ComputerNetworksShyamGollakota

ComputerNetworks 2

ProtocolsandLayers•  Protocolsandlayeringisthemainstructuringmethodusedtodivideupnetworkfunctionality–  Eachinstanceofaprotocoltalksvirtuallytoitspeerusingtheprotocol

–  Eachinstanceofaprotocolusesonlytheservicesofthelowerlayer

ProtocolsandLayers(3)•  Protocolsarehorizontal,layersarevertical

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X

YY

XInstanceofprotocolX

Peerinstance

Node1 Node2

Lowerlayerinstance(ofprotocolY)

ProtocolX

ServiceprovidedbyProtocolY

ProtocolsandLayers(4)•  Setofprotocolsinuseiscalledaprotocolstack

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ProtocolsandLayers(6)•  Protocolsyou’veprobablyheardof:

–  TCP,IP,802.11,Ethernet,HTTP,SSL,DNS,…andmanymore

•  Anexampleprotocolstack–  UsedbyawebbrowseronahostthatiswirelesslyconnectedtotheInternet

HTTP

TCP

IP

802.11

Browser

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Encapsulation•  Encapsulationisthemechanismusedtoeffectprotocollayering–  Lowerlayerwrapshigherlayercontent,addingitsowninformationtomakeanewmessagefordelivery

–  Likesendingaletterinanenvelope;postalservicedoesn’tlookinside

Encapsulation(3)•  Message“onthewire”beginstolooklikeanonion

–  Lowerlayersareoutermost

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HTTP

TCP

IP

802.11

HTTP

TCP HTTP

TCP HTTPIP

TCP HTTPIP802.11

Encapsulation(4)

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HTTP

TCP

IP

802.11

HTTP

TCP HTTP

TCP HTTPIP

TCP HTTPIP802.11

HTTP

TCP

IP

802.11(wire)

HTTP

TCP HTTP

TCP HTTPIP

TCP HTTPIP802.11

TCP HTTPIP802.11

AdvantageofLayering•  Informationhidingandreuse

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HTTP

Browser

HTTP

Server

HTTP

Browser

HTTP

Server

or

AdvantageofLayering(2)•  Informationhidingandreuse

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HTTP

TCP

IP

802.11

Browser

HTTP

TCP

IP

802.11

Server

HTTP

TCP

IP

Ethernet

Browser

HTTP

TCP

IP

Ethernet

Server

or

AdvantageofLayering(3)•  Usinginformationhidingtoconnectdifferentsystems

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HTTP

TCP

IP

802.11

Browser

HTTP

TCP

IPEthernet

Server

AdvantageofLayering(4)•  Usinginformationhidingtoconnectdifferentsystems

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HTTP

TCP

IP

802.11

Browser

IP

802.11

IP

Ethernet

HTTP

TCP

IPEthernet

Server

IP TCP HTTP

802.11 IP TCP HTTP Ethernet IP TCP HTTP

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DisadvantageofLayering•  ??

InternetReferenceModel•  Afourlayermodelbasedonexperience;omitssomeOSIlayersandusesIPasthenetworklayer.

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4Application–Programsthatusenetworkservice3Transport–Providesend-to-enddatadelivery2Internet –Sendpacketsovermultiplenetworks

1Link –Sendframesoveralink

InternetReferenceModel(3)•  IPisthe“narrowwaist”oftheInternet

–  Supportsmanydifferentlinksbelowandappsabove

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4Application3Transport

2Internet

1Link Ethernet802.11

IP

TCP UDP

HTTPSMTP RTP DNS

3GDSLCable

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Layer-basedNames(2)•  Fordevicesinthenetwork:

NetworkLink

NetworkLink

Link Link

Physical PhysicalRepeater(orhub)

Switch(orbridge)

Router

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Layer-basedNames(3)•  Fordevicesinthenetwork:

Proxyormiddleboxorgateway

NetworkLink

NetworkLink

AppTransport

AppTransport

Buttheyalllooklikethis!

