codigoslinea line codes

LoCicero , J.L. & Patel, B.P. “Line Coding ” Mobile Communications HandbookEd. Suthan S. Suthersan Boca Raton: CRC Press LLC, 1999 c/circlecopyrt1999byCRCPressLLC LineCoding Josep hL.LoCicero Illinoi sInstitut eofTechnology Bhaske rP.Patel Illinoi sInstitut eofTechnology6.1 Introduction 6.2 Commo nLineCodingFormats Unipola rNRZ(Bina ryOn-Of fKeying)Unipola rRZPolar NRZPolarRZ[Bipola r,Alternat eMarkInversio n(AMI) ,or Pseudoterna ry]Mancheste rCodin g(SplitPhaseorDigital Biphase) 6.3 AlternateLineCodes DelayModulatio n(Mille rCode)SplitPhase(Mark)Biphase (Mark)CodeMarkInversio n(CMI)NRZ(I)BinaryN ZeroSubstitutio n(BNZS)High-Densi tyBipola rN(HDBN) TernaryCoding 6.4 MultilevelSignallin g,PartialRespons eSignallin g,and Duobina ryCoding MultilevelSignallingPartialRespons eSignallin gandDuobi- naryCoding 6.5 BandwidthComparison 6.6 Concludin gRemarks Definin gTerms References 6.1 Introduction Theterminolo gylinecodin goriginate dintelepho nywiththeneedtotransmi tdigitalinformation acrossacoppe rtelephon eline;morespecificall y,binarydataoveradigitalrepeate redline.The conceptoflinecoding,however,readilyapplie stoanytransmissio nlineorchannel .Inadigitalcom- municatio nsystem ,thereexistsaknownsetofsymbol stobetransmitted .Thes ecanbedesignatedas fmig,iD1;2;:::;N,withaprobabili tyofoccurrencefpig,iD1;2;:::;N,wherethesequentially transmitte dsymbol saregenerall yassume dtobestatisticall yindependent .Theconversio norcoding oftheseabstrac tsymbol sintoreal,tempora lwaveform stobetransmitte dinbaseban distheprocess oflinecoding.Sincethemostcommo ntypeoflinecodingisforbinarydata,suchawaveformcanbe succinctl yterme dadirectforma tforserialbits.Theconcentratio ninthissectio nwillbelinecoding forbinarydata. Diffe rentchanne lcharacte ristics ,aswellasdifferentapplication sandperforman cerequirements, haveprovidedtheimpetu sforthedevelopmen tandstudyofvarioustypesoflinecoding[1,2]. Forexample ,thechanne lmightbeaccouple dand,thus,couldnotsuppo rtalinecodewithadc componen torlargedccontent .Synch ronizatio nortimin grecoveryrequirement smightnecessitat ea discretecomponen tatthedatarate.Thechanne lband widthandcrosstal klimitation smightdictate c/circlecopyrt1999byCRCPressLLC thetypeoflinecodingempl oyed.Evensuchfactor sasthecomplexi tyoftheencoderandtheeconomy ofthedecodercoulddetermin ethelinecodechosen .Eachlinecodehasitsowndistinc tproperties. Dependin gontheapplication ,onepropertymaybemoreimpo rtantthantheother.Inwhatfollows, wedescribe,ingeneral ,themostdesirabl efeatu resthatareconside redwhenchoosin galinecode. Itiscommonl yaccepted[1,2,5,8]thatthedominan tconsideration seffectin gthechoiceofaline codeare:1)timin g,2)dccontent ,3)powerspectrum ,4)performan cemonito ring,5)probabili tyof error,and6)transpa rency.Eachofthesearedetaile dinthefollowingparagraphs. 1)Timing :Thewaveformproduce dbyalinecodeshoul dcontai nenou ghtimin ginformation suchthatthereceivercansynch ronizewiththetransmitte randdecodethereceivedsignalproperl y. Thetimin gconten tshoul dberelativelyindependen tofsourcestatistics ,i.e.,alongstringof1sor0s shoul dnotresultinlossoftimin gorjitteratthereceiver. 2)DCcontent :Sincetherepeater susedintelepho nyareaccoupled ,itisdesirabl etohavezero dcinthewaveformproduce dbyagivenlinecode.Ifasignalwithsignifican tdcconten tisused inaccouple dlines,itwillcausedcwande rinthereceivedwaveform .Thatis,thereceivedsignal baselin ewillvarywithtime.Telephon elinesdonotpassdcduetoaccouplin gwithtransformers andcapacitor stoeliminat edcgroundloops .Becaus eofthis,thetelephon echanne lcause sadroop inconstan tsignals.Thiscause sdcwande r.Itcanbeeliminate dbydcrestoratio ncircuits,feedback systems ,orwithspeciall ydesignedlinecodes. 3)Powerspectrum:Thepowerspectru mandband widthofthetransmitte dsignalshoul dbe matche dtothefrequenc yrespons eofthechanne ltoavoidsignifican tdisto rtion.Also,thepower spectru mshoul dbesuchthatmostoftheenergyiscontaine dinassmallband widthaspossible .The smalle ristheband width,thehigheristhetransmissio nefficienc y. 4)Performanc emonito ring:Itisverydesirabl etodetec terrorscause dbyanoisytransmission channel .Theerrordetectio ncapabili tyinturnallowsperforman cemonito ringwhilethechanne lis inuse(i.e.,withou telaborat etestin gproceduresthatrequiresuspendin guseofthechannel). 5)Probabilit yoferror:Theaverageerrorprobabili tyshoul dbeassmallaspossibl eforagiven transmitte rpower.Thisreflect sthereliabili tyofthelinecode. 6)Transparency :Alinecodeshoul dallowallthepossibl epattern sof1sand0s.Ifacertainpattern isundesirabl eduetootherconsiderations ,itshoul dbemappe dtoauniqu ealternati vepattern. 