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HammingCode•  Givesamethodforconstruc=ngacodewithadistanceof3–  Usesn=2k–k–1,e.g.,n=4,k=3–  Putcheckbitsinposi=onspthatarepowersof2,star=ngwithposi=on1

–  Checkbitinposi=onpisparityofposi=onswithaptermintheirvalues

•  Plusaneasywaytocorrect[soon]

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HammingCode(2)•  Example:data=0101,3checkbits–  7bitcode,checkbitposi=ons1,2,4–  Check1coversposi=ons1,3,5,7–  Check2coversposi=ons2,3,6,7–  Check4coversposi=ons4,5,6,7

_______ 1234567

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HammingCode(3)•  Example:data=0101,3checkbits–  7bitcode,checkbitposi=ons1,2,4–  Check1coversposi=ons1,3,5,7–  Check2coversposi=ons2,3,6,7–  Check4coversposi=ons4,5,6,7

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)tellserrorposi=on–  Valueofzeromeansnoerror–  Otherwise,flipbittocorrect

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HammingCode(5)•  Example,con=nued

0100101p1=p2=p4=

Syndrome=Data=

1234567

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HammingCode(6)•  Example,con=nued

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,con=nued

0100111p1=p2=p4=

Syndrome=Data=

1234567

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HammingCode(8)•  Example,con=nued

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

Syndrome=110,flipposi=on6Data=0101(correcta^erflip!)

1234567

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OtherErrorCorrec=onCodes•  Codesusedinprac=cearemuchmoreinvolvedthanHamming

•  Convolu=onalcodes(§3.2.3)–  Takeastreamofdataandoutputamixoftherecentinputbits

– Makeseachoutputbitlessfragile–  DecodeusingViterbialgorithm(whichcanusebitconfidencevalues)

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OtherCodes(2)–LDPC•  LowDensityParityCheck(§3.2.3)–  LDPCbasedonsparsematrices–  Decodeditera=velyusingabeliefpropaga=onalgorithm

–  Stateofthearttoday•  InventedbyRobertGallagerin1963aspartofhisPhDthesis–  Promptlyforgofenun=l1996…

Source:IEEEGHN,©2009IEEE

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Detec=onvs.Correc=on•  Whichisbeferwilldependonthepafernoferrors.Forexample:–  1000bitmessageswithabiterrorrate(BER)of1in10000

•  Whichhaslessoverhead?

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Detec=onvs.Correc=on•  Whichisbeferwilldependonthepafernoferrors.Forexample:–  1000bitmessageswithabiterrorrate(BER)of1in10000

•  Whichhaslessoverhead?–  Its=lldepends!Weneedtoknowmoreabouttheerrors

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Detec=onvs.Correc=on(2)1.  Assumebiterrorsarerandom

–  Messageshave0ormaybe1error

•  Errorcorrec=on:–  Need~10checkbitspermessage–  Overhead:

•  Errordetec=on:–  Need~1checkbitspermessageplus1000bit

retransmission1/10ofthe=me–  Overhead:

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Detec=onvs.Correc=on(3)2.  Assumeerrorscomeinburstsof100

–  Only1or2messagesin1000haveerrors

•  Errorcorrec=on:–  Need>>100checkbitspermessage–  Overhead:

•  Errordetec=on:–  Need32?checkbitspermessageplus1000

bitresend2/1000ofthe=me–  Overhead:

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Detec=onvs.Correc=on(4)•  Errorcorrec=on:– Neededwhenerrorsareexpected– Orwhenno=meforretransmission

•  Errordetec=on:– Moreefficientwhenerrorsarenotexpected

– Andwhenerrorsarelargewhentheydooccur

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ErrorCorrec=oninPrac=ce•  Heavilyusedinphysicallayer

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

–  Convolu=onalcodeswidelyusedinprac=ce

•  Errordetec=on(w/retransmission)isusedinthelinklayerandaboveforresidualerrors

•  Correc=onalsousedintheapplica=onlayer–  CalledForwardErrorCorrec=on(FEC)–  Normallywithanerasureerrormodel–  E.g.,Reed-Solomon(CDs,DVDs,etc.)

Topic•  Mul=plexingisthenetworkwordforthesharingofaresource

•  Classicscenarioissharingalinkamongdifferentusers–  TimeDivisionMul=plexing(TDM)»–  FrequencyDivisionMul=plexing(FDM)»

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TimeDivisionMul=plexing(TDM)

•  Userstaketurnsonafixedschedule

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2 2 2 2

FrequencyDivisionMul=plexing(FDM)•  Putdifferentusersondifferentfrequencybands

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OverallFDMchannel

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TDMversusFDM•  InTDMausersendsatahighrateafrac=onofthe=me;inFDM,ausersendsatalowrateallthe=me

Rate

TimeFDM

TDM

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TDMversusFDM(2)•  InTDMausersendsatahighrateafrac=onofthe=me;inFDM,ausersendsatalowrateallthe=me

Rate

TimeFDM

TDM

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TDM/FDMUsage•  Sta=callydividearesource–  Suitedforcon=nuoustraffic,fixednumberofusers

•  Widelyusedintelecommunica=ons–  TVandradiosta=ons(FDM)–  GSM(2Gcellular)allocatescallsusingTDMwithinFDM