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ScopeofthePhysicalLayer•  Concernshowsignalsareusedtotransfermessagebitsoveralink– Wiresetc.carryanalogsignals– Wewanttosenddigitalbits

…1011010110…

Signal

SimpleLinkModel•  We’llendwithanabstractionofaphysicalchannel

–  Rate(orbandwidth,capacity,speed)inbits/second–  Delayinseconds,relatedtolength

•  Otherimportantproperties:– Whetherthechannelisbroadcast,anditserrorrate

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DelayD,RateR

Message

MessageLatency•  Latencyisthedelaytosendamessageoveralink

–  Transmissiondelay:timetoputM-bitmessage“onthewire”

–  Propagationdelay:timeforbitstopropagateacrossthewire

–  Combiningthetwotermswehave:

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MessageLatency(2)•  Latencyisthedelaytosendamessageoveralink

–  Transmissiondelay:timetoputM-bitmessage“onthewire”

T-delay=M(bits)/Rate(bits/sec)=M/Rseconds

–  Propagationdelay:timeforbitstopropagateacrossthewire

P-delay=Length/speedofsignals=Length/⅔c=Dseconds

–  Combiningthetwotermswehave:L=M/R+D

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MetricUnits•  Themainprefixesweuse:

•  Usepowersof10forrates,2forstorage–  1Mbps=1,000,000bps,1KB=210bytes

•  “B”isforbytes,“b”isforbits

Prefix Exp. prefix exp. K(ilo) 103 m(illi) 10-3

M(ega) 106 µ(micro) 10-6

G(iga) 109 n(ano) 10-9

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LatencyExamples(2)•  “Dialup”withatelephonemodem:

D=5ms,R=56kbps,M=1250bytes

L=5ms+(1250x8)/(56x103)sec=184ms!

•  Broadbandcross-countrylink:D=50ms,R=10Mbps,M=1250bytes

L=50ms+(1250x8)/(10x106)sec=51ms

•  Alonglinkoraslowratemeanshighlatency–  Often,onedelaycomponentdominates

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Bandwidth-DelayProduct•  Messagestakespaceonthewire!

•  Theamountofdatainflightisthebandwidth-delay(BD)product

BD=RxD– Measureinbits,orinmessages–  SmallforLANs,bigfor“longfat”pipes

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Bandwidth-DelayExample(2)•  Fiberathome,cross-country

R=40Mbps,D=50msBD=40x106x50x10-3bits

=2000Kbit=250KB

•  That’squitealotofdata“inthenetwork”!

110101000010111010101001011

weightsofharmonicfrequenciesSignalovertime

=

FrequencyRepresentation•  Asignalovertimecanberepresentedbyitsfrequencycomponents(calledFourieranalysis)

26am

plitu

de

Lost!

EffectofLessBandwidth•  Fewerfrequencies(=lessbandwidth)degradessignal

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Lost!

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Lost!Bandwidth

SignalsoveraWire(2)•  Example:

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2:Attenuation:

3:Bandwidth:

4:Noise:

Sentsignal

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SignalsoverWireless•  Signalstransmittedonacarrierfrequency,likefiber

•  Travelatspeedoflight,spreadoutandattenuatefasterthan1/dist2

•  Multiplesignalsonthesamefrequencyinterfereatareceiver

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SignalsoverWireless(5)•  Variousothereffectstoo!

– Wirelesspropagationiscomplex,dependsonenvironment

•  Somekeyeffectsarehighlyfrequencydependent,–  E.g.,multipathatmicrowavefrequencies

WirelessMultipath•  Signalsbounceoffobjectsandtakemultiplepaths

–  Somefrequenciesattenuatedatreceiver,varieswithlocation– Messesupsignal;handledwithsophisticatedmethods(§2.5.3)

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Wireless•  Senderradiatessignaloveraregion

–  Inmanydirections,unlikeawire,topotentiallymanyreceivers

–  Nearbysignals(samefreq.)interfereatareceiver;needtocoordinateuse

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WiFi

WiFi

Wireless(2)•  Microwave,e.g.,3G,andunlicensed(ISM)frequencies,e.g.,WiFi,arewidelyusedforcomputernetworking

