COMMUNICATIONS, INFORMATION AND

NETWORK SECURITY

THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE

COMMUNICATIONS AND INFORMATION THEORY Consulting Editor Robert Gallager

Other books in the series: INFORMATION, CODING AND MATHEMATICS, edited by Mario Blaum, Patrick G. Farrell,

Henk C.A. van Tilborg, ISBN: 1-4020-7079-9 CODES, GRAPHS, AND SYSTEMS, edited by Richard E. Blahut and RalfKoetter,

ISBN: 0-7923-7686-2 CODES, CURVES AND SIGNALS: Common Threads in Communications, edited by Alexander

Vardy; ISBN: 0-7923-8374-5 PERSPECTIVES IN SPREAD SPECTRUM, Amer A. Hassan, John E. Hershey, and Gary J.

Saulnier; ISBN: 0-7923-8265-X WIRELESS PERSONAL COMMUNICATIONS: Advances in Coverage and Capacity, Jeffrey H.

Reed, Theodore S. Rappaport, Brian D. Woerner; ISBN: 0-7923-9788-6 ASYMPTOTIC COMBINATORIAL CODING THEORY, Volodia Blinovsky;

ISBN: 0-7923-9988-9 PERSONAL AND WIRELESS COMMUNICATIONS: Digital Technology and SlIlndards, Kun II

Park; ISBN: 0-7923-9727-4 WIRELESS INFORMATION NETWORKS: Architecture, Resource Managment, and Mobile Data,

Jack M. Holtzman; ISBN: 0-7923-9694-4 DIGITAL IMAGE COMPRESSION: Algorithms and Standards, Weidong Kou;

ISBN: 0-7923-9626-X CONTROL AND PERFORMANCE IN PACKET, CIRCUIT, AND ATM NETWORKS, XueDao

Gu, Kazem Sohraby and Dhadesugoor R. Vaman; ISBN: 0-7923-9625-1 DISCRETE STOCHASTIC PROCESSES, Robert G. Gallager; ISBN: 0-7923-9583-2 WIRELESS PERSONAL COMMUNICATIONS: Research Developments, Brian D. Woerner,

Theodore S. Rappaport and Jeffrey H. Reed; ISBN: 0-7923-9555-7 PLANNING AND ARCHITECTURAL DESIGN OF INTEGRATED SERVICES DIGITAL

NETWORKS, A. Nejat Inee, Dag Wilhelmsen and Biilent Sankur; ISBN: 0-7923-9554-9 WIRELESS INFRARED COMMUNICATIONS, John R. Barry; ISBN: 0-7923-9476-3 COMMUNICATIONS AND CRYPTOGRAPHY: Two sides of One Tapestry, Richard E. Blahut,

Daniel J. Costello, Jr., Ueli Maurer and Thomas Mittelholzer; ISBN: 0-7923-9469-0 WIRELESS AND MOBILE COMMUNICATIONS, Jack M. Holtzman and David J. Goodman;

ISBN: 0-7923-9464-X INTRODUCTION TO CONVOLUTIONAL CODES WITH APPLICATIONS, Ajay Dholakia;

ISBN: 0-7923-9467-4 CODED-MODULATION TECHNIQUES FOR FADING CHANNELS, S. Hamidreza Jamali, and

Tho Le-Ngoc; ISBN: 0-7923-9421-6 WIRELESS PERSONAL COMMUNICATIONS: Trends and ChaUenges, Theodore S. Rappaport,

Brian D. Woerner, Jeffrey H. Reed; ISBN: 0-7923-9430-5 ELLIPTIC CURVE PUBLIC KEY CRYPTOSYSTEMS, Alfred Menezes; ISBN: 0-7923-9368-6 SATELLITE COMMUNICATIONS: Mobile and Fixed Services, Michael Miller, Branka Vucetic

and Les Berry; ISBN: 0-7923-9333-3 WIRELESS COMMUNICATIONS: Future Directions, Jack M. Holtzman and David J. Goodman;

ISBN: 0-7923-9316-3 DISCRETE-TIME MODELS FOR COMMUNICATION SYSTEMS INCLUDING A TM, Herwig

Bruneel and Byung G. Kim; ISBN: 0-7923-9292-2 APPLICATIONS OF FINITE FIELDS, Alfred 1. Menezes, Ian F. Blake, XuHong Gao, Ronald C.

Mullin, Scott A. Vanstone, Tomik Yaghoobian; ISBN: 0-7923-9282-5 WIRELESS PERSONAL COMMUNICATIONS, Martin J. Feuerstein, Theodore S. Rappaport;

ISBN: 0-7923-9280-9 SEQUENCE DETECTION FOR HIGH-DENSITY STORAGE CHANNEL, Jaekyun Moon, L.

Richard Carley; ISBN: 0-7923-9264-7 DIGITAL SATELLITE COMMUNICATIONS SYSTEMS AND TECHNOLOGIES: Military and

Civil Applications, A. Nejat Ince; ISBN: 0-7923-9254-X IMAGE AND TEXT COMPRESSION, James A. Storer; ISBN: 0-7923-9243-4

COMMUNICATIONS, INFORMATION AND

NETWORK SECURITY

edited by

Vijay K. Bhargava University of Victoria, Canada

H. Vincent Poor Princeton University, US.A.

Vahid Tarokh Harvard University, US.A.

