Error Correcting Coding and Security for Data Networks: Analysis of the Superchannel Concept

290 Pages·2005·2.432 MB·English

by  Grigorii Kabatiansky, Evgenii Krouk, Sergei Semenov

Error Correcting Coding and Security
for Data Networks
Analysis of the Superchannel Concept
G. Kabatiansky
Institute of Information Transmission Problems RAN, Russia
and INRIA-Projet CODES, France
E. Krouk
St. Petersburg State University of Aerospace Instrumentation, Russia
S. Semenov
Nokia Technology Platforms, Finland
Error Correcting Coding and Security
for Data Networks

Error Correcting Coding and Security
for Data Networks
Analysis of the Superchannel Concept
G. Kabatiansky
Institute of Information Transmission Problems RAN, Russia
and INRIA-Projet CODES, France
E. Krouk
St. Petersburg State University of Aerospace Instrumentation, Russia
S. Semenov
Nokia Technology Platforms, Finland
Copyright#2005 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,
WestSussexPO198SQ,England
Telephone [phone]
Email(forordersandcustomerserviceenquiries):[email protected]
VisitourHomePageonwww.wiley.com
AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted
inanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,except
underthetermsoftheCopyright,DesignsandPatentsAct1988orunderthetermsofalicenceissuedbythe
CopyrightLicensingAgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermission
inwritingofthePublisher.RequeststothePublishershouldbeaddressedtothePermissionsDepartment,
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussexPO198SQ,England,or
[email protected],orfaxedto([phone].
Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmatter
covered.ItissoldontheunderstandingthatthePublisherisnotengagedinrenderingprofessionalservices.If
professionaladviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbe
sought.
OtherWileyEditorialOffices
JohnWiley&SonsInc.,111RiverStreet,Hoboken,NJ07030,USA
Jossey-Bass,989MarketStreet,SanFrancisco,CA94103-1741,USA
Wiley-VCHVerlagGmbH,Boschstr.12,D-69469Weinheim,Germany
JohnWiley&SonsAustraliaLtd,33ParkRoad,Milton,Queensland4064,Australia
JohnWiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,JinXingDistripark,Singapore129809
JohnWiley&SonsCanadaLtd,22WorcesterRoad,Etobicoke,Ontario,CanadaM9W1L1
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsin
printmaynotbeavailableinelectronicbooks.
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN0-470-86754-X
Typesetin10/12ptTimesbyThomsonPress(India)Limited,NewDelhi.
PrintedandboundbyAntonyRowe,Chippenham,Wiltshire.
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestry
inwhichatleasttwotreesareplantedforeachoneusedforpaperproduction.
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Problems Facing Error Control Coding in Data Networks . . . . . . . . . . . . 1
1.1 International Recommendations on Using Error Control Coding
at Different Network Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Classification of Problems on Coding in Networks. . . . . . . . . . . . . . . . 4
2 Block Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Main Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Algebraic Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Linear Block Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Cyclic Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Bounds on Minimum Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 General Methods of Decoding of Linear Codes. . . . . . . . . . . . . . . . . . . . 51
3.1 Minimum Distance Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Information Set Decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 A Supercode Decoding Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4 The Complexity of Decoding in the Channel with Independent Errors. . 65
4 Codes with Algebraic Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.1 Hamming Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 Reed-Solomon Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 BCH Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Decoding of BCH Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5 The Sudan Algorithm and its Extensions . . . . . . . . . . . . . . . . . . . . . . 91
5 Decoding of LDPC Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.1 Low-Density Parity-Check Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 LDPC Constructions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3 Estimating the Minimum Distance of EG-LDPC Codes . . . . . . . . . . . . 113
5.4 Burst-Error-Correcting LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.5 Decoding Schemes of LDPC Codes. . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.6 Simulation Results in AWGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Appendix 5.A Euclidean Geometries . . . . . . . . . . . . . . . . . . . . . . . . 138
6 Convolutional Codes and Turbo-Codes. . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.1 Convolutional Codes Representation and Encoding . . . . . . . . . . . . . . . 141
6.2 Viterbi Decoding Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.3 List Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.4 Sequential Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
vi CONTENTS
6.5 Parallel-Concatenated Convolutional Codes and Soft Input
Soft Output Decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.6 SISO Decoding Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7 Coding of Messages at the Transport Layer of the Data Network . . . . . . 191
7.1 Decreasing the Message Delay with the help of Transport Coding. . . . . 191
7.2 Transmission of Message during Limited Time. . . . . . . . . . . . . . . . . . 197
7.3 Transmission of Priority Messages without using Priority Packets . . . . . 200
7.4 Estimation of the Effectiveness of Transport Coding for the
Nonexponential Model of Packet Delay . . . . . . . . . . . . . . . . . . . . . . . 203
8 Providing Security of Data in a Network with the Help
of Coding Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.1 Public-Key Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.2 Codebased Cryptosystems: McEliece and Niederreiter . . . . . . . . . . . . . 219
8.3 Cryptosystems Based on Full Decoding . . . . . . . . . . . . . . . . . . . . . . . 228
8.4 Further Development of Codebased Cryptosystems . . . . . . . . . . . . . . . 233
8.5 Codebased Cryptosystems and RSA: Comparison and Perspectives . . . . 237
8.6 Codebased Signature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9 Reconciliation of Coding at Different Layers of a Network . . . . . . . . . . . 247
9.1 Transport Coding in a Network with Unreliable Channels. . . . . . . . . . . 247
9.2 Reconciliation of Channel and Transport Coding. . . . . . . . . . . . . . . . . 249