6.2 Commo nLineCodin gFormats Alinecodingforma tconsist sofaforma ldefinitio nofthelinecodethatspecifie showastringof binarydigitsareconvertedtoalinecodewaveform .Therearetwomajo rclasse sofbinarylinecodes: levelcodesandtransitio ncodes .Levelcodescarryinformatio nintheirvoltag elevel,whichmaybe highorlowforafullbitperiodorpartofthebitperiod.Levelcodesareusuall yinstantaneou ssince theytypicall yencodeabinarydigitintoadistinc twaveform ,independen tofanypastbinarydata. However,somelevelcodesdoexhibi tmemo ry.Transitio ncodescarryinformatio ninthechang ein levelappea ringinthelinecodewaveform .Transitio ncodesmaybeinstantaneous ,buttheygenerally havememo ry,usingpastbinarydatatodictat ethepresentwaveform .Therearetwocommo nforms oflevellinecodes:oneiscalledreturntozero(RZ)andtheotheriscallednonretu rntozero(NRZ) . InRZcoding,thelevelofthepulsereturn stozeroforaportionofthebitinterval.InNRZcoding, thelevelofthepulseismaintaine dduringtheentirebitinterval. Linecodingformat sarefurtherclassifie daccordingtothepolarityofthevoltag elevelsusedto representthedata.Ifonlyonepolarityofvoltag elevelisused,i.e.,positi veornegati ve(inaddition tothezerolevel)thenitiscalledunipola rsignallin g.Ifbothposit iveandnegat ivevoltag elevelsare beingused,withorwithou tazerovoltag elevel,thenitiscalledpolarsignallin g.Thetermbipolar c/circlecopyrt1999byCRCPressLLC signalling is used by some authors to designate a specific line coding scheme with positive, negative, and zero voltage levels. This will be described in detail later in this section. The formal definitionof five common line codes is given in the following along with a representative waveform, the power spectral density (PSD), the probability of error, and a discussion of advantages and disadvantages. In some cases specific applications are noted. 6.2.1 Unipolar NRZ (Binary On-Off Keying) In this line code, a binary 1is represented by a non-zero voltage level and a binary 0is represented by a zero voltage level as shown in Fig. 6.1(a). This is an instantaneous level code. The PSD of this code with equally likely 1s and 0si sg i v e nb y[ 5,8] S1.f /DV2T 4sinf T f T2 CV2 4.f/ (6.1) where Vis the binary 1voltage level, TD1=Ris the bit duration, and Ris the bit rate in bits per second. The spectrum of unipolar NRZ is plotted in Fig. 6.2a. This PSD is a two-sided even spectrum, although only half of the plot is shown for efficiency of presentation. If the probability of a binary1isp, and the probability of a binary 0is.1−p/, then the PSD of this code, in the most general case, is4p.1−p/ S 1.f /. Considering the frequency of the first spectral null as the bandwidth of the waveform, the bandwidth of unipolar NRZ is Rin hertz. The error rate performance of this code, for equally likely data, with additive white Gaussian noise (AWGN) and optimum, i.e., matched filter,d e t e c t i o ni sg i v e nb y[ 1,5] P eD1 2erfc s Eb 2N0! (6.2) where Eb=N0is a measure of the signal-to-noise ratio (SNR) of the received signal. In general, Ebis the energy per bit and N0=2is the two-sided PSD of the AWGN. More specifically, for unipolar NRZ, Ebis the energy in a binary 1,which is V2T. The performance of the unipolar NRZ code is plotted in Fig. 6.3 The principle advantages of unipolar NRZ are ease of generation, since it requires only a single power supply, and a relatively low bandwidth of RHz. There are quite a few disadvantages of this line code. A loss of synchronization and timing jitter can result with a long sequence of 1so r0s because no pulse transition is present. The code has no error detection capability and, hence, performancecannot be monitored. There is a significant dc component as well as a dc content. The error rateperformance is not as good as that of polar line codes. 6.2.2 Unipolar RZ Inthislinecode, abinary 1isrepresentedbyanonzerovoltagelevelduringaportionofthebitduration, usually for half of the bit period, and a zero voltage level for rest of the bit duration. A binary 0is represented by a zero voltage level during the entire bit duration. Thus, this is an instantaneous levelcode. Figure 6.1(b) illustrates a unipolar RZ waveform in which the 1is represented by a nonzero voltage level for half the bit period. The PSD of this line code, with equally likely binary digits, isg i v e nb y[ 5,6,8] S 2.f /DV2T 16sinf T =2 f T =22 c/circlecopyrt1999 by CRC Press LLC 1 Unipolar RZ (a)0110001110 T3 T2T 4T 5T 6T 7T 8T 9T 10T 11T T3 T2T 4T 5T 6T 7T 8T 9T 10T 11TUnipolar RZ (b) Polar NRZ (c) Bipolar (AMI) (d) Manchester (Bi-phase) (e) Delay Modulation (f) Split Phase (Mark) (g) Split Phase (Space) (h) Bi-Phase (Mark) (i) Bi-Phase (Space) (j) Code Mark Inversion (k) NRZ (M) (l) NRZ (s) (m) FIGURE 6.1: Waveforms for different line codes.c/circlecopyrt1999 by CRC Press LLC Figure 6.2a Power spectral density of different line codes, where RD1=T is the bit rate. CV2 42" 2 4.f/C1X nD−11 .2nC1/2.f−.2nC1/R/# (6.3) where again Vis the binary 1voltage level, and TD1=Ris the bit period. The spectrum of this code is drawn in Fig. 6.2a. In the most general case, when the probability of a 1isp, the continuous portion of the PSD in Eq. ( 6.3) is scaled by the factor 4p.1−p/and the discrete portion is scaled by the factor 4p2. The first null bandwidth of unipolar RZ is 2RHz. The error rate performance of this line code is the same as that of the unipolar NRZ provided we increase the voltage level of this codesuch that the energy in binary 1,E b, is the same for both codes. The probability of error is given by Eq. ( 6.2) and identified in Fig. 6.3. If the voltage level and bit period are the same for unipolar NRZ and unipolar RZ, then the energy in a binary 1for unipolar RZ will be V2T=2and the probability of e r r o ri sw o r s eb y3d B . The main advantages of unipolar RZ are, again, ease of generation since it requires a single power supply and the presence of a discrete spectral component at the symbol rate, which allows simpletiming recovery. A number of disadvantages exist for this line code. It has a nonzero dc componentand