Seokho Yoon Harvard University, US.A.

Springer Science+Business Media, LLC

..... " Electronic Services < http://www.wkap.nl>

Library of Congress Cataloging-in-Publication Data

Communications, information, and network security / Edited by: Vijay K. Bhargava, H. Vincent Poor, Vahid Tarokh, and Seokho Yoon

p.cm. Includes bibliographical references.

1. Telecommunication--Security measures.

TK5102.85 .C66 2003 621.38211 21

Copyright © 2003 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003. Softcover reprint of the hardcover 1 st edition 2003

2002035711

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo­copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC

Permission for books published in Europe: permissions@wkap.nl Permissions for books published in the United States of America: permissions@wkap.com

Printed on acid-free paper.

ISBN 978-1-4419-5318-6 ISBN 978-1-4757-3789-9 (eBook)DOI 10.1007/978-1-4757-3789-9

Contents

List of Figures

List of Tables

Preface

Contributing Authors

Foreword

1 Modulation Diversity for Wireless Communications: Impact of Chan­

nel Estimation Errors and Doppler Effects on System Performance Waslon Terllizzie A. Lopes, Marcelo S. Alencar, Juraci F. Galdino

2

1 Introduction 2 The System Model 3 Estimation Algorithms

3.1 The Amplitude Estimator 3.2 The Phase Estimator

4 Simulation Results 4.1 Searching for the Optimum Rotation Angle 4.2 Impact of the Interleaving Depth on the System Per­

formance 4.3 Impact of the Estimation Errors on the System Perfor­

mance 5 Conclusion

Xlll

XIX

XXI

XXIll

XXIX

1

2 4 7 8 8 8 9

10

11 14

Performance of Error Control Codes on Finite State Channels via 17 an Enumerative Technique

Cecilio Pimentel 1 Introduction 17 2 The Communication System 19 3 Performance Analysis 20

3.1 The Effect of Interleaving 24 4 Performance Bounds for Convolutional Codes 27

VI COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

5 Conclusions 30

3 Bounds on Distance Distributions in Codes of Given Size Gerard Cohen, Michael Krivelevich, Simon Litsyn

33

1 Introduction 2 Basic inequalities 3 Distance distributions 4 A Lower Bound

4

33 35 38 40

Low Density Pari~ Check Convolutional Codes Derived from Quasi­Cyclic Block Codes

43

Daniel J. Costello Jr., Arvind Sridharan, Deepak Sridhara, R. Michael Tanner

5

1 Introduction 44 2 Code Construction 44

3 4 5

2.1 The Block Codes [3] 44 2.2 The Convolutional Codes 46 Decoding 49 Results 50 Conclusions 51

A New Algorithm for Decoding Reed-Solomon Codes Shuhong Gao

55

1 Introduction 2 Encoding Reed-Solomon codes 3 Decoding Reed-Solomon codes 4 Decoding with errors and erasures 5 Fast Fourier transforms 6 Conclusions

6

55 56 57 63 64 67

A Noncoherent Detection Scheme for Space-Time Block Codes 69 Hamid Jafarkhani

1 Introduction 69 2 Space-Time Block Coding Assuming Coherent Detection 71

2.1 The System Model 71 2.2 Encoding 72 2.3 Decoding 74

3 Differential Encoding 79 4 Differential Decoding 83 5 Conclusions 85

7 Advances in Quantum Detection Julio 1. Concha, H. Vincent Poor

89

1 Introduction 2 Quantum-Theoretic Models in Communication Theory

89 92

Contents

2.1 Quantum Mechanics 2.1.1 States 2.1.2 Observables and POVM's 2.2 Quantum Communications

3 Bayesian Detector Design 4 The Square-Root Detector

4.1 Pure States 4.2 Mixed States

5 Unambiguous Discrimination 6 Inverse Channel Detector

6.1 Detector Design 6.2 Application to a Multiaccess Problem

7 Some Common Measurements in Quantum Optics 8 Concluding Remarks

8 Toward the True Random Cipher: On Expected Linear Probability

Values for SPNs with Randomly Selected S-Boxes Liam Keliher, Henk Meijer, Stafford Tavares

1 Introduction 2 Substitution-Permutation Networks 3 Linear Probability 4 Linear Cryptanalysis of Markov Ciphers

4.1 Markov Ciphers 4.2 Linear Cryptanalysis 4.2.1 Notational Issues 4.3 Linear Characteristics 4.4 Choosing the Best Characteristic 4.5 Linear Hulls 4.6 Maximum Average Linear Hull Probability

