LoCicero, J.L. & Patel, B.P. “Line Coding” Mobile Communications Handbook Ed. Suthan S. Suthersan Boca Raton: CRC Press LLC, 1999 c 1999byCRCPressLLC LineCoding 6.1 Introduction 6.2 CommonLineCodingFormats UnipolarNRZ(BinaryOn-OffKeying) • UnipolarRZ • Polar NRZ • PolarRZ[Bipolar,AlternateMarkInversion(AMI),or Pseudoternary] • ManchesterCoding(SplitPhaseorDigital Biphase) 6.3 AlternateLineCodes DelayModulation(MillerCode) • SplitPhase(Mark) • Biphase (Mark) • CodeMarkInversion(CMI) • NRZ(I) • BinaryN ZeroSubstitution(BNZS) • High-DensityBipolarN(HDBN) • TernaryCoding 6.4 MultilevelSignalling,PartialResponseSignalling,and DuobinaryCoding MultilevelSignalling • PartialResponseSignallingandDuobi- naryCoding JosephL.LoCicero 6.5 BandwidthComparison IllinoisInstituteofTechnology 6.6 ConcludingRemarks BhaskerP.Patel DefiningTerms IllinoisInstituteofTechnology References 6.1 Introduction Theterminologylinecodingoriginatedintelephonywiththeneedtotransmitdigitalinformation acrossacoppertelephoneline;morespecifically,binarydataoveradigitalrepeateredline.The conceptoflinecoding,however,readilyappliestoanytransmissionlineorchannel.Inadigitalcom- municationsystem,thereexistsaknownsetofsymbolstobetransmitted.Thesecanbedesignatedas {mi},i=1;2;:::;N,withaprobabilityofoccurrence{pi},i=1;2;:::;N,wherethesequentially transmittedsymbolsaregenerallyassumedtobestatisticallyindependent.Theconversionorcoding oftheseabstractsymbolsintoreal,temporalwaveformstobetransmittedinbasebandistheprocess oflinecoding.Sincethemostcommontypeoflinecodingisforbinarydata,suchawaveformcanbe succinctlytermedadirectformatforserialbits.Theconcentrationinthissectionwillbelinecoding forbinarydata. Differentchannelcharacteristics,aswellasdifferentapplicationsandperformancerequirements, haveprovidedtheimpetusforthedevelopmentandstudyofvarioustypesoflinecoding[1,2]. Forexample,thechannelmightbeaccoupledand,thus,couldnotsupportalinecodewithadc componentorlargedccontent.Synchronizationortimingrecoveryrequirementsmightnecessitatea discretecomponentatthedatarate.Thechannelbandwidthandcrosstalklimitationsmightdictate c 1999byCRCPressLLC thetypeoflinecodingemployed.Evensuchfactorsasthecomplexityoftheencoderandtheeconomy ofthedecodercoulddeterminethelinecodechosen.Eachlinecodehasitsowndistinctproperties. Dependingontheapplication,onepropertymaybemoreimportantthantheother.Inwhatfollows, wedescribe,ingeneral,themostdesirablefeaturesthatareconsideredwhenchoosingalinecode. Itiscommonlyaccepted[1,2,5,8]thatthedominantconsiderationseffectingthechoiceofaline codeare:1)timing,2)dccontent,3)powerspectrum,4)performancemonitoring,5)probabilityof error,and6)transparency.Eachofthesearedetailedinthefollowingparagraphs. 1)Timing:Thewaveformproducedbyalinecodeshouldcontainenoughtiminginformation suchthatthereceivercansynchronizewiththetransmitteranddecodethereceivedsignalproperly. Thetimingcontentshouldberelativelyindependentofsourcestatistics,i.e.,alongstringof1sor0s shouldnotresultinlossoftimingorjitteratthereceiver. 2)DCcontent:Sincetherepeatersusedintelephonyareaccoupled,itisdesirabletohavezero dcinthewaveformproducedbyagivenlinecode.Ifasignalwithsignificantdccontentisused inaccoupledlines,itwillcausedcwanderinthereceivedwaveform.Thatis,thereceivedsignal baselinewillvarywithtime.Telephonelinesdonotpassdcduetoaccouplingwithtransformers andcapacitorstoeliminatedcgroundloops.Becauseofthis,thetelephonechannelcausesadroop inconstantsignals.Thiscausesdcwander.Itcanbeeliminatedbydcrestorationcircuits,feedback systems,orwithspeciallydesignedlinecodes. 3)Powerspectrum:Thepowerspectrumandbandwidthofthetransmittedsignalshouldbe matchedtothefrequencyresponseofthechanneltoavoidsignificantdistortion.Also,thepower spectrumshouldbesuchthatmostoftheenergyiscontainedinassmallbandwidthaspossible.The smalleristhebandwidth,thehigheristhetransmissionefficiency. 4)Performancemonitoring:Itisverydesirabletodetecterrorscausedbyanoisytransmission channel.Theerrordetectioncapabilityinturnallowsperformancemonitoringwhilethechannelis inuse(i.e.,withoutelaboratetestingproceduresthatrequiresuspendinguseofthechannel). 5)Probabilityoferror:Theaverageerrorprobabilityshouldbeassmallaspossibleforagiven transmitterpower.Thisreflectsthereliabilityofthelinecode. 