nonzero dc content, which can lead to dc wander. A long string of 0s will lack pulse transitions and could lead to loss of synchronization. There is no error detection capability and, hence, performancemonitoring is not possible. The bandwidth requirement ( 2RHz) is higher than that of NRZ signals. The error rate performance is worse than that of polar line codes. Unipolar NRZ as well as unipolar RZ are examples of pulse =no-pulse type of signalling. In this c/circlecopyrt1999 by CRC Press LLC Figure 6.2b Power spectral density of different line codes, where RD1=T is the bit rate. type of signalling, the pulse for a binary 0,g2.t/, is zero and the pulse for a binary 1is specified generically as g1.t/Dg.t/. Using G.f / as the Fourier transform of g.t/, the PSD of pulse =no-pulse signalling is given as [ 6,7,10] SPNP.f /Dp.1−p/RjG.f /j2Cp2R21X nD−1jG.nR/ j2.f−nR/ (6.4) where pis the probability of a binary 1,andRis the bit rate. 6.2.3 Polar NRZ In this line code, a binary 1is represented by a positive voltage CVand a binary 0is represented by a negative voltage −Vover the full bit period. This code is also referred to as NRZ (L), since a bit is represented by maintaining a level (L) during its entire period. A polar NRZ waveform is shownin Fig. 6.1(c). This is again an instantaneous level code. Alternatively, a 1may be represented by a −Vvoltage level and a 0by aCVvoltage level, without changing the spectral characteristics and c/circlecopyrt1999 by CRC Press LLC FIGURE 6.3: Bit error probability for different line codes. performance of the line code. The PSD of this line code with equally likely bits is given by [ 5,8] S3.f /DV2Tsinf T f T2 (6.5) This is plotted in Fig. 6.2b. When the probability of a 1isp, andpis not 0.5, a dc component exists, and the PSD becomes [ 10] S3p.f /D4V2Tp.1−p/sinf T f T2 CV2.1−2p/2.f/ (6.6) c/circlecopyrt1999 by CRC Press LLC Thefirstnullband widthforthislinecodeisagainRHz,independen tofp.Theprobabili tyoferror ofthislinecodewhenpD0:5isgivenby[1,5] PeD1 2erfc s Eb N0! (6.7) Theperforman ceofpolarNRZisplotte dinFig.6.3.Thisisbette rthantheerrorperforman ceofthe unipola rcodesby3dB. Theadvantage sofpolarNRZinclud ealow-band widthrequirement ,RHz,comparabl etounipo- larNRZ ,verygooderrorprobabili ty,andgreatlyreduceddcbecaus ethewaveformhasazerodc componen twhenpD0:5eventhoughthedcconten tisneverzero.Afewnotabl edisadvantages arethatthereisnoerrordetectio ncapabili ty,andthatalongstringof1sor0scouldresultinlossof synch ronization ,sincetherearenotransition sduringthestringduration .Twopowersupplie sare requiredtogenerat ethiscode. 6.2.4 PolarRZ[Bipola r,AlternateMarkInversio n(AMI) ,orPseudote rnary] Inthisscheme ,abinary1isrepresente dbyalternatin gthepositi veandnegati vevoltag elevels,which returntozeroforaportionofthebitduration ,generall yhalfthebitperiod.Abinary0isrepresented byazerovoltag elevelduringtheentirebitduration .Thislinecodingschem eisoftencalledalternate markinversio n(AMI )since1s(marks )arerepresente dbyalternatin gpositi veandnegati vepulses. Itisalsocalledpseudote rnarysincethreedifferentvoltag elevelsareusedtorepresentbinarydata. Someauthor sdesignatethislinecodeasbipola rRZ(BRZ) .AnAMIwaveformisshowninFig.6.1(d). Notethatthisisalevelcodewithmemo ry.TheAMIcodeiswellknownforitsuseintelepho ny.The PSDofthislinecodewithmemo ryisgivenby[1,2,7] S4p.f/D2p.1−p/RjG.f/j21−cos2fT 1C.2p−1/2C2.2p−1/cos2fT (6.8) whereG.f/istheFouriertransfor mofthepulseusedtorepresentabinary1,andpistheprobabili ty ofabinary1.WhenpD0:5andsquarepulse swithamplitud eVandduratio nT=2areusedto representbinary1s,thePSDbecomes S4.f/DV2T 4sinfT=2 fT=22 sin2.fT/ (6.9) ThisPSDisplotte dinFig.6.2a.Thefirstnullband widthofthiswaveformisRHz.Thisistruefor RZrectangula rpulses ,independen tofthevalueofpinEq.(6.8).Theerrorrateperforman ceofthis linecodeforequall ylikelybinarydataisgivenby[5] Pe3 4erfc s Eb 2N0! ;E b=N0>2 (6.10) Thiscurveisplotte dinFig.6.3andisseentobenomorethan0.5dBworsethantheunipola rcodes. Theadvantage sofpolarRZ(orAMI,asitismostcommonl ycalled )outwei ghthedisadvantages. Thiscodehasnodccomponen tandzerodccontent ,completel yavoidin gthedcwande rproblem. Timingrecoveryisrathe reasysincesquaring,orfull-w averectifying,thistypeofsignalyieldsa unipola rRZwaveformwithadiscretecomponen tatthebitrate,RHz.Becaus eofthealternating c/circlecopyrt1999byCRCPressLLC polarity pulses for binary 1s, this code has error detection and, hence, performance monitoring capability. It has a low-bandwidth requirement, RHz, comparable to unipolar NRZ. The obvious disadvantage is that the error rate performance is worse than that of the unipolar and polar waveforms.Al o n gs t r i n go f 0s could result in loss of synchronization, and two power supplies are required for this code. 6.2.5 Manchester Coding (Split Phase or Digital Biphase) In this coding, a binary 1is represented by a pulse that has positive voltage during the first-half of the bit duration and negative voltage during second-half of the bit duration. A binary 0is represented by a pulse that is negative during the first-half of the bit duration and positive during the second-half of the bit duration. The negative or positive midbit transition indicates a binary 1or binary 0,respectively. Thus, a Manchester code is classified as an instantaneous transition code; it has no memory. The