5 SPN-Specific Considerations 6 Expected ELP Values over all SPNs

6.1 Distribution of LP Values for Randomly Selected boxes

6.2 Counting Characteristics 6.2.1 Recursive Formulation for Ca,b[A] 6.3 Main Result

7 Example SPN Structure 7.1 Evaluating Ca,b[A] 7.2 Computational Results 7.3 Generalized Conjecture

8 Conclusions

9 Geometric Constructions of Gallager Codes Shu Lin, Jun Xu, Heng Tang, Yu Kou

1 Introduction 2 Gallager Codes 3 Construction of Finite Geometry Gallager Codes 4 Construction of Circulant EG-Gallager Codes

vii

92 92 93 95 98

101 101 102 103 107 108 110 112 114

123

124 125 125 127 127 128 129 129 130 130 131 131 133

S-133 135 136 138 139 139 141 142 144

147

148 148 149 153

Vlll COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

10

5 6

Construction of Circulant PG-Gallager Codes Conclusion

157 160

A Call Admission Strategy for Multirate Wideband CDMA Systems 163 Jon W. Mark, Shihua Zhu

1 Introduction 163 2 Problem Statement 165 3 Power Distribution 166

3.1 SolvingforS 170 3.2 CaseM=2 170 3.3 Condition for Convergence 171 3.4 General Case 172 3.5 Asymptotic Case 173

4 Call Admission Algorithm 174 5 Numerical Results 176 6 Conclusions 177 Appendix: Sufficient Condition for .x < 1 178

11 Average Level Crossing Rate and Average Fade Duration of 181

Diversity Methods Xiaofei Dong, Norman C. Beaulieu

1 Introduction 181 2 System Model 182 3 Level Crossing Rate and Fade Duration of MRC in lID Ricean

Fading 183 4 Level Crossing Rate and Fade Duration of EGC 188 5 Average LCR and AFD of MRC with non-identical branch

powers 192 6 Average LCR and AFD of SC in Generalized Fading 195

12 Connection Admission Control for MC-CDMA Systems Supporting 205

Multi-Rate Services Xuemin Shen, Jon W. Mark, Dongmei Zhao

1 Introduction 206 2 System Model 208 3 Power Distribution under Perfect Power Control 209

13

4 5 6 7 8

Power Distribution under Imperfect Power Control Connection Admission Control Grade of Service Performance Numerical Results Conclusions

Multiuser Detection and Statistical Mechanics Dongning Guo, Sergio Verdti

1 Introduction

211 214 215 216 224

229

229

Contents ix

2 The CDMA Channel and Multiuser Detectors 232 2.1 The CDMA Channel 232 2.2 Multiuser Detectors: Known Results 233 2.2.1 The Single-user Matched Filter 234 2.2.2 The MMSE Detector 235 2.2.3 The Decorrelator 236 2.2.4 The Optimal Detectors 237 2.3 Spectral Efficiency 237

3 Conditional Mean Estimator and Statistical Mechanics 238 3.1 Bayes Retrochannel and Conditional Mean Estimator 238 3.2 CDMA Multiuser Detectors 239 3.2.1 The Linear Detectors 240 3.2.2 The Optimal Detectors 241 3.3 Preliminaries of Statistical Mechanics 242 3.4 Spin Glass and the Bayes Retrochannel 244 3.5 Overlap 245

4 Performance Analysis of Linear Detectors 247 4.1 Free Energy 247 4.2 Solving the Overlap 258 4.3 Arbitrary Energy Distribution 264 4.4 Linear Multiuser Detectors 265 4.4.1 The Matched Filter 265 4.4.2 The MMSE Detector 265 4.4.3 The Decorrelator 266

5 The Optimal Detectors 267 6 Discussions 270 7 Spectral Efficiency 272 8 Conclusions 274

14 Critical Density Thresholds in Distributed Wireless Networks 279 Bhaskar Krishnamachari, Stephen B. Wicker, Ramon Bejar, Marc Pearlman

1 Introduction 279 2 Connectivity in Multi-hop Wireless Networks 280 3 Theory of Random Graphs 283

3.1 Models of Random Graphs with Independence 283 3.2 Phase Transitions in Random Graphs 284

4 Random Graphs in Wireless Networks 285 5 Density-Critical Transitions in Wireless Networks 287

5.1 Neighbor Count 287 5.2 Multi-Path Connectivity 287 5.3 Partition into Cliques 288 5.4 Hamiltonian Cycle 289 5.5 Probabilistic Flooding 290

6 Analysis of Critical Thresholds 291 7 Conclusions 292

15 Precoding Techniques for Nonlinear Constant-Envelope Modulations 297 P.H. Wittke, M.A. Low

1 Introduction 297

x COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

16

2 General System 3 Precoding 4 Performance Results

4.1 MMSE Precoding 4.2 Tomlinson Precoding

5 Conclusions Appendix: Minimum Mean-Square Phase Error Correction Appendix: Iterative Precoding Table Construction

298 300 302 302 304 306 309 312

Spherically Invariant Random Processes: Theory and Applications Kung Yao

315

17

1 Introduction 2 Theoretical Properties of SIRP

2.1 Conditional Expectation, Mean-Square Estimation, and Closure of SIRP

2.2 Detection under SIRP 2.3 SIRP and Heavy-Tailed Processes

3 Application of SIRP to System Modelings 3.1 SIRP Modeling of Bandlimited Speech Waveform 3.2 SIRP Modeling of Radar Clutters 3.3 SIRP Model of Radio Propagation Disturbances 3.4 SIRP Modeling in Equalization and Array Processing 3.5 Generation and Simulation of SIRP