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Mul=plexingNetworkTraffic•  Networktrafficisbursty

–  ON/OFFsources–  Loadvariesgreatlyover=me

Rate

TimeRate

Time

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Mul=plexingNetworkTraffic(2)•  Networktrafficisbursty–  InefficienttoalwaysallocateusertheirONneedswithTDM/FDM

Rate

TimeRate

Time

R

R

Mul=plexingNetworkTraffic(3)•  Mul=pleaccessschemesmul=plexusersaccordingtotheirdemands–forgainsofsta=s=calmul=plexing

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Rate

TimeRate

Time

Rate

Time

R

R

R’<2R

Twousers,eachneedR TogethertheyneedR’<2R

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Mul=pleAccess•  Wewilllookattwokindsofmul=ple

accessprotocols1.  Randomized.Nodesrandomizetheir

resourceaccessafempts–  Goodforlowloadsitua=ons

2.  Conten=on-free.Nodesordertheirresourceaccessafempts–  Goodforhighloadorguaranteed

qualityofservicesitua=ons

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Topic•  Howdonodesshareasinglelink?Whosendswhen,e.g.,inWiFI?–  Explorewithasimplemodel

•  Assumeno-oneisincharge;thisisadistributedsystem

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Topic(2)•  Wewillexplorerandommul=pleaccesscontrol(MAC)protocols–  ThisisthebasisforclassicEthernet–  Remember:datatrafficisbursty

Zzzz..Busy! Hohum

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ALOHANetwork•  Seminalcomputernetworkconnec=ngtheHawaiianislandsinthelate1960s– Whenshouldnodessend?–  AnewprotocolwasdevisedbyNormAbramson…

Hawaii

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ALOHAProtocol•  Simpleidea:–  Nodejustsendswhenithastraffic.–  Iftherewasacollision(noACKreceived)thenwaitarandom=meandresend

•  That’sit!

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ALOHAProtocol(2)•  Someframeswillbelost,butmanymaygetthrough…

•  Goodidea?

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ALOHAProtocol(3)•  Simple,decentralizedprotocolthatworkswellunderlowload!

•  Notefficientunderhighload–  Analysisshowsatmost18%efficiency–  Improvement:divide=meintoslotsandefficiencygoesupto36%

•  We’lllookatotherimprovements

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ClassicEthernet•  ALOHAinspiredBobMetcalfetoinventEthernetforLANsin1973–  Nodesshare10Mbpscoaxialcable–  Hugelypopularin1980s,1990s

:©2009IEEE

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CSMA(CarrierSenseMul=pleAccess)•  ImproveALOHAbylisteningforac=vitybeforewesend(Doh!)–  Candoeasilywithwires,notwireless

•  Sodoesthiseliminatecollisions?– Whyorwhynot?

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CSMA(2)•  S=llpossibletolistenandhearnothingwhenanothernodeissendingbecauseofdelay

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CSMA(3)•  CSMAisagooddefenseagainstcollisionsonlywhenBDissmall

X

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CSMA/CD(withCollisionDetec=on)•  Canreducethecostofcollisionsbydetec=ngthemandabor=ng(Jam)therestoftheframe=me–  Again,wecandothiswithwires

XXXXXXXXJam! Jam!

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CSMA/CDComplica=ons•  Wanteveryonewhocollidestoknowthatithappened–  Timewindowinwhichanodemayhearofacollisionis2Dseconds

X

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CSMA/CDComplica=ons(2)•  Imposeaminimumframesizethatlastsfor2Dseconds–  Sonodecan’tfinishbeforecollision–  Ethernetminimumframeis64bytes

X

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CSMA“Persistence”•  Whatshouldanodedoifanothernodeissending?

•  Idea:Waitun=litisdone,andsend

Whatnow?

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CSMA“Persistence”(2)•  Problemisthatmul=plewai=ngnodeswillqueueupthencollide– Moreload,moreofaproblem

Now! Now!Uhoh

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CSMA“Persistence”(3)•  Intui=onforabefersolu=on–  IfthereareNqueuedsenders,wewanteachtosendnextwithprobability1/N

Sendp=½WhewSendp=½

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BinaryExponen=alBackoff(BEB)•  Cleverlyes=matestheprobability

–  1stcollision,wait0or1frame=mes–  2ndcollision,waitfrom0to3=mes–  3rdcollision,waitfrom0to7=mes…

•  BEBdoublesintervalforeachsuccessivecollision–  Quicklygetslargeenoughtowork–  Veryefficientinprac=ce

ClassicEthernet,orIEEE802.3•  MostpopularLANofthe1980s,1990s–  10Mbpsoversharedcoaxialcable,withbasebandsignals– Mul=pleaccesswith“1-persistentCSMA/CDwithBEB”

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EthernetFrameFormat•  Hasaddressestoiden=fythesenderandreceiver•  CRC-32forerrordetec=on;noACKsorretransmission•  Startofframeiden=fiedwithphysicallayerpreamble

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PacketfromNetworklayer(IP)

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ModernEthernet•  Basedonswitches,notmul=pleaccess,buts=llcalledEthernet– We’llgettoitinalatersegment

Switch

TwistedpairSwitchports