code is also called diphase because a square wave with a 0 phase is used to represent a binary 1and a square wave with a phase of 180used to represent a binary 0;or vice versa. This line code is used in Ethernet local area networks (LANs). The waveform for Manchester coding is shownin Fig. 6.1(e). The PSD of a Manchester waveform with equally likely bits is given by [ 5,8] S 5.f /DV2Tsinf T =2 f T =22 sin2.f T =2/ (6.11) where Vare used as the positive =negative voltage levels for this code. Its spectrum is plotted in Fig.6.2b. When the probability pof a binary 1,is not equal to one-half, the continuous portion of the PSD is reduced in amplitude and discrete components appear at integer multiples of the bit rate,RD1=T. The resulting PSD is [ 6,10] S 5p.f /DV2T4p.1−p/sinf T =2 f T =22 sin2f T 2 CV2.1−2p/21X nD−1 ;n6D02 n2 .f−nR/ (6.12) The first null bandwidth of the waveform generated by a Manchester code is 2RHz. The error rate performance of this waveform when pD0:5is the same as that of polar NRZ, given by Eq. ( 6.9), and plotted in Fig. 6.3. The advantages of this code include a zero dc content on an individual pulse basis, so no pattern of bits can cause dc buildup; midbit transitions are always present making it is easy to extract timinginformation; and it has good error rate performance, identical to polar NRZ. The main disadvantageof this code is a larger bandwidth than any of the other common codes. Also, it has no error detectioncapability and, hence, performance monitoring is not possible. Polar NRZ and Manchester coding are examples of the use of pure polar signalling where the pulse for a binary 0,g 2.t/is the negative of the pulse for a binary 1,i.e.,g2.t/D−g1.t/. This is also referred to as an antipodal signal set. For this broad type of polar binary line code, the PSD is givenby [10] S BP.f /D4p.1−p/RjG.f /j2C.2p−1/2R21X nD−1jG.nR/ j2.f−nR/ (6.13) where jG.f /jis the magnitude of the Fourier transform of either g1.t/org2.t/. c/circlecopyrt1999 by CRC Press LLC A further generalization of the PSD of binary line codes can be given, wherein a continuous spectrum and a discrete spectrum is evident. Let a binary 1,with probability p, be represented by g1.t/over the TD1=Rsecond bit interval; and let a binary 0,with probability 1−p, be represented byg2.t/over the same Tsecond bit interval. The two-sided PSD for this general binary line code is [10] SGB.f /Dp.1−p/RjG1.f /−G2.f /j2 CR21X nD−1jpG1.nR/C.1−p/G2.nR/j2.f−nR/ (6.14) where the Fourier transform of g1.t/andg2.t/are given by G1.f /andG2.f /, respectively. 6.3 Alternate Line Codes Most of the line codes discussed thus far were instantaneous level codes. Only AMI had memory, and Manchester was an instantaneous transition code. The alternate line codes presented in this sectionall have memory. The first four are transition codes, where binary data is represented as the presenceor absence of a transition, or by the direction of transition, i.e., positive to negative or vice versa. Thelast four codes described in this section are level line codes with memory. 6.3.1 Delay Modulation (Miller Code) In this line code, a binary 1is represented by a transition at the midbit position, and a binary 0is represented by no transition at the midbit position. If a 0is followed by another 0,however, the signal transition also occurs at the end of the bit interval, that is, between the two 0s. An example of delay modulation is shown in Fig. 6.1(f). It is clear that delay modulation is a transition code with memory. This code achieves the goal of providing good timing content without sacrificing bandwidth. ThePSD of the Miller code for equally likely data is given by [ 10] S 6.f /DV2T 2.f T /2.17C8cos2 f T / .23−2cosf T−22cos2 f T −12cos3 f TC5cos4 f TC12cos5 f T C2cos6 f T−8cos7 f TC2cos8 f T / (6.15) This spectrum is plotted in Fig. 6.2b. The advantages of this code are that it requires relatively low bandwidth, most of the energy is contained in less than 0:5R. However, there is no distinct spectral null within the 2R-Hz band. It has low dc content and no dc component. It has very good timing content, and carrier tracking is easier than Manchester coding. Error rate performance iscomparable to that of the common line codes. One important disadvantage is that it has no errordetection capability and, hence, performance cannot be monitored. 6.3.2 Split Phase (Mark) This code is similar to Manchester in the sense that there are always midbit transitions. Hence,this code is relatively easy to synchronize and has no dc. Unlike Manchester, however, split phase(mark) encodes a binary digit into a midbit transition dependent on the midbit transition in the c/circlecopyrt1999 by CRC Press LLC previousbitperiod[12].Specificall y,abinary1producesareversalofmidbi ttransitio nrelativeto thepreviousmidbi ttransition .Abinary0produce snoreversalofthemidbi ttransition .Certainly thisisatransitio ncodewithmemo ry.Anexampl eofasplitphase(mark )codedwaveformisshown inFig.6.1(g),wherethewaveforminthefirstbitperiodischose narbitrarily.Sincethismethod encodesbitsdifferentiall y,thereisno180-phas eambigui tyassociate dwithsomelinecodes.This phaseambigui tymaynotbeanissueinmostbaseban dlinksbutisimpo rtantifthelinecodeis modulated .Splitphase(space)isverysimila rtosplitphase(mark) ,wheretheroleofthebinary 1andbinary0areinterchanged .Anexampl eofasplitphase(space)codedwaveformisgivenin Fig.6.1(h);again ,thefirstbitwaveformisarbitrary. 