9.3 Use of Tornado Codes for Reconciliation of Channel
and Transport Coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9.4 Development of Coding Methods at the Presentation Layer . . . . . . . . . 258
9.5 Reconciliation of Coding at Neighbour Layers of a Network . . . . . . . . 265
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Preface
Thisbookprovidesasystematicapproachtotheproblemsinvolvedintheapplicationof
error-correcting codes in data networks.
Over the last two decades the importance of coding theory has become apparent.
Thirty years ago developers of communication systems considered error-correcting
coding to be somewhat exotic. It was considered as an area of interest only for
mathematical engineers or mathematicians involved in the problems of engineering.
Todayhowever,theoryisanimportantpartofanytextbookoncommunications,andthe
results of coding theory have become standards in data communication. The increasing
demand for communications quality and the progress in information technologies has
ledtotheimplementationoferror-correctingproceduresinpracticeandanexpansionin
the area of error-correcting codes applications.
Following the growth of coding theory in practice the number of publications on
codingtheoryanditsapplicationshasalsoincreased.However,mostofthesebooksare
concernedwiththeproblemofcodingofphysicalordata-linknetworklayers,whichare
the traditional application of error-control codes.
There are several classes of errors that are inherent in the process of information
transfer over networks. One of these classes is formed by normal errors originating in
communication links, and other classes are formed by special distortions, connected to
theorganisationofthenetwork.However,inmoderndata networkstheerror-correcting
(or controlling) codes are used only as a means of increasing the reliability of
information during data transmission over different channels – no correlation between
coding and other network procedures is considered. There is also a lack of research on
the capability of codes to improve the operation of the network as a whole. Recently a
number of non-traditional directions have appeared for applying coding at network
layers higher than the data-link layer. In particular, the authors of this book have
succeeded in showing the effectiveness of using error-correcting codes for reducing the
delivery time of the message and increasing the reliability of the message itself. The
desire to demonstrate these possibilities was the first reason for writing this book.
However, during the preparation of the book it became clear that we had collected
enough examples of using error-correcting codes at application and presentation layers
ofnetworks(codingforimagecompressionandcode-basedcryptosystemsforexample)
to enable us to apply the results of coding theory to all network layers.
The basic concept considers the data network as some superchannel (consisting of
several layers of the network). This concept allows us to solve the problems of error-
correctingcodinginadatanetworkasawhole.Asmosterrorsdependonprotocolsused
at the corresponding network layer, the suggested ‘global’ approach to coding in a
network is connected with other network procedures, and this fact determines the
complexity and originality of coding problems in a network. Surprisingly, results
indicate that coding in a network helps not only to increase the reliability of the
viii PREFACE
transmitted information, but can also be used to improve such important characteristics
of a network as the mean message delay. We may also consider the encryption of
messages just as a coding process at the presentation layer in a network. We can
therefore distinguish different coding processes in different network layers and so it is
necessary to consider the impact of coding in one layer on another layer. Thus, the
problem of reconciliation of coding in different network layers arises. In this book we
set out some solutions to this problem.
Theimportanceofsolvingthisproblemandourperspectivesonthepossiblesolutions
wereespeciallyemphasisedbythereviewersofthisbook.Weareverygratefulfortheir
helpfulcomments.Itistheattempttoconsidertheproblemsofcodingathighernetwork
layers which, in our opinion, is the distinguishing feature of this book.
The theoretical material is accompanied by concrete recommendations for the use of
codesin data networks and bycalculationsof the benefits thatcan be obtainedwith the
help of error-correctingcoding. The organisationof the book (from the problemsto the
theory and from the theory to the problems, and the relative independence of chapters
fromeachother)ischoseninsuchawayastofacilitatereadingforengineerswhowould
like to familiarise themselves with new approaches to the use of error-correcting codes
in data networks. Since a significant part of the material is new or is not reflected in
the literature, we hope that this book will be of interest to readers from different
disciplines who are interested in issues of data communication and applications of
coding theory.
The book is organised as follows. Chapter 1 introduces the problems of coding is
differentnetworklayers.Chapter2presentsthemainalgebraicstructuresusedincoding
theory and one of the most studied class of codes: linear block codes. Chapter 3 covers
thedifferentmethodsoflinearcodesdecodingandintroducessomenewresultsobtained
by authors in this field. Chapter 4 describes the very widely used codes: Hamming
codes, BCH codes, and Reed-Solomon codes. The decoding of these helps to
demonstrate very important and comprehensive results of coding theory. Chapter 5
introduces the problems of LDPC codes decoding. Chapter 6 presents another very
widely-used class of codes: convolutional codes and turbo codes, and covers some
problems of iterative decoding. Chapter 7 is devoted to the new area of application of
error-correcting codes: transport coding. In this chapter the possibility of using error-
correctingcodestocontrolsuchimportantdatacharacteristicsasmeanmessagedelayis
demonstrated. Chapter 8 covers coding methods used in cryptography. Chapter 9
analyses the problems of reconciliation of coding in different network layers. In this
chapter some solutions based on the superchannel approach are considered.
Additional research results including some new constructions of LDPC codes, joint
error-controlcodingandsynchronization,Reed-Mullercodesandtheirlistdecodingcan
be obtained from the book’s companion website at ftp://ftp.wiley.co.uk/pub/books/
kabatiansky.
The problem of error control coding in data networks is very wide and not yet fully
defined today so the authors do not claim to provide a full solution of the problem but
are hoping that this book can become a first step to further research in the field.