

(4)

11.8 Rough Sets

856

(13)

11.8.1 Basics

856

(4)

11.8.2 Reduct and Core

860

(5)

11.8.3 Decision System

865

(2)

11.8.4 Decision Rules

867

(2)

11.9 High-Dimensional Data

869

(2)

11.10 Statistical Techniques

871

(3)

11.10.1 Prediction via Regression Analysis

871

(2)

11.10.2 Principal Component Analysis

873

(1)

11.11 Social Network Analysis

874

(12)

11.11.1 Node Centrality

874

(4)

11.11.2 Node-Group Centrality

878

(1)

11.11.3 Node Similarity

879

(2)

11.11.4 Linking Structure

881

(1)

11.11.5 Community Detection

882

(4)

11.12 Hidden Markov Model

886

(14)

11.12.1 Model Description and the Problems

886

(3)

11.12.2 Probability Evaluation

889

(3)

11.12.3 Decoding of State Sequence

892

(1)

11.12.4 Model Evaluation

893

(7)

11.13 Kalman Filtering

900

(9)

11.13.1 Stochastic Dynamical System

901

(1)

11.13.2 Filtering Scheme

902

(4)

11.13.3 A Probabilistic Perspective on Kalman Filtering

906

(3)

Reference Notes

909

(1)

Problems

910

(12)

References

922

(5)

12 Quantum Computation, Communication, and Cryptography

927

(78)

12.1 Introduction

929

(1)

12.2 Quantum Mechanics

930

(12)

12.2.1 Preliminaries

930

(3)

12.2.2 Pure and Mixed States, and Density Operator

933

(4)

12.2.3 Evolution of a Quantum System

937

(1)

12.2.4 Observables

938

(1)

12.2.5 Postulates of Quantum Mechanics

939

(1)

12.2.6 Heisenberg's Uncertainty Principle

940

(1)

12.2.7 Quantum Operations

940

(2)

12.2.8 Quantum Entanglement

942

(1)

12.3 Quantum Computing Elements

942

(6)

12.3.1 Boolean Gates and Circuits

942

(2)

12.3.2 Quantum Bits and Registers

944

(1)

12.3.3 Quantum Gates and Circuits

945

(3)

12.3.4 No-Cloning Theorem

948

(1)

12.4 What is Quantum Computation?

948

(1)

12.5 Models of Computation

949

(9)

12.5.1 Deterministic Turing Machine

950

(4)

12.5.2 Nondeterministic Turing Machine

954

(1)

12.5.3 Probabilistic Turing Machine

955

(2)

12.5.4 Quantum Turing Machine

957

(1)

12.6 Quantum Algorithms

958

(14)

12.6.1 Deutsch's Problem and Algorithm

959

(2)

12.6.2 Deutsch-Josza's Problem and Algorithm

961

(2)

12.6.3 Shor's Factorization Algorithm

963

(5)

12.6.4 Grover's Search Algorithm

968

(4)

12.7 Quantum Information Theory

972

(3)

12.8 Quantum Communication Theory

975

(4)

12.8.1 Data Compression

12.8.2 Typical Subspaces

976

(1)

12.8.3 Fidelity

977

(2)

12.8.4 Schumacher's Noiseless Channel Coding Theorem

979

(1)

12.9 Quantum Error-Correction

979

(6)

12.9.1 Difficulties Encountered

975

(5)

12.9.2 Types of Errors

980

(1)

12.9.3 Basics of Quantum Error-Correction

981

(3)

12.9.4 A Bound on Quantum Error-Correcting Codes

984

(1)

12.9.5 Shor's Nine-Qubit Code

984

(1)

12.9.6 Barenco's Three-Qubit Code

985

(1)

12.10 Quantum Cryptography

985

(7)

12.10.1 Classical Cryptographic Communication

985

(1)

12.10.2 Modern Cryptographic Communication

986

(1)

12.10.3 Quantum Cryptographic Communication

986

(6)

Reference Notes

992

(1)

Problems

992

(10)

References

1002

(3)

Index

1005

Nirdosh Bhatnagar works, both in the academia and industry in Silicon Valley, California, USA. He is the author of several papers and reports. Nirdosh earned an MS in operations research, and MS and PhD in electrical engineering, all from Stanford University, Stanford, California.

Lisainfo e-raamatute kohta