4 Conclusions

315 317

319 320 321 321 322 322 323 325 325 326

On Entropy, Information Inequalities, and Groups 333 Raymond W. Yeung

1 Introduction 333 2 Entropy Functions and Information Inequalities 335 3 ITIP - Machine-Proving of Information Inequalities 340 4 I-Measure and Information Diagrams 341 5 Examples of Application 346 6 Entropy and Groups 355 7 Conclusions 355 Appendix: The Proof for the Equivalence of the Polymatroidal Ax-

ioms and the Basic Inequalities 356

18 Dynamic Inter-SLA Resources Sharing in Differentiated Services

Networks Based on Effective Bandwidth Allocation 361

Yu Cheng, Weihua Zhuang 1 Introduction 2 Resource Allocation Architecture

2.1 Inter-Domain Resource Allocation 2.2 MPLS DiffServ Domain

3 Dynamic Bandwidth Borrowing 3.1 The Lendable Trunk 3.2 Bandwidth Borrowing

362 364 365 366 367 367 369

Contents

3.3 MPLS Rerouting 4 Effective Bandwidth for Assured Services

4.1 The Partitioned Buffer Model 4.2 Fluid Model Analysis 4.3 Effective Bandwidth and Admission Control

5 Numerical Results 5.1 Throughput Analysis 5.2 Rerouting Effect

6 Conclusions Appendix: Stationary Analysis of the Two-Trunk Markovian Model

xi

369 370 370 371 372 374 374 375 377 378

List of Figures

1.1 Effect of fading on QPSK constellations: transmit-ted symbols (e) and received symbols (0). 3

1.2 QPSK constellation: reference (0) and rotated by angle () (e). 5

1.3 Block diagram of the simulated system. 5

1.4 Autocorrelation function ofthe process a(t) for some values of maximum Doppler frequency (fD), and sampling frequency equals 24.3 kbauds. 6

1.5 Bit error rate for the proposed system as function of the rotation angle () considering the QPSK con-stellation and perfect channel estimation. 9

1.6 Bit error rate for the proposed system as function of the signal-to-noise ratio considering the QPSK constellation and perfect channel estimation. 10

1.7 Bit error rate of the proposed system as function of the interleaving depth (k, expressed in symbol intervals) considering the QPSK constellation and fD = 100 Hz. 11

1.8 Bit error rate of the proposed system as function of the signal-to-noise ratio (Eb/NO) considering the QPSK constellation and fD = 50 Hz. 13

1.9 Bit error rate of the proposed system as function of the signal-to-noise ratio (Eb/NO) considering the QPSK constellation and fD = 100 Hz. 13

2.1 Gilbert-Elliott model for burst channels. 21

2.2 peE versus memory It, for RS codes over GEe mod-els having the number of information symbols k as a parameter, for n = 127, c = 7. GEe model with parameters p = 20, b = 0.4, 9 = 0.001. 24

xiv COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

2.3 PCE versus memory for the interleaved RS (127,71) code over GEC models, having Id as a parameter. Id = 1, 2, 4, 8, 16, 32, 64. GEC model with param-eters p = 20, b = 0.4, 9 = 0.001. 26

2.4 Comparison of bit interleaving (dashed curve) and symbol interleaving (solid curve) for the RS (127,71) code over GF(27), for Id = 50. GEC model with parameters p = 20, b = 0.4, 9 = 0.001. 28

2.5 Bounds to the bit error probability versus the av-erage burst length of the GEC model having Id as a parameter. Id = 50,100,200. Convolutional code of rate Rc = 1/2, K = 4. The channel parameters are b = 0.4, 9 = 1 X 10-3, and p = 43. The dotted lines are obtained by simulations. 31

3.1 Upper and lower bounds on the distance distribu-tion exponent for codes of rate 0.5. 41

4.1 Tanner graph for Tanner's [155,64,20] quasi-cyclic code 46 4.2 Tanner graph for a (15,5) quasi-cyclic code 50 4.3 Tanner graph for the convolutional code derived

from a (15,5) quasi-cyclic code 50 4.4 Performance of rate 2/5 convolutional codes derived

from quasi-cyclic (QC) codes. The dotted lines cor-respond to codes derived from a block length 1055 LDPC code and the solid lines correspond to codes derived from a block length 2105 LDPC code. 52

4.5 Performance of rate 2/7 convolutional codes derived from quasi-cyclic (QC) codes. The dotted lines cor-respond to codes derived from a block length 1477 LDPC code and the solid lines correspond to codes derived from a block length 7357 LDPC code. 52