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802.11b/g/n

802.11a/g/n

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Topic•  We’vetalkedaboutsignalsrepresentingbits.How,exactly?–  Thisisthetopicofmodulation

…1011010110…

Signal

ASimpleModulation•  Letahighvoltage(+V)representa1,andlowvoltage(-V)representa0– ThisiscalledNRZ(Non-ReturntoZero)

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Bits

NRZ

0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0

+V

-V

ASimpleModulation(2)•  Letahighvoltage(+V)representa1,andlowvoltage(-V)representa0– ThisiscalledNRZ(Non-ReturntoZero)

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Bits

NRZ

0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0

+V

-V

Modulation

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NRZsignalofbits

Amplitudeshiftkeying

Frequencyshiftkeying

Phaseshiftkeying

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KeyChannelProperties•  Thebandwidth(B),signalstrength(S),andnoisestrength(N)–  Blimitstherateoftransitions–  SandNlimithowmanysignallevelswecandistinguish

BandwidthB SignalS,NoiseN

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ClaudeShannon(1916-2001)•  Fatherofinformationtheory

–  “AMathematicalTheoryofCommunication”,1948

•  Fundamentalcontributionstodigitalcomputers,security,andcommunications

Credit:CourtesyMITMuseum

Electromechanicalmousethat“solves”mazes!

ShannonCapacity•  HowmanylevelswecandistinguishdependsonS/N

–  OrSNR,theSignal-to-NoiseRatio–  Notenoiseisrandom,hencesomeerrors

•  SNRgivenonalog-scaleindeciBels:–  SNRdB=10log10(S/N)

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0

1

2

3

N

S+N

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ShannonCapacity(2)•  Shannonlimitisforcapacity(C),themaximuminformationcarryingrateofthechannel:

C=Blog2(1+S/(BN))bits/sec

Wired/WirelessPerspective•  Wires,andFiber

– EngineerlinktohaverequisiteSNRandB→ Canfixdatarate

•  Wireless– GivenB,butSNRvariesgreatly,e.g.,upto60dB!→ Can’tdesignforworstcase,mustadaptdatarate

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Wired/WirelessPerspective(2)•  Wires,andFiber

– EngineerlinktohaverequisiteSNRandB→ Canfixdatarate

•  Wireless– GivenB,butSNRvariesgreatly,e.g.,upto60dB!→ Can’tdesignforworstcase,mustadaptdatarate

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EngineerSNRfordatarate

AdaptdataratetoSNR

Puttingitalltogether–DSL•  DSL(DigitalSubscriberLine)iswidelyusedforbroadband;manyvariantsoffer10sofMbps–  Reusestwistedpairtelephonelinetothehome;ithasupto~2MHzofbandwidthbutusesonlythelowest~4kHz

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DSL(2)•  DSLusespassbandmodulation(calledOFDM)

–  Separatebandsforupstreamanddownstream(larger)– Modulationvariesbothamplitudeandphase(calledQAM)–  HighSNR,upto15bits/symbol,lowSNRonly1bit/symbol

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Upstream Downstream

26–138kHz

0-4kHz 143kHzto1.1MHz

Telephone

Freq.

Voice Upto1Mbps Upto12Mbps

ADSL2:

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Topic•  Somebitswillbereceivedinerrordue

tonoise.Whatcanwedo?–  Detecterrorswithcodes»–  Correcterrorswithcodes»–  Retransmitlostframes

•  Reliabilityisaconcernthatcutsacrossthelayers–we’llseeitagain

Later

Problem–Noisemayflipreceivedbits

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Signal0 0 0 0

11 10

0 0 0 011 1

0

0 0 0 011 1

0

SlightlyNoisy

Verynoisy

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Approach–AddRedundancy•  Errordetectioncodes

–  Addcheckbitstothemessagebitstoletsomeerrorsbedetected

•  Errorcorrectioncodes–  Addmorecheckbitstoletsomeerrorsbecorrected

•  Keyissueisnowtostructurethecodetodetectmanyerrorswithfewcheckbitsandmodestcomputation

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MotivatingExample•  Asimplecodetohandleerrors:

–  Sendtwocopies!Errorifdifferent.

