Network coding : an introduction

184 Pages·2008·3.132 MB·English

by  Tracey Ho, Desmond S Lun

This page intentionally left blank
NETWORKCODING
Networkcoding,withthepotentialtodeliverincreasednetworkcapacity,promises
to have a significant impact on the way communications networks are designed,
operated,andunderstood.Thisisthefirstbooktopresentaunifiedandintuitive
overview of the theory, applications, challenges, and future directions of this
emerging field, making this a must-have resource for those working in wireless
communications.
By explaining the ideas and practical techniques, Ho and Lun take an
engineering-oriented approach, which starts with the basic ideas, models, and
theory, then covers a core subset of results in detail with full proofs, while sur-
veyingothers.Themathematicalunderpinnings,practicalalgorithms,andissues
such as code selection, security, and network management are all covered. The
keytopicsofinter-session(non-multicast)networkcoding,lossynetworks,loss-
lessnetworks,andsubgraphselectionalgorithmsarediscussedindetail.There-
sultisanauthoritativeintroductiontonetworkcodingthatprovidesnotonlythe
background to support research efforts, but also the practical considerations for
thoseinvolvedindesigningwirelesssystems.
Organized in a modular way so that you can quickly access your topic of
interest,be ittheoretical capacity bounds or practical implementation, this book
is an essential resource for graduate students and researchers in electrical and
computerengineering,aswellasforpractitionersinthecommunicationsindustry.
TraceyHoisAssistantProfessorofElectricalEngineeringandComputerScience
atthe California Instituteof Technology. In2004, she was awarded her Ph.D.in
electricalengineeringandcomputersciencefromMITand,in2005,wasnamed
oneofthe35toptechnologyinnovatorsundertheageof35byTechnologyReview.
DesmondS.LunisaComputationalBiologistattheBroadInstituteofMITand
HarvardandaResearchFellowinGeneticsatHarvardMedicalSchool.In2006,
he was awarded his Ph.D. in electrical engineering and computer science from
MIT.

NETWORK CODING
An Introduction
TRACEY HO
CaliforniaInstituteofTechnology
DESMOND S. LUN
BroadInstituteofMITandHarvard
CAMBRIDGEUNIVERSITYPRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB28RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521873109
© Cambridge University Press 2008
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2008
ISBN-13 978-0-511-39826-1 eBook (EBL)
ISBN-13 978-0-521-87310-9 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Preface pageix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Whatisnetworkcoding? 1
1.2 Whatisnetworkcodinggoodfor? 2
1.2.1 Throughput 2
1.2.2 Robustness 5
1.2.3 Complexity 7
1.2.4 Security 8
1.3 Networkmodel 8
1.4 Outlineofbook 11
1.5 Notesandfurtherreading 12
2 LosslessMulticastNetworkCoding . . . . . . . . . . . . . . . . . . . . 13
2.0 Notationalconventions 13
2.1 Basicnetworkmodelandmulticastnetworkcoding
problemformulation 13
2.2 Delay-freescalarlinearnetworkcoding 14
2.3 Solvabilityandthroughput 17
2.3.1 Theunicastcase 17
2.3.2 Themulticastcase 18
2.3.3 Multicastingfrommultiplesourcenodes 19
2.3.4 Maximumthroughputadvantage 19
2.4 Multicastnetworkcodeconstruction 21
2.4.1 Centralizedpolynomial-timeconstruction 21
2.4.2 Randomlinearnetworkcoding 23
2.5 Packetnetworks 27
2.5.1 Distributedrandomlinearcodingforpacket
networks 28
2.6 Networkswithcyclesandconvolutionalnetworkcoding 30
v
vi CONTENTS
2.6.1 Algebraicrepresentationofconvolutionalnetwork
coding 31
2.7 Correlatedsourceprocesses 34
2.7.1 Jointsource-networkcoding 35
2.7.2 Separationofsourcecodingandnetworkcoding 37
2.8 Notesandfurtherreading 37
2.A Appendix:Randomnetworkcoding 39
3 Inter-SessionNetworkCoding . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1 Scalarandvectorlinearnetworkcoding 50
3.2 Fractionalcodingproblemformulation 51
3.3 Insufficiencyoflinearnetworkcoding 52
3.4 Informationtheoreticapproaches 54
3.4.1 Multipleunicastnetworks 58
3.5 Constructiveapproaches 58
3.5.1 PairwiseXORcodinginwirelinenetworks 59
3.5.2 XORcodinginwirelessnetworks 60
3.6 Notesandfurtherreading 63
4 NetworkCodinginLossyNetworks . . . . . . . . . . . . . . . . . . . . 65
4.1 Randomlinearnetworkcoding 67
4.2 Codingtheorems 68
4.2.1 Unicastconnections 68
4.2.2 Multicastconnections 82
4.3 ErrorexponentsforPoissontrafficwithi.i.d.losses 83
4.4 Notesandfurtherreading 85
5 SubgraphSelection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.1 Flow-basedapproaches 87
5.1.1 Intra-sessioncoding 87
5.1.2 Computation-constrainedcoding 110
5.1.3 Inter-sessioncoding 111
5.2 Queue-length-basedapproaches 114
5.2.1 Intra-sessionnetworkcodingformultiple
multicastsessions 115
5.2.2 Inter-sessioncoding 128
5.3 Notesandfurtherreading 129
6 SecurityAgainstAdversarialErrors . . . . . . . . . . . . . . . . . . . . 130
6.0 Notationalconventions 130
6.1 Errorcorrection 131
6.1.1 Errorcorrectionboundsforcentralizednetwork
coding 131
CONTENTS vii
6.1.2 Distributedrandomnetworkcodingand
polynomial-complexityerrorcorrection 142
6.2 Detectionofadversarialerrors 147
6.2.1 Modelandproblemformulation 148
6.2.2 Detectionprobability 150
6.3 Notesandfurtherreading 151
6.A Appendix:Proofofresultsforadversarialerrordetection 152
Bibliography 157
Index 169