6.1 Encoder Block Diagram; Coherent Detection. 73

6.2 Decoder Block Diagram; Coherent Detection. 78 6.3 Encoder Block Diagram; Noncoherent Detection. 80 6.4 Decoder Block Diagram; Noncoherent Detection. 84 7.1 Quantum communication channel. 96 7.2 Probability of error achieved by the inverse-channel

detector in a two-level system, as a function of the interaction strength c. 111

8.1 SPN with N = 16, M = n = 4, R = 3 126 8.2 Summary of linear cryptanalysis (Algorithm 2) 128

List of Figures xv

8.3 Distribution of LP values for randomly selected 8 x 8 s-box 134

8.4 SPN with M = n = 4 (N = 16), R = 3, and permutation of Kam and Davida 140

8.5 ESPN [ELP(a, b)] for M = n = 4 and a = DOOO(hex) , b = 0050(hex) 142

8.6 ESPN [ELP(a, b)] for M = n = 8 and wt(-ya) = wt(-Yb) = 1 143

9.1 Error performance comparison of the (512,256) EG-Gallager LDPC code with three computer generated Gallager codes and a rate-1/2 convolutional code. 152

9.2 Error performances of two EG-Gallager codes based on parallel bundles of EG(2, 43) with the SPA de-coding. 152

9.3 Error performances of two EG-Gallager codes based on parallel bundles of EG(2, 52) and EG(2,72), re-spectively, with the SPA decoding. 153

9.4 Error performances of a circulant EG-Gallager code based on EG(3, 32) with the SPA decoding. 156

9.5 Error performances of the (65520, 53237) circulant EG-Gallager code based on EG(3, 24) with the SPA decoding. 156

9.6 Error performances of the (4686, 2345) circulant PG-Gallager code based on PG(4, 5) with the SPA decoding. 159

9.7 Error performances of the (74273, 56797) circulant PG-Gallager code based on PG(3, 24) with the SPA decoding. 159

9.8 Error performances of the (572320, 511002) circu-lant PG-Gallager code based on PG(3, 33) with the SPA decoding. 160

10.1 Two-layered spreading 166 10.2 Eigenvalue vs traffic demand 176 10.3 System capacity vs traffic demand variation 177 11.1 A verage normalized level crossing rate of MRC for

different diversity orders with f( = 7 dB. 186 11.2 Average normalized fade duration of MRC for dif-

ferent diversity orders with f( = 7 dB. 187 11.3 A verage normalized level crossing rate of EGC for

different diversity orders with f( = 7 dB. 191

XVI COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

11.4 Average normalized fade duration of EGC for dif-ferent diversity orders with K = 7 dB. 192

11.5 The average normalized LCR of MRC with expo-nential decay profile input signal powers with decay factor 1. 194

11.6 The normalized AFD of MRC with exponential de-cay profile input signal powers with decay factor 1. 196

11.7 Average normalized level crossing rate of SC for dif-ferent diversity orders with exponentially decaying mean signal power profile with decay factor 0.25. 199

11.8 A verage normalized fade duration of SC for different diversity orders with exponentially decaying mean signal power profile with decay factor 0.25. 201

12.1 Power increase factor vs. number of voice connections. 218 12.2 Power increase factor vs. number of video connections 218 12.3 Power increase factor vs. power control imperfection 219 12.4 Comparison of connection blocking probability be-

tween analytical and simulation results 219 12.5 Comparison of resource utilization between analyt-

ical and simulation results 220 12.6 Comparison of connection blocking probability un-

der perfect and imperfect power control (vs. average arrival interval of voice traffic) 220

12.7 Comparison of connection blocking probability un-der perfect and imperfect power control (vs. average arrival interval of video traffic) 221

12.8 Comparison of resource utilization under perfect and imperfect power control 221

12.9 Effect of imperfect power control on connection block-ing probability 223

12.10 Effect of imperfect power control on resource utilization 224 12.11 Comparison of CBP between FCFS CAC and "fair" CAC 225 12.12 Comparison of resource utilization between FCFS

CAC and "fair" CAC 225 13.1 The Bayes retrochannel and the conditional mean

estimator. 238 13.2 A canonical interference canceller. 272 14.1 Phase Transitions in Probability of Connectivity in

Fixed Radius Ad-hoc Wireless Networks 282 14.2 Bernoulli Random Graphs 284

List of Figures xvii

14.3 Fixed Radius Random Graphs 285 14.4 Dynamic Probabilistic Flooding Random Graphs 286 14.5 Phase Transitions for Neighbor Count (n = 100) 288 14.6 Phase Transition in Biconnectivity (n = 100) 288 14.7 Phase Transition in Probability of Partitioning Net-

work into 3-Cliques (Triangles) (n=9) 289 14.8 Phase Transition in Existence of Hamiltonian Cycle (n=7) 290 14.9 Phase Transition in Probabilistic Flooding (n=100) 291 14.10 Bounds on Probability of all Nodes having 2 Neigh-

bors (n = 100) 292 15.1 General CPM transmitter. 299 15.2 Block diagram of a general transversal precoder. 300 15.3 Contribution of overlapping 2RC pulses over one