•  Howgoodisthiscode?–  Howmanyerrorscanitdetect/correct?–  Howmanyerrorswillmakeitfail?

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MotivatingExample(2)•  Wewanttohandlemoreerrorswithlessoverhead– Willlookatbettercodes;theyareappliedmathematics

–  But,theycan’thandleallerrors–  Andtheyfocusonaccidentalerrors(willlookatsecurehasheslater)

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UsingErrorCodes•  CodewordconsistsofDdataplusR

checkbits(=systematicblockcode)

•  Sender:–  ComputeRcheckbitsbasedontheDdatabits;sendthecodewordofD+Rbits

D R=fn(D)Databits Checkbits

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UsingErrorCodes(2)•  Receiver:

–  ReceiveD+Rbitswithunknownerrors–  RecomputeRcheckbitsbasedontheDdatabits;errorifRdoesn’tmatchR’

D R’Databits Checkbits

R=fn(D)=?

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IntuitionforErrorCodes•  ForDdatabits,Rcheckbits:

•  Randomlychosencodewordisunlikelytobecorrect;overheadislow

AllcodewordsCorrect

codewords

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R.W.Hamming(1915-1998)•  Muchearlyworkoncodes:

–  “ErrorDetectingandErrorCorrectingCodes”,BSTJ,1950

•  Seealso:–  “YouandYourResearch”,1986

Source:IEEEGHN,©2009IEEE

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HammingDistance•  DistanceisthenumberofbitflipsneededtochangeD1toD2

•  Hammingdistanceofacodeistheminimumdistancebetweenanypairofcodewords

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HammingDistance(2)•  Errordetection:

–  Foracodeofdistanced+1,uptoderrorswillalwaysbedetected

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HammingDistance(3)•  Errorcorrection:

–  Foracodeofdistance2d+1,uptoderrorscanalwaysbecorrectedbymappingtotheclosestcodeword

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Topic•  Somebitsmaybereceivedinerror

duetonoise.Howdowedetectthis?–  Parity»–  Checksums»–  CRCs»

•  Detectionwillletusfixtheerror,forexample,byretransmission(later).

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SimpleErrorDetection–ParityBit•  TakeDdatabits,add1checkbitthatisthesumoftheDbits–  Sumismodulo2orXOR

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ParityBit(2)•  Howwelldoesparitywork?

– Whatisthedistanceofthecode?–  Howmanyerrorswillitdetect/correct?

•  Whataboutlargererrors?

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Checksums•  Idea:sumupdatainN-bitwords

– Widelyusedin,e.g.,TCP/IP/UDP

•  Strongerprotectionthanparity

1500bytes 16bits

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InternetChecksum•  Sumisdefinedin1scomplementarithmetic(mustaddbackcarries)–  Andit’sthenegativesum

•  “Thechecksumfieldisthe16bitone'scomplementoftheone'scomplementsumofall16bitwords…”–RFC791

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InternetChecksum(2)Sending:1. Arrangedatain16-bitwords

2. Putzeroinchecksumposition,add

3. Addanycarryoverbacktoget16bits

4. Negate(complement)togetsum

0001 f203 f4f5 f6f7

+(0000) ------ 2ddf0

ddf0

+ 2 ------ ddf2

220d

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InternetChecksum(3)Sending:1. Arrangedatain16-bitwords2. Putzeroinchecksumposition,add

3. Addanycarryoverbacktoget16bits

4. Negate(complement)togetsum

0001 f203 f4f5 f6f7

+(0000) ------ 2ddf0

ddf0

+ 2 ------ ddf2

220d

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InternetChecksum(4)Receiving:1. Arrangedatain16-bitwords2. Checksumwillbenon-zero,add

3. Addanycarryoverbacktoget16bits

4. Negatetheresultandcheckitis0

0001 f203 f4f5 f6f7

+ 220d ------ 2fffd

fffd

+ 2 ------ ffff

0000

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InternetChecksum(5)Receiving:1. Arrangedatain16-bitwords2. Checksumwillbenon-zero,add

3. Addanycarryoverbacktoget16bits

4. Negatetheresultandcheckitis0

0001 f203 f4f5 f6f7

+ 220d ------ 2fffd

fffd

+ 2 ------ ffff

0000

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InternetChecksum(6)•  Howwelldoesthechecksumwork?