6.3.3 Biphas e(Mark) Thiscode,designatedasBi-M,issimila rtoaMille rcodeinthatabinary1isrepresente dbyamidbit transition ,andabinary0hasnomidbi ttransition .However,thiscodealwayshasatransitio natthe beginnin gofabitperio d[10].Thus ,thecodeiseasytosynch ronizeandhasnodc.Anexampl eofBi -MisgiveninFig.6.1(i),wherethedirectio nofthetransitio natt=0isarbitrarilychosen .Biphase (space)orBi-Sissimila rtoBi-M,excepttheroleofthebinarydataisreversed .Hereabinary0 (space)producesamidbi ttransition ,andabinary1doesnothaveamidbi ttransition .Awaveform exampl eofBi-SisshowninFig.6.1(j).BothBi-SandBi-Maretransitio ncodeswithmemo ry. 6.3.4 CodeMarkInversio n(CMI) Thislinecodeisusedastheinterfa cetoaConsultati veCommitte eonInternationa lTelegraphyand Telepho ny(CCI TT)multiple xerandisverysimila rtoBi-S.Abinary1isencodedasanNRZpulse withalternat epolarity,CVor−V.Abinary0isencodedwithadefiniti vemidbi ttransitio n(or squarewavephase )[1].Anexampl eofthiswaveformisshowninFig.6.1(k)whereanegat iveto positi vetransitio n(or180phase )isusedforabinary0.Thevoltag elevelofthefirstbinary1in thisexampl eischose narbitrarily.Thisexampl ewaveformisidentica ltoBi-SshowninFig.6.1(j), exceptforthelastbit.CMIhasgoodsynch ronizatio npropertiesandhasnodc. 6.3.5 NRZ(I) Thistypeoflinecodeusesaninversio n(I)todesignatebinarydigits,specificall y,achang einlevelor nochang einlevel.Therearetwovariantsofthiscode,NRZmark(M)andNRZspace(S)[5,12].In NRZ(M),achang eoflevelisusedtoindicat eabinary1,andnochang eoflevelisusedtoindicat ea binary0.InNRZ(S)achang eoflevelisusedtoindicat eabinary0,andnochang eoflevelisusedto indicat eabinary1.Waveform sforNRZ(M)andNRZ(S)aredepicte dinFig.6.1(l)andFig.6.1(m), respecti vely,wherethevoltag elevelofthefirstbinary1intheexampl eischose narbitrarily.These codesarelevelcodeswithmemo ry.Ingeneral ,linecodesthatusedifferentia lencoding,likeNRZ (I),areinsensiti veto180phaseambigui ty.ClockrecoverywithNRZ(I)isnotparticularl ygood, anddcwande risaproblemaswell.Itsband widthiscomparabl etopolarNRZ. 6.3.6 Bina ryNZeroSubstitutio n(BNZS) Thecommo nbipola rcodeAMIhasmanydesirabl epropertiesofalinecode.Itsmajo rlimitation, however,isthatalongstringofzeroscanleadtolossofsynch ronizatio nandtimin gjitterbecause therearenopulse sinthewaveformforrelativelylongperiodsoftime.Bina ryNzerosubstitution (BNZS )attempt stoimproveAMIbysubstitutin gaspecia lcodeoflengt hNforallstringsofNzeros. c/circlecopyrt1999byCRCPressLLC This special code contains pulses that look like binary 1s but purposely produce violations of the AMI pulse convention. Two consecutive pulses of the same polarity violate the AMI pulse convention,independent of the number of zeros between the two consecutive pulses. These violations can bedetected at the receiver, and the special code replaced by Nzeros. The special code contains pulses facilitating synchronization even when the original data has long string of zeros. The special code ischosen such that the desirable properties of AMI coding are retained despite the AMI pulse conventionviolations, i.e., dc balance and error detection capability. The only disadvantage of BNZS comparedto AMI is a slight increase in crosstalk due to the increased number of pulses and, hence, an increasein the average energy in the code. Choosing different values of Nyields different BNZS codes. The value of Nis chosen to meet the timing requirements of the application. In telephony, there are three commonly used BNZS codes:B6ZS, B3ZS, and B8ZS. All BNZS codes are level codes with memory. In a B6ZS code, a string of six consecutive zeros is replaced by one of two the special codes according to the rule: If the last pulse was positive ( C), the special code is: 0C−0−C . If the last pulse was negative ( −), the special code is: 0−C0C− . Here a zero indicates a zero voltage level for the bit period; a plus designates a positive pulse; and a minus indicates a negative pulse. This special code causes two AMI pulse violations: in its second bit position and in its fifth bit position. These violations are easily detected at the receiver and zeros resubstituted. If the number ofconsecutive zeros is 12;18;24;:::; the substitution is repeated 2;3;4;:::times. Since the number of violations is even, the B6ZS waveform is the same as the AMI waveform outside the special code,i.e., between special code sequences. There are four pulses introduced by the special code that facilitates timing recovery. Also, note that the special code is dc balanced. An example of the B6ZS code is given as follows, where the specialcode is indicated by the bold characters. Original data: 01000000110100000011 B6ZS format: 0C 0+ − 0− +−C 0− 0− +0+ −C− The computation of the PSD of a B6ZS code is tedious. Its shape is given in Fig. 6.4, for comparison purposes with AMI, for the case of equally likely data. In a B3ZS code, a string of three consecutive zeros is replaced by either B0Vor00V,w h e r e Bdenotes a pulse obeying the AMI (bipolar) convention and Vdenotes a pulse violating the AMI convention. B0Vor00Vis chosen such that the number of bipolar ( B) pulses between the violations is odd. The B3ZS rules are summarized in Table 6.1. TABLE 6.1 B3ZS Substitution Rules Number of BPulses