symbol interval. 303 15.4 Spectrum of MMSE precoded quaternary 2RC (h = 0.25).304 15.5 Bit error rate of MMSE precoded quaternary 2RC

in AWGN. 305 15.6 Bit error rate of MMSE precoded quaternary 2RC

in AWGN and Rician fading (J< = 10 dB). 306 15.7 Bit error rate of MMSE precoded quaternary 2RC

with rate ~ convolutional coding in AWGN and Ri-cian fading (I( = 10 dB). 308

15.8 Tomlinson Precoder and Receiver Post-detection Sig-nal Processing 308

15.9 Bit error rate of Tomlinson precoded quaternary 2RC (h = 0.25) in AWGN and Rician fading (J< = 10 dB). 309

17.1 f(h) ~ 0 always holds. 336 17.2 f(h) ~ 0 does not always hold. 336 17.3 An illustration ofr:, f4' and g(h) ~ O. 339 17.4 An information diagram for X, Y, and Z. 342 17.5 An example for which J(X;Y;Z) is negative. 344 17.6 An illustration for the construction of Xl and X 2 345

17.7 The information diagram for Example 1. 347 17.8 The schematic diagram for Example 2. 348 17.9 The information diagram for Example 2. 348 17.10 The schematic diagram for Example 3. 349 17.11 The information diagram for Example 3. 349 17.12 The information diagram for the Markov chain X -t

Y -t Z -t T. 350

xviii COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

17.13 The dependency structure of the random variables involved in the feedback channel problem. 351

18.1 The advanced two-tier resource management model. 365 18.2 Throughput of the CS, CP and BR schemes, ex-

pressed as Vcs, Vcp and VBR respectively. 375 18.3 Normalized preemption probability with or without

rerouting. 377 18.4 The state transition diagram of the two-dimensional

Markov process. 378

List of Tables

1.1 Steps of the LMS (JL) and of the PLL(~). 12 8.1 Success rates for LC Algorithm 2 129 15.1 Tomlinson and transversal equalizer filter taps matched

to quaternary 2RC signaling and a receiver with a 4th-order Butterworth filter (f-3dB = ~) and the indicated post-detection filter. 305

15.2 Summary of results: SNR required to achieve BER=10-3

for quaternary 2RC signaling (h=O.25). 307 18.1 Parameters used to analyze rerouting effect. 376

Preface

This book is dedicated to our friend and colleague Ian F. Blake of the University of Toronto. Preparations for this volume were initiated at a symposium held in Ian's honor in Victoria, Be, on June 7-8, 2001, on the occasion of his sixtieth birthday. The chapters in this book, many of which describe work that was presented at the symposium, span a wide range of areas in which Ian's contributions have been influential, either through his own research contributions, or through his mentoring and advising of other researchers. These areas include coding, cryptog­raphy, networking, stochastic processes, and wireless communications. The book also includes a foreword, written by Richard Blahut of the University of Illinois, reflecting on Ian's life and career to date. We are grateful to the authors whose work appears in this volume, and to Ian Blake, both for his friendship and for his many contributions to our field.

Vijay Bhargava Victoria, Be

H. Vincent Poor Princeton, NJ

Vahid Tarokh Cambridge, MA

Seokho Yoon Cambridge, MA

This book is dedicated to Ian F. Blake

Contributing Authors

M. S. Alencar Universidade Federal da Paraiba, Brazil.

N. C. Beaulieu University of Alberta, Canada.

R. Bejar Cornell University.

R. E. Blahut University of Illinois at Urbana-Champaign.

Y. Cheng University of Waterloo, Canada.

G. Cohen ENST, France.

J. I. Concha Princeton University.

D. J. Costello, Jr. University of Notre Dame.

X. Dong University of Alberta, Canada.

J. F. Galdino Instituto Militar de Engenharia, Brazil.

S. Gao Clemson University.

D. Guo Princeton University.

H. Jafarkhani University of California, Irvine.

xxiv COMMUNICATIONS, INFORMATION AND NETWORK SECURITY

L. Keliher Mount Allison University, Canada.

Y. Kou University of California, Davis.

B. Krishnamachari Cornell University.

M. Krivelevich Tel Aviv University, Israel.

S. Lin University of California, Davis.

S. Litsyn Tel Aviv University, Israel.

W. T. A. Lopes Universidade Federal da Paraiba, Brazil.

M. A. Low SpaceBridge Semiconductors Inc., Canada.

J. W. Mark University of Waterloo, Canada.

H. Meijer Queen's University, Canada.

M. Pearlman Cornell University.

C. Pimentel Federal University of Pernambuco, Brazil.

H. V. Poor Princeton University.

X. Shen University of Waterloo, Canada.

D. Sridhara University of Notre Dame

A. Sridharan University of Notre Dame.

H. Tang University of California, Davis.

R. M. Tanner University of Illinois at Chicago.

Contributing Authors

S. Tavares Queen's University, Canada.

S. Verdu Princeton University.

S. B. Wicker Cornell University.

P. H. Wittke Queen's University, Canada.

J. Xu University of California, Davis.

K. Yao University of California, Los Angeles.

R. W. Yeung The Chinese University of Hong Kong.

D. Zhao University of Waterloo, Canada.

S. Zhu Xi an Jiaotong University, China.

W. Zhuang University of Waterloo, Canada.

xxv

Ian F. Blake

Foreword

Ian Blake made the principal decisions of life in his late formative years, and he never looked back. In 1964, as he was finishing his studies at Queen's University in Ontario, he was teetering between his love of mathematics and his interest in engineering. Ian's life can be understood in terms of the decisions he made at this juncture.

