*Goals of Line Coding (qualities to look for)A line code is designed to meet one or more of the following goals:Self-synchronizationThe ability to recover timing from the signal itselfThat is, self-clocking (self-synchronization) - ease of clock lock or signal recovery for symbol synchronizationLong series of ones and zeros could cause a problemLow probability of bit errorReceiver needs to be able to distinguish the waveform associated with a mark from the waveform associated with a spaceBER performancerelative immunity to noiseError detection capabilityenhances low probability of error

*Spectrum Suitable for the channelSpectrum matching of the channele.g. presence or absence of DC levelIn some cases DC components should be avoidedThe transmission bandwidth should be minimizedPower Spectral DensityParticularly its value at zeroPSD of code should be negligible at the frequency near zeroTransmission BandwidthShould be as small as possibleTransparencyThe property that any arbitrary symbol or bit pattern can be transmitted and received, i.e., all possible data sequence should be faithfully reproducible

Line Coder

The input to the line encoder is the output of the A/D converter or a sequence of values an that is a function of the data bitThe output of the line encoder is a waveform:

*where f(t) is the pulse shape and Tb is the bit period (Tb=Ts/n for n bit quantizer)This means that each line code is described by a symbol mapping function an and pulse shape f(t)Details of this operation are set by the type of line code that is being used

Summary of Major Line Codes

*Categories of Line CodesPolar - Send pulse or negative of pulseUnipolar - Send pulse or a 0Bipolar (a.k.a. alternate mark inversion, pseudoternary)Represent 1 by alternating signed pulsesGeneralized Pulse ShapesNRZ -Pulse lasts entire bit periodPolar NRZBipolar NRZRZ - Return to Zero - pulse lasts just half of bit periodPolar RZBipolar RZManchester Line CodeSend a 2- pulse for either 1 (high low) or 0 (low high)Includes rising and falling edge in each pulseNo DC component

*When the category and the generalized shapes are combined, we have the following:Polar NRZ:Wireless, radio, and satellite applications primarily use Polar NRZ because bandwidth is preciousUnipolar NRZTurn the pulse ON for a 1, leave the pulse OFF for a 0Useful for non-coherent communication where receiver cant decide the sign of a pulsefiber optic communication often use this signaling formatUnipolar RZRZ signaling has both a rising and falling edge of the pulseThis can be useful for timing and synchronization purposes

*Bipolar RZA unipolar line code, except now we alternate between positive and negative pulses to send a 1Alternating like this eliminates the DC componentThis is desirable for many channels that cannot transmit the DC componentsGeneralized GroupingNon-Return-to-Zero: NRZ-L, NRZ-M NRZ-SReturn-to-Zero: Unipolar, Bipolar, AMIPhase-Coded: bi-f-L, bi-f-M, bi-f-S, Miller, Delay ModulationMultilevel Binary: dicode, doubinary

Commonly Used Line Codes

Polar line codes use the antipodal mapping

Polar NRZ uses NRZ pulse shapePolar RZ uses RZ pulse shape*

Unipolar NRZ Line CodeUnipolar non-return-to-zero (NRZ) line code is defined by unipolar mapping

In addition, the pulse shape for unipolar NRZ is:where Tb is the bit period

*Where Xn is the nth data bit

Bipolar Line CodesWith bipolar line codes a space is mapped to zero and a mark is alternately mapped to -A and +A

*Either RZ or NRZ pulse shape can be usedIt is also called pseudoternary signaling or alternate mark inversion (AMI)

Summary of Line Codes*

Summary of Line Codes

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Comparison of Line Codes

*Self-synchronizationManchester codes have built in timing information because they always have a zero crossing in the center of the pulsePolar RZ codes tend to be good because the signal level always goes to zero for the second half of the pulseNRZ signals are not good for self-synchronizationError probabilityPolar codes perform better (are more energy efficient) than Unipolar or Bipolar codesChannel characteristicsWe need to find the power spectral density (PSD) of the line codes to compare the line codes in terms of the channel characteristics

Figure Line codes for the electrical representations of binary data. (a) Unipolar NRZ signaling. (b) Polar NRZ signaling.(c) Unipolar RZ signaling. (d) Bipolar RZ signaling. (e) Split-phase or Manchester code.*

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