Polarity of Last Substitution Substitution Since Last Violation BPulse Code Code Form Odd Negative ( −) 00– 0 0 V Odd Positive ( C) 00+ 0 0 V Even Negative ( −) +0+ B0V Even Positive ( C) –0– B0V Observe that the violation always occurs in the third bit position of the substitution code, and c/circlecopyrt1999 by CRC Press LLC FIGURE 6.4: Power spectral density of different line codes, where RD1=T is the bit rate. so it can be easily detected and zero replacement made at the receiver. Also, the substitution code selection maintains dc balance. There is either one or two pulses in the substitution code, facilitatingsynchronization. The error detection capability of AMI is retained in B3ZS because a single channelerror would make the number of bipolar pulses between violations even instead of being odd. UnlikeB6ZS, the B3ZS waveform between violations may not be the same as the AMI waveform. B3ZS isused in the digital signal-3 (DS-3) signal interface in North America and also in the long distance-4(LD-4) coaxial transmission system in Canada. Next is an example of a B3ZS code, using the samesymbol meaning as in the B6ZS code. Original data: 100100011000010001 B3ZS format: Even No. of Bpulses: C00 − +0+ −C− 0−0C 00+ − Odd No. of Bpulses: C00 − 00 −C− +0+ 0− 00 −C The last BNZS code considered here uses ND8. A B8ZS code is used to provide transparent channels for the Integrated Services Digital Network (ISDN) on T1 lines and is similar to the B6ZScode. Here a string of eight consecutive zeros is replaced by one of two special codes according to the c/circlecopyrt1999 by CRC Press LLC followingrule: Ifthelastpulsewaspositi ve(C),thespecia lcodeis: 000 C−0−C: Ifthelastpulsewasnegat ive(−),thespecia lcodeis: 000 −C0C−: Therearetwobipola rviolation sinthespecia lcodes,atthefourthandseventhbitpositions .The codeisdcbalan ced,andtheerrordetectio ncapabili tyofAMIisretained .Thewaveformbetween substitution sisthesameasthatofAMI.Ifthenumbe rofconsecuti vezerosis16;24;:::;thenthe substitutio nisrepeate d2;3;:::;times. 6.3.7 High-Densit yBipola rN(HDBN) ThiscodingalgorithmisaCCITTstanda rdrecommende dbytheConfe renceofEuropeanPosts andTelecommunication sAdministration s(CEP T),aEuropeanstanda rdsbody.Itisquitesimila rto BNZ Scoding.Itisthusalevelcodewithmemo ry.Whene verthereisastringofNC1consecut ive zeros,theyarereplacedbyaspecia lcodeoflengt hNC1containin gAMIviolations .Specifi ccodes canbeconstructe dfordifferentvalue sofN.Aspecifi chigh-densi tybipola rN(HDBN )code,HDB3, isimplemente dasaCEPTprimarydigitalsignal.Itisverysimila rtotheB3ZScode.Inthiscode,a stringoffourconsecuti vezerosisreplacedbyeithe rB00Vor000V.B00Vor000Vischose nsuch thatthenumbe rofbipola r(B)pulse sbetwee nviolation sisodd.TheHDB 3rulesaresumma rized inTable6.2. TABLE6.2 HDB 3Substitutio nRules Numbe rofBPulses PolarityofLast Substitution Substitution SinceLastViolation BPulse Code CodeForm Odd Negative(−) 000– 000V Odd Positive(C) 000+ 000V Even Negative(−) +00+ B00V Even Positive(C) –00– B00V Heretheviolatio nalwaysoccursinthefourthbitpositio nofthesubstitutio ncode,sothatitcan beeasilydetecte dandzeroreplacemen tmadeatthereceiver.Also,thesubstitutio ncodeselection maintain sdcbalan ce.Thereiseithe roneortwopulse sinthesubstitutio ncodefacilitatin gsynch ro- nization .Theerrordetectio ncapabili tyofAMIisretaine dinHDB 3becaus easinglechanne lerror wouldmakethenumbe rofbipola rpulse sbetwee nviolation seveninstea dofbeingodd. 6.3.8 TernaryCoding Manylinecodingscheme sempl oythreesymbol sorlevelstorepresentonlyonebitofinformation, likeAMI.Theo reticall y,itshoul dbepossibl etotransmi tinformatio nmoreefficientl ywiththree symbols ,specificall ythemaximu mefficienc yislog23D1:58bitspersymbol .Alternati vely,the redundanc yinthecodesignalspacecanbeusedtoprovidebette rerrorcontrol.Twoexample sof terna rycodingaredescribednext[1,2]:pairselecte dternary(PST)and4binary3ternary(4B3 T). ThePSTcodehasmanyofthedesirabl epropertiesoflinecodes,butitstransmissio nefficienc yisstill 1bitpersymbol .The4B3Tcodealsohasmanyofthedesirabl epropertiesoflinecodes,andithas increasedtransmissio nefficienc y. c/circlecopyrt1999byCRCPressLLC In the PST code, two consecutive bits, termed a binary pair, are grouped together to form a word. These binary pairs are assigned codewords consisting of two ternary symbols, where each ternarysymbol can be C,−, or 0, just as in AMI. There are nine possible ternary codewords. Ternary codewords with identical elements, however, are avoided, i.e., CC,−−, and 00. The remaining six codewords are transmitted using two modes called Cmode and −mode. The modes are switched whenever a codeword with a single pulse is transmitted. The PST code and mode switching rules aresummarized in Table 6.3. TABLE 6.3 PST Codeword Assignment and Mode Switching Rules Ternary Codewords Mode Binary Pair CMode −Mode Switching 11 C− C− No 10 C0 −0Y e s 01 0 C 0− Yes 00 −C −C No PST is designed to maintain dc balance and include a strong timing component. One drawback of this code is that the bits must be framed into pairs. At the receiver, an out-of-frame condition is signalled when unused ternary codewords ( CC,−−, and 00) are detected. The mode switching property of PST provides error detection capability. PST can be classified as a level code with memory. If the original data for PST coding contains only 1so r0s, an alternating sequence of C− C−