6)Transparency:Alinecodeshouldallowallthepossiblepatternsof1sand0s.Ifacertainpattern isundesirableduetootherconsiderations,itshouldbemappedtoauniquealternativepattern. 6.2 CommonLineCodingFormats Alinecodingformatconsistsofaformaldefinitionofthelinecodethatspecifieshowastringof binarydigitsareconvertedtoalinecodewaveform.Therearetwomajorclassesofbinarylinecodes: levelcodesandtransitioncodes.Levelcodescarryinformationintheirvoltagelevel,whichmaybe highorlowforafullbitperiodorpartofthebitperiod.Levelcodesareusuallyinstantaneoussince theytypicallyencodeabinarydigitintoadistinctwaveform,independentofanypastbinarydata. However,somelevelcodesdoexhibitmemory.Transitioncodescarryinformationinthechangein levelappearinginthelinecodewaveform.Transitioncodesmaybeinstantaneous,buttheygenerally havememory,usingpastbinarydatatodictatethepresentwaveform.Therearetwocommonforms oflevellinecodes:oneiscalledreturntozero(RZ)andtheotheriscallednonreturntozero(NRZ). InRZcoding,thelevelofthepulsereturnstozeroforaportionofthebitinterval.InNRZcoding, thelevelofthepulseismaintainedduringtheentirebitinterval. Linecodingformatsarefurtherclassifiedaccordingtothepolarityofthevoltagelevelsusedto representthedata.Ifonlyonepolarityofvoltagelevelisused,i.e.,positiveornegative(inaddition tothezerolevel)thenitiscalledunipolarsignalling.Ifbothpositiveandnegativevoltagelevelsare beingused,withorwithoutazerovoltagelevel,thenitiscalledpolarsignalling.Thetermbipolar c 1999byCRCPressLLC 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 definition of 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 1 is represented by a non-zero voltage level and a binary 0 is 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 0sisgivenby[5, 8] V 2T sin πf T 2 V 2 S .f / = + δ(f/ (6.1) 1 4 πf T 4 where V is the binary 1 voltage level, T = 1=R is the bit duration, and R is 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 binary 1 is p, and the probability of a binary 0 is .1 − p/, then the PSD of this code, in the most general case, is 4p.1 − p/ S1.f /. Considering the frequency of the first spectral null as the bandwidth of the waveform, the bandwidth of unipolar NRZ is R in hertz. The error rate performance of this code, for equally likely data, with additive white Gaussian noise (AWGN) and optimum, i.e., matched filter, detectionisgivenby[1, 5] s ! 1 Eb Pe = erfc (6.2) 2 2N0 where Eb=N0 is a measure of the signal-to-noise ratio (SNR) of the received signal. In general, Eb is the energy per bit and N0=2 is the two-sided PSD of the AWGN. More specifically, for unipolar NRZ, Eb is the energy in a binary 1, which is V 2T . 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 R Hz. There are quite a few disadvantages of this line code. A loss of synchronization and timing jitter can result with a long sequence of 1sor0s because no pulse transition is present. The code has no error detection capability and, hence, performance cannot be monitored. There is a significant dc component as well as a dc content. The error rate performance is not as good as that of polar line codes. 6.2.2 Unipolar RZ Inthislinecode, abinary1isrepresentedbyanonzerovoltagelevelduringaportionofthebitduration, usually for half of the bit period, and a zero voltage level for rest of the bit duration. A binary 0 is represented by a zero voltage level during the entire bit duration. Thus, this is an instantaneous level code. Figure 6.1(b) illustrates a unipolar RZ waveform in which the 1 is represented by a nonzero voltage level for half the bit period. The PSD of this line code, with equally likely binary digits, is givenby[5, 6, 8] V 2T πf T = 2 S .f / = sin 2 2 16 πf T =2 c 1999 by CRC Press LLC 1 0110001110 Unipolar RZ (a) T3T2T 4T 5T 6T 7T 8T 9T 10T 11T Unipolar 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) T3T2T 4T 5T 6T 7T 8T 9T 10T 11T NRZ (M) (l) NRZ (s) (m) c 1999 by CRC Press LLC FIGURE 6.1: Waveforms for different line codes. Figure 6.2a Power spectral density of different line codes, where R = 1=T is the bit rate. " # ∞ V 2 π 2 X 1 + δ(f/ + δ(f − .2n + 1/R/ (6.3) π 2 . n + /2 4 4 n=−∞ 2 1 where again V is the binary 1 voltage level, and T = 1=R is the bit period. The spectrum of this code is drawn in Fig. 6.2a. In the most general case, when the probability of a 1 is p, 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