Ian started his life and ended his adolescence in the same place in Canada. He was born on June 7, 1941, in Saskatoon, Saskatchewan and graduated from high school in 1958 in that city, but he spent many of the intervening years elsewhere as a consequence of his father's position in government service. Some four of those years were spent in England and six were spent in Australia. Only the final year of high school was actually in Canada, and he was then already marked as a citizen and a gentleman of the old British Empire.

His undergraduate years at Queen's University were spent studying engineering physics and courting the love of his life, Betty Shaver, whom he met while studying functions of a complex variable at Queen's. Per­haps because of Betty, perhaps for other reasons, after graduating in 1962, he stayed at Queen's to obtain a Master's degree in 1964 - this time in electrical engineering - but then felt the call to study elsewhere. His next two major decisions defined his adult life.

His first key decision was to go to Princeton. In 1964, Ian simul­taneously discovered: a Princeton campus that was a bit of Britain in the midst of New Jersey; a powerful and influential graduate advisor in the person of the legendary John Thomas; an electrical engineering department that views engineering as a form of serious scholarship; and a world-class mathematics department on that very same campus. One can only imagine that this combination was a perfect fit to Ian's needs, and he had no hesitation in making his decision.

His second key decision came shortly thereafter. Ian and Betty were married while he was a Princeton graduate student and, ever since, Betty

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has been his principal and loyal supporter. As the years unfolded, the marriage produced two children, Lauren and Michael, who have now gone on to their own bright careers.

Ian's love of mathematics took deep root during the years at Prince­ton and, ever after, his career was balanced among pure mathematics, applied mathematics, and engineering. There is always another math­ematics book to read and another bit of mathematics that needs to be learned, and not enough evenings to do it all. For his thesis research he chose a topic that neatly combined his desire to interact with John Thomas, the influence of his environment in electrical engineering, and his need to work in mathematics. The thesis title "On the Characteri­zation of Random Processes" gives some hint of this triangularization.

After receiving a Ph.D. from Princeton in 1967, Ian entered the work­force and gathered experiences and collaborators during his many years at the University at Waterloo and during his short stay at a rich vari­ety of other well-known institutions. His first position after his Ph.D., during the years from 1967 to 1969, was as a Research Associate with the Jet Propulsion Laboratories in Pasadena, California, working mostly with Bill Lindsey.

In 1969, while at JPL, Ian was offered a position as an Assistant Pro­fessor at the University of Waterloo in Ontario, Canada. A new ener­getic program was underway at Waterloo, and the premier engineering program in Canada was being built there. This was an exciting time at Waterloo and a perfect environment for the fresh young academic. Ian returned to Canada to join the faculty of Waterloo and spent 27 years helping it to reach its current reputation as the best engineering school in Canada. He was Chairman of the Department of Electrical and Computer Engineering from 1978 to 1984, Associate Chair for Gradu­ate Studies from 1977 to 1978, Director of the University of Waterloo Institute of Computer Research from 1990 to 1994, and also served the Department in many other ways.

During these years of heavy administrative duties, Ian remained close to his students, always with the view that they are the first prior­ity. I have had the opportunity to know three of them well - Tomik Yaghoobian (who died so young, so sadly), Dariush Dabiri (now devot­ing his career to industry), and Vahid Tarokh (now well-known in aca­demic circles), and I know a few more by reputation. In Ian's students, I see a little of Ian's style. Always look for the nugget of mathematics that unlocks an engineering problem.

In 1975 - 1976 he spent a sabbatical year at IBM Yorktown Heights working on problems of computer security, combinatorial aspects of com­puter storage, and coding theory. He spent the summer of 1982 at IBM

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Zurich working on problems of error correcting codes and runlength cod­ing for the magnetic storage channels. He was a visiting scientist with Mj A - Com Linkabit during the 1984 - 85 academic year working in the area of data security and data processing, and contributing to the de­sign and simulation of the acquisition and tracking system of a multirate modem for the U.S. Army.

Ian also found time to put his pen to paper - or his finger to keypad - during these years. He is the author or co-author of five books and the editor or co-editor of two edited books. His collaboration with Ron Mullin of the Waterloo Mathematics Department led to their 1976 book The Mathematics of Coding Theory, an early book in the field, and Ian's first hardcover publication.

