TABLE OF CONTENTS LIST OF TABLES................................... vii

AThesis

Presentedto

TheAcademicFaculty

by

HosseinPishro-Nik

InPartialFul llment

oftheRequirementsfortheDegree

DoctorofPhilosophy

SchoolofElectricalandComputerEngineering

GeorgiaInstituteofTechnology

December2005

TABLE OF CONTENTS LIST OF TABLES................................... vii

Approvedby:

Dr.FaramarzFekri,Advisor

SchoolofElectricalandComputerEngi-

neering

GeorgiaInstituteofTechnology

Dr.IanF.Akyildiz

SchoolofElectricalandComputerEngi-

neering

GeorgiaInstituteofTechnology

Dr.StevenW.McLaughlin

SchoolofElectricalandComputerEngi-

neering

GeorgiaInstituteofTechnologyDr.AliAdibiSchoolofElectricalandComputerEngi-neeringGeorgiaInstituteofTechnologyDr.ChristopherE.HeilSchoolofMathematicsGeorgiaInstituteofTechnology

DateApproved:August18,2005

TABLE OF CONTENTS LIST OF TABLES................................... vii

TABLEOFCONTENTS

LISTOFTABLES...................................LISTOFFIGURESvii..................................viiiSUMMARY........................................IINTRODUCTION.................................IIBACKGROUND..................................

2.1ErrorControlCoding..............................

2.2EnsemblesofLDPCCodes...........................

2.3IterativeDecoding................................

2.4PropertiesoftheIterativeDecoding......................

2.5DensityEvolution................................

2.6OtherDevelopments..............................

2.7WirelessSensorNetworks............................IIIDECODINGPROBLEMSFORLDPCCODES..............

3.1Introduction...................................

3.2BoundsonthePerformanceofMLDecodingovertheBEC.........

3.3ImprovingtheIterativeDecoding.......................

3.3.1DescriptionofAlgorithms.......................

3.3.2BoundsontheNumberofGuessesinAlgorithmsBandC.....

3.3.3ImprovingAlgorithmsBandCbyReductionofNumberofGuesses

3.3.4SimulationResults...........................

3.4ImprovedDecodingAlgorithmsforMBIOSChannels............

3.5ImprovedDecodingforNon-UniformChannels................

3.6ApplicationofPseudo-CodewordstotheAnalysisofAlgorithmD.....

3.7StoppingSets..................................

3.7.1IntractabilityofSS...........................

3.8Conclusion....................................

iiixii16689101113131616172525313338465055575863

TABLE OF CONTENTS LIST OF TABLES................................... vii

IVPERFORMANCEOFLDPCCODESWITHLINEARMINIMUMDIS-

TANCE........................................

4.1Introduction...................................

4.2DistributionsofSmallCyclesandStoppingSets...............

4.3ErrorFloorDuetoSmallStoppingSets....................

4.4EnsembleswithGoodErrorFloorPerformance...............

4.5LDPCCodeswithLinearMinimumDistance................

4.5.1LowerBoundsontheAchievableRates................

4.5.2UpperBoundsontheAchievableRates................

4.6Conclusion....................................VNON-UNIFORMERRORCORRECTIONUSINGLDPCCODES.

5.1Introduction...................................

5.2Non-uniformErrorCorrection.........................

5.2.1VHMSystems..............................

5.2.2Ensembleg(Λ,ρ)............................

5.2.3AsymptoticAnalysis..........................

5.2.4AdvantagesoftheEnsembleg(Λ,ρ)..................

5.3Rate-CompatibleLDPCCodes.........................

5.4UnequalErrorProtectionUsingLDPCCodes................

5.4.1PerfectProtection............................

5.4.2AnUnequalErrorProtectionScheme.................

5.4.3DecodingofHighlyProtectedBits..................

5.5PracticalCodeDesignandSimulationResults................

5.5.1PracticalCodeDesignforNon-UniformChannels..........

5.5.2ApplicationofNon-uniformLDPCCodesinVolumeHolographic

MemorySystems............................

5.5.3SimulationResultsforVHMSystems.................

5.5.4SimulationResultsforUnequalErrorProtection..........

5.6Otherapplications................................

5.7Conclusion....................................

iv64646769747676868991919494959699100107107108111112112117123126129130

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VIRATE-COMPATIBLECODES.........................132

6.1

6.2Introduction...................................PuncturedLDPCcodes.............................

6.2.1

6.2.2

6.2.3

6.2.4

6.2.5

6.3

6.4PuncturingthresholdofLDPCcodes.................AchievingArbitraryRatesViaPuncturing..............OptimalityofPuncturedLDPCCodes................PuncturingovertheBinaryErasureChannel.............DesignofGoodPuncturedLDPCCodes...............132133136137140143146CapacityAchievingSequencesforMBIOSChannelsUsingPuncturedcodes148RaptorCodes..................................

6.4.1

6.4.2

6.4.3ConventionalRaptorCodes......................GeneralizedRaptorCodes.......................SimulationResults...........................150152153156

1566.5Conclusion....................................

VIICONNECTIVITYPROPERTIESOFLARGE-SCALEWIRELESSSEN-

SORNETWORKS.................................158

7.1

7.2

7.3

http://www.77cn.com.cnworkswithunreliablelinks.........................

7.4.1

7.4.2

7.5Connectivity...............................K-Connectivity.............................158161163166166173174

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