– Whatisthedistanceofthecode?–  Howmanyerrorswillitdetect/correct?

•  Whataboutlargererrors?

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CyclicRedundancyCheck(CRC)•  Evenstrongerprotection

–  Givenndatabits,generatekcheckbitssuchthatthen+kbitsareevenlydivisiblebyageneratorC

•  Examplewithnumbers:–  n=302,k=onedigit,C=3

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CRCs(2)•  Thecatch:

–  It’sbasedonmathematicsoffinitefields,inwhich“numbers”representpolynomials

–  e.g,10011010isx7+x4+x3+x1

•  Whatthismeans:– Weworkwithbinaryvaluesandoperateusingmodulo2arithmetic

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CRCs(3)•  SendProcedure:1.  Extendthendatabitswithkzeros2.  DividebythegeneratorvalueC3.  Keepremainder,ignorequotient4.  Adjustkcheckbitsbyremainder

•  ReceiveProcedure:1.  Divideandcheckforzeroremainder

CRCs(4)

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Databits:1101011111

Checkbits:C(x)=x4+x1+1C=10011

k=4

100111101011111

CRCs(5)

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CRCs(6)•  Protectiondependongenerator

–  StandardCRC-32is100000100110000010001110110110111

•  Properties:–  HD=4,detectsuptotriplebiterrors–  Alsooddnumberoferrors–  Andburstsofuptokbitsinerror–  Notvulnerabletosystematicerrorslikechecksums

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ErrorDetectioninPractice•  CRCsarewidelyusedonlinks

– Ethernet,802.11,ADSL,Cable…•  ChecksumusedinInternet

–  IP,TCP,UDP…butitisweak•  Parity

–  Islittleused

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Topic•  Somebitsmaybereceivedinerrorduetonoise.Howdowefixthem?–  Hammingcode»–  Othercodes»

•  Andwhyshouldweusedetectionwhenwecanusecorrection?

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WhyErrorCorrectionisHard•  Ifwehadreliablecheckbitswecouldusethemtonarrowdownthepositionoftheerror–  Thencorrectionwouldbeeasy

•  Buterrorcouldbeinthecheckbitsaswellasthedatabits!–  Datamightevenbecorrect

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IntuitionforErrorCorrectingCode•  Supposeweconstructacodewitha

Hammingdistanceofatleast3–  Need≥3biterrorstochangeonevalidcodewordintoanother

–  Singlebiterrorswillbeclosesttoauniquevalidcodeword

•  Ifweassumeerrorsareonly1bit,wecancorrectthembymappinganerrortotheclosestvalidcodeword–  WorksforderrorsifHD≥2d+1

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Intuition(2)•  Visualizationofcode:

A

B

Validcodeword

Errorcodeword

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Intuition(3)•  Visualizationofcode:

A

B

Validcodeword

Errorcodeword

SinglebiterrorfromA

ThreebiterrorstogettoB

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HammingCode•  Givesamethodforconstructingacodewithadistanceof3–  Usesn=2k–k–1,e.g.,n=4,k=3–  Putcheckbitsinpositionspthatarepowersof2,startingwithposition1

–  Checkbitinpositionpisparityofpositionswithaptermintheirvalues

•  Plusaneasywaytocorrect[soon]

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HammingCode(2)•  Example:data=0101,3checkbits

–  7bitcode,checkbitpositions1,2,4–  Check1coverspositions1,3,5,7–  Check2coverspositions2,3,6,7–  Check4coverspositions4,5,6,7