is transmitted. As a result, an out-of-frame condition can not be detected. This problem can beminimized by using the modified PST code as shown in Table 6.4. TABLE 6.4 Modified PST Codeword Assignment and Mode Switching Rules Ternary Codewords Mode Binary Pair CMode −Mode Switching 11 C00 − Yes 10 C− C− No 01 −C −C No 00 0 C− 0Y e s It is tedious to derive the PSD of a PST coded waveform. Again, Fig. 6.4shows the PSD of the PST code along with the PSD of AMI and B6ZS for comparison purposes, all for equally likely binarydata. Observe that PST has more power than AMI and, thus, a larger amount of energy per bit, whichtranslates into slightly increased crosstalk. In 4B3T coding, words consisting of four binary digits are mapped into three ternary symbols. Four bits imply 2 4D16possible binary words, whereas three ternary symbols allow 33D27possible ternary codewords. The binary-to-ternary conversion in 4B3T insures dc balance and a strong timingcomponent. The specific codeword assignment is as shown in Table 6.5. There are three types of codewords in Table 6.5, organized into three columns. The codewords in c/circlecopyrt1999 by CRC Press LLC TABLE 6.5 4B3T Codeword Assignment Ternary Codewords Binary Words Column 1 Column 2 Column 3 0000 −−− CCC 0001 −−0 CC0 0010 −0−C 0C 0011 0−− 0CC 0100 −−C CC− 0101 −C− C−C 0110 C−− −CC 0111 −00 C00 1000 0−00 C0 1001 00− 00C 1010 0C− 1011 0−C 1100 C0− 1101 −0C 1110 C−0 1111 −C0 the first column have negative dc, codewords in the second column have zero dc, and those in the third column have positive dc. The encoder monitors the integer variable IDNp−Nn; (6.16) where Npis the number of positive pulses transmitted and Nnare the number of negative pulses transmitted. Codewords are chosen according to following rule: IfI<0, choose the ternary codeword from columns 1 and 2. IfI>0, choose the ternary codeword from columns 2 and 3. IfID0, choose the ternary word from column 2, and from column 1 if the previous I>0or from column 3 if the previous I<0. Note that the ternary codeword 000 is not used, but the remaining 26 codewords are used in a complementary manner. For example, the column 1 codeword for 0001 is −−0, whereas the column 3c o d e w o r di s CC0. The maximum transmission efficiency for the 4B3T code is 1.33 bits per symbol compared to 1 bit per symbol for the other line codes. The disadvantages of 4B3T are that framing isrequired and that performance monitoring is complicated. The 4B3T code is used in the T148 spanline developed by ITT Telecommunications. This code allows transmission of 48 channels using only50% more bandwidth than required by T1 lines, instead of 100% more bandwidth. 6.4 Multilevel Signalling, Partial Response Signalling, and Duobinary Coding Ternary coding, such as 4B3T, is an example of the use of more than two levels to improve the trans- mission efficiency. To increase the transmission efficiency further, more levels and =or more signal c/circlecopyrt1999 by CRC Press LLC processin gisneeded .Multile velsignallin gallowsanimprovemen tinthetransmissio nefficienc yat theexpens eofanincreaseintheerrorrate,i.e.,moretransmitte rpowerwillberequiredtomaintain agivenprobabili tyoferror.Inpartialrespons esignallin g,inters ymbolinterfe renceisdeliberately introducedbyusingpulse sthatarewiderand,hence,requirelessband width.Thecontrolledamount ofinterfe rencefromeachpulsecanberemovedatthereceiver.Thisimprovesthetransmissio neffi- cienc y,attheexpens eofincreasedcomplexi ty.Duobina rycoding ,aspecia lcaseofpartialresponse signallin g,requiresonlytheminimu mtheoreticalband widthof0:5RHz.Inwhatfollowsthese technique sarediscusse dinslightlymoredetail. 6.4.1 Multileve lSignalling Thenumbe roflevelsthatcanbeusedforalinecodeisnotrestrictedtotwoorthree.Sincemore levelsorsymbol sallowhighertransmissio nefficienc y,multile velsignallin gcanbeconside redin band width-limite dapplications .Specificall y,ifthesignallin grateorbaudrateisRsandthenumber oflevelsusedisL,theequivalen ttransmissio nbitrateRbisgivenby RbDRslog2TLU: (6.17) Alternati vely,multile velsignallin gcanbeusedtoreducethebaudrate,whichinturncanreduce crosstal kforthesameequivalen tbitrate.Thepenal ty,however,isthattheSNRmustincreaseto achie vethesameerrorrate.TheT1GcarriersystemofAT&Tusesmultile velsignallin gwithLD4 andabaudrateof3.152mega-s ymbols=stodoubl ethecapaci tyoftheT1Csystemfrom48channels to96channels .Also,afourlevelsignallin gschem eat80-kBisusedtoachie ve160kb=sasabasic rateinadigitalsubsc riberloop(DSL )forISDN. 6.4.2 PartialRespons eSignallin gandDuobina ryCoding Thisclassofsignallin gisalsocalledcorrelativ ecodingbecaus eitpurposel yintroducesacontrolledor correlatedamoun tofinters ymbolinterfe renceineachsymbol .Atthereceiver,theknownamoun tof interfe renceiseffecti velyremovedfromeachsymbol .Theadvantag eofthissignallin gisthatwider pulse scanbeusedrequiringlessband width,buttheSNRmustbeincreasedtorealizeagivenerror rate.Also,errorscanpropagat eunles sprecodin gisused. Therearemanycommonl yusedpartialrespons esignallin gschemes ,oftendescribedinterms ofthedelayoperato rD,whichrepresent sonesignallin gintervaldelay.Forexample ,in.1CD/ signallin gthecurrentpulseandthepreviouspulseareadded .TheT1DsystemofAT&Tuses.1CD/ signallin gwithprecoding,referredtoasduobina rysignallin g,toconvertbinary(twolevel)datainto terna ry(threelevel)dataatthesamerate.Thisrequirestheminimu mtheoreticalchanne lband width withou tthedelete riouseffect sofinters ymbolinterfe renceandavoidserrorpropagation .Complete detail sregardingduobina rycodingarefoundinLende r,1963andSchwartz,1980 .Somepartial respons esignallin gschemes ,suchas.1−D/,areusedtoshapetheband widthrathe rthancontrolit. Anothe rinterestingexampl eofduobina rycodingisa.1−D2/,whichcanbeanalyze dastheproduct .1−D/.1CD/.ItisusedbyGTEinitsmodifie dTcarriersystem .AT&Talsouses.1−D2/with fourinputlevelstoachie veanequivalen tdatarateof1.544Mb=sinonlya0.5-MH zband width. 