In 1996, Ian decided that a big chapter of his life was coming to a close, and it was time to open the next chapter. He took advantage of a retirement offer from Waterloo and joined Hewlett-Packard Lab­oratories in Palo Alto as a Member of the Technical Staff. The new position at Hewlett-Packard gave him the chance to devote himself full time to the exciting field of mathematical cryptography. He had become interested in this topic much earlier during his 1975 - 1976 sabbatical at IBM Yorktown Heights, shortly after DES appeared as a cryptography standard. That occasion had led to the book, with B. J. Walker, Com­puter Security and Protection Structures, which was published after this IBM sabbatical, in 1976. Although this book was limited in its scope, it generated interest and was translated into Russian. This new interest in cryptography continued after the sabbatical. Waterloo was, and is, an excellent university in which to study cryptography, and Ian benefited from a continuing collaboration with Scott Vanstone and others, but did not fully dedicate himself to cryptography until joining HP. Ian's second book in cryptography, Elliptic Curves in Cryptography, was written with Gadial Seroussi and Nigel Smart during his time at Hewlett-Packard and was published in 1999. This book is now widely regarded as the stan­dard book in elliptic-curve cryptography, and has been translated into Japanese. In addition to the coding theory book with Mullin and the two coauthored cryptography books, Ian has his name on two other books. An Introduction to Applied Probability was published by Wiley in 1979, and Applications of Finite Fields, with Menezes et al. was published in 1993.

In 1999, partly for family reasons, the Blakes left California and again settled in Ontario; this time in Toronto, as Ian accepted a faculty posi­tion in the Department of Electrical and Computer Engineering of the University of Toronto, where he continues to work on problems of coding theory and mathematical cryptography.

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Ian has left his own special mark on a variety of research topics. His early work, flowing from his dissertation, was in the area of random processes. Most of this work on random processes concentrated on trying to define specific classes of random processes for which certain types of questions, such as filtering, prediction, and level crossing, had simple of interesting answers. Thus the class of linear processes has relatively simple predictors, and the class of random processes with piecewise linear correlation functions, although continuous, has discrete predictors. Ian made significant progress in trying to find classes of random processes that had simple answers to level crossing problems. The paper on level crossings of random processes - the most cited of any of Ian's papers - was actually meant to be an internal report at JPL but due to its significance was submitted to the IEEE Transactions on Information Theory without Ian's knowledge.

Ian's long-standing interest in codes for the Gaussian noise channel arose out of a suggesting of Elwyn Berlekamp and led to his fundamental paper "The Leech Lattice as a Code for the Gaussian Channel," an early and often-cited paper underlying the large body of continuing work in lattices and coding theory. Most of his interest in this topic was con­cerned with the use of group representations in constructing good codes, as by using the matrices of a group representation to act on an initial vector to generate sets of points with good distance properties on the unit sphere in n dimensions. The idea here is to use the character table of the group to deduce the optimum initial vector and the minimum dis­tance of the code. This is a very difficult problem in general and involves high dimensions. Ian had major success here. The most general result, published in the Transactions of the American Mathematical Society, was to actually construct an initial vector that always achieved the best distance possible, given exactly by group characters. This interest in the subject of lattices stayed with Ian and, years later, together with his students, he studied the complexity of trellis descriptions of lattices.

His work on codes over integer residue rings was motivated by the thought that if the carry circuit of an ordinary processor could be dis­abled, then codes over the integers modulo 10 might be of interest for ordinary computer applications. Ian was led to his work on codes over integer residue rings. Although Ian soon abandoned this topic, the few papers in this area that he published seemed to have spawned a rather large number of other papers. The general line of work may have played a later role in the interpretation of certain nonlinear codes over the bi­nary alphabet as linear codes in a ring.

Ian's interest in discrete mathematics and combinatories led him to an interest in the construction and application of combinatorial designs,

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this both for applications in combinatories and for applications to coding and majority logic decoding. Perhaps the most interesting parts of this work were the notions of generalized Room squares that Jack Stiffler and Ian worked on (which I think was quite original and picked up to a small extent by the combinatorial community) and generalized Steiner systems (I am not aware of earlier literature on this topic). Ian also had a few students who worked in spread spectrum systems from the coding and performance point of view.

Ian has a few miscellaneous papers on a variety of topics including coding and decoding algorithms, algebraic geometry codes, enumeration techniques for burst channels, and fractal compression.

Ian's growing interest in cryptography led to a variety of papers on finite fields from both the theoretical and the computational aspects. Ian worked with Vanstone and Mullin and others on low complexity normal bases and this work proved to be of interest in cryptographic ap­plications (although it now seems that polynomial bases are as efficient in implementations, although perhaps not for VLSI implementations). There were a few papers on the construction of irreducible polynomials that were of interest from a theoretical view. Ultimately the work on cryptography went toward elliptic curve cryptography and this now ab­sorbs most of Ian's time, one way or another. The book written while Ian was at HP Labs arose out of a need to understand how to count points on an elliptic curve.

Also the paper published in 1984 on computing discrete logarithms was the first real implementation of the index calculus method. It later turned out that Adleman et al., and others had proposed it before him. However, this paper had some impact. I believe that industry was devel­oping a Diffie-Hellman chip that used GF(2128) and Ian's paper showed that the exponent was far too low to be secure.

Richard E. Blahut University of Illinois at Urbana-Champaign