_______ 1234567

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HammingCode(3)•  Example:data=0101,3checkbits

–  7bitcode,checkbitpositions1,2,4–  Check1coverspositions1,3,5,7–  Check2coverspositions2,3,6,7–  Check4coverspositions4,5,6,7

0100101p1=0+1+1=0,p2=0+0+1=1,p4=1+0+1=0

1234567

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HammingCode(4)•  Todecode:

–  Recomputecheckbits(withparitysumincludingthecheckbit)

–  Arrangeasabinarynumber–  Value(syndrome)tellserrorposition–  Valueofzeromeansnoerror–  Otherwise,flipbittocorrect

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HammingCode(5)•  Example,continued

0100101p1=p2=p4=

Syndrome=Data=

1234567

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HammingCode(6)•  Example,continued

0100101p1=0+0+1+1=0,p2=1+0+0+1=0,p4=0+1+0+1=0

Syndrome=000,noerrorData=0101

1234567

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HammingCode(7)•  Example,continued

0100111p1=p2=p4=

Syndrome=Data=

1234567

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HammingCode(8)•  Example,continued

0100111p1=0+0+1+1=0,p2=1+0+1+1=1,p4=0+1+1+1=1

Syndrome=110,flipposition6Data=0101(correctafterflip!)

1234567

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OtherErrorCorrectionCodes•  CodesusedinpracticearemuchmoreinvolvedthanHamming

•  Convolutionalcodes(§3.2.3)–  Takeastreamofdataandoutputamixoftherecentinputbits

– Makeseachoutputbitlessfragile–  DecodeusingViterbialgorithm(whichcanusebitconfidencevalues)

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OtherCodes(2)–LDPC•  LowDensityParityCheck(§3.2.3)

–  LDPCbasedonsparsematrices–  Decodediterativelyusingabeliefpropagationalgorithm

–  Stateofthearttoday•  InventedbyRobertGallagerin1963aspartofhisPhDthesis–  Promptlyforgottenuntil1996…

Source:IEEEGHN,©2009IEEE

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Detectionvs.Correction•  Whichisbetterwilldependonthepatternoferrors.Forexample:–  1000bitmessageswithabiterrorrate(BER)of1in10000

•  Whichhaslessoverhead?

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Detectionvs.Correction•  Whichisbetterwilldependonthepatternoferrors.Forexample:–  1000bitmessageswithabiterrorrate(BER)of1in10000

•  Whichhaslessoverhead?–  Itstilldepends!Weneedtoknowmoreabouttheerrors

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Detectionvs.Correction(2)1.  Assumebiterrorsarerandom

–  Messageshave0ormaybe1error

•  Errorcorrection:–  Need~10checkbitspermessage–  Overhead:

•  Errordetection:–  Need~1checkbitspermessageplus1000bit

retransmission1/10ofthetime–  Overhead:

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Detectionvs.Correction(3)2.  Assumeerrorscomeinburstsof100

–  Only1or2messagesin1000haveerrors

•  Errorcorrection:–  Need>>100checkbitspermessage–  Overhead:

•  Errordetection:–  Need32?checkbitspermessageplus1000

bitresend2/1000ofthetime–  Overhead:

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Detectionvs.Correction(4)•  Errorcorrection:

– Neededwhenerrorsareexpected– Orwhennotimeforretransmission

•  Errordetection:– Moreefficientwhenerrorsarenotexpected

– Andwhenerrorsarelargewhentheydooccur

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ErrorCorrectioninPractice•  Heavilyusedinphysicallayer

–  LDPCisthefuture,usedfordemandinglinkslike802.11,DVB,WiMAX,LTE,power-line,…

–  Convolutionalcodeswidelyusedinpractice

•  Errordetection(w/retransmission)isusedinthelinklayerandaboveforresidualerrors

•  Correctionalsousedintheapplicationlayer–  CalledForwardErrorCorrection(FEC)–  Normallywithanerasureerrormodel–  E.g.,Reed-Solomon(CDs,DVDs,etc.)