6.5 Bandwidt hComparison WehaveprovidedthePSDexpression sformostofthecommonl yusedlinecodes.Theactual band widthrequirement ,however,depend sonthepulseshapeusedandthedefinitio nofband width c/circlecopyrt1999byCRCPressLLC itself. There are many ways to define bandwidth, for example, as a percentage of the total power or the sidelobe suppression relative to the main lobe. Using the first null of the PSD of the code as thedefinition of bandwidth, Table 6.6provides a useful bandwidth comparison. TABLE 6.6 First Null Bandwidth Comparison Bandwidth Codes Unipolar NRZ BNZS R Polar NRZ HDBN Polar RZ (AMI) PST 2R Unipolar RZ Split Phase Manchester CMI The notable omission in Table 6.6is delay modulation (Miller code). It does not have a first null in the2R-Hz band, but most of its power is contained in less than 0:5RHz. 6.6 Concluding Remarks An in-depth presentation of line coding, particularly applicable to telephony, has been included in this chapter. The most desirable characteristics of line codes were discussed. We introduced five commonline codes and eight alternate line codes. Each line code was illustrated by an example waveform. Inmost cases expressions for the PSD and the probability of error were given and plotted. Advantagesand disadvantages of all codes were included in the discussion, and some specific applications werenoted. Line codes for optical fiber channels and networks built around them, such as fiber distributeddata interface (FDDI) were not included in this section. A discussion of line codes for optical fiberchannels, and other new developments in this topic area can be found in [ 1,3,4]. Defining Terms Alternate mark inversion (AMI): A popular name for bipolar line coding using three levels: zero, positive, and negative. Binary Nzero substitution (BNZS): A class of coding schemes that attempts to improve AMI line coding. Bipolar: A particular line coding scheme using three levels: zero, positive, and negative. Crosstalk: An unwanted signal from an adjacent channel. DC wander: The dc level variation in the received signal due to a channel that cannot support dc. Duobinary coding: A coding scheme with binary input and ternary output requiring the min- imum theoretical channel bandwidth. 4 Binary 3 Ternary (4B3T): A line coding scheme that maps four binary digits into three ternary symbols. High-density bipolar N(HDBN): A class of coding schemes that attempts to improve AMI. c/circlecopyrt1999 by CRC Press LLC Level codes: Line codes carrying information in their voltage levels. Line coding: The process of converting abstract symbols into real, temporal waveforms to be transmitted through a baseband channel. Nonreturn to zero (NRZ): A signal that stays at a nonzero level for the entire bit duration. Pair selected ternary (PST): A coding scheme based on selecting a pair of three level symbols. Polar: A line coding scheme using both polarity of voltages, with or without a zero level. Return to zero (RZ): A signal that returns to zero for a portion of the bit duration. Transition codes: Line codes carrying information in voltage level transitions. Unipolar: A line coding scheme using only one polarity of voltage, in addition to a zero level. References [1] Bellamy, J., Digital Telephony, John Wiley & Sons, New York, NY, 1991. [2] Bell Telephone Laboratories Technical Staff Members. Transmission Systems for Communica- tions, 4th ed., Western Electric Company, Technical Publications, Winston-Salem, NC, 1970. [3] Bic, J.C., Duponteil, D., and Imbeaux, J.C., Elements of Digital Communication, John Wiley & Sons, New York, NY, 1991. [4] Bylanski, P ., Digital Transmission Systems, Peter Peregrinus, Herts, England, 1976. [5] Couch, L.W., Modern Communication Systems: Principles and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1994. [6] Feher, K., Digital Modulation Techniques in an Interference Environment, EMC Encyclopedia Series, Vol. IX. Don White Consultants, Germantown, MD, 1977. [7] Gibson, J.D., Principles of Analog and Digital Communications, MacMillan Publishing, New York, NY, 1993. [8] Lathi, B.P ., Modern Digital and Analog Communication Systems, Holt, Rinehart and Winston, Philadelphia, PA, 1989. [9] Lender, A., Duobinary Techniques for High Speed Data Transmission, IEEE Trans. Commun. Electron., CE-82, 214–218, May 1963. [10] Lindsey, W.C. and Simon, M.K., Telecommunication Systems Engineering, Prentice-Hall, En- glewood Cliffs, NJ, 1973. [11] Schwartz, M., Information Transmission, Modulation, and Noise, McGraw-Hill, New York, NY, 1980. [12] Stremler, F.G., Introduction to Communication Systems, Addison-Wesley Publishing, Reading, MA, 1990. c/circlecopyrt1999 by CRC Press LLC