LINE CODING

By Vandana Matai

Introdunction• The output of an ADC can be transmitted over a baseband channel. The

digital information must first be converted into a physical signal. The physical signal is called a line code. Line coders use the terminology mark to mean binary one and space to mean binary zero and the choice is generally made on the grounds of one or more of the following considerations

– Presence or absence of a DC level.– Power Spectral Density- particularly its value at 0 Hz.– Bandwidth.– BER performance (this particular aspect is not covered in this lecture).– Transparency (i.e. the property that any arbitrary symbol, or bit, pattern can

be transmitted and received).– Ease of clock signal recovery for symbol synchronisation.– Presence or absence of inherent error detection properties.

Goals of Line Coding

• A line code is designed to meet several goals:

Self-synchronization.• The ability to recover timing from the signal itself.• Long series of ones and zeros could cause a problem.

Low probability of bit error.• The receiver needs to be able to distinguish the waveform associated

with a mark from the waveform associated with a space, even if there is a considerable amount of noise and distortion in the channel.

Spectrum that is suitable for the channel.• In some cases DC components should be avoided if the channel has a

DC blocking capacitance.• The transmission bandwidth should be minimized.

Line Coder

• The input to the line encoder is a sequence of values ak that is a function of a data bit or an ADC output bit.

• The output of the line encoder is a waveform:

• Where p(t) is the Pulse Shape and Tb is the Bit Period – Tb =Ts/n for n bit quantizer (and no parity bits).– Rb =1/Tb=nfs for n bit quantizer (and no parity bits).

• The operational details of this function are set by the particular type of line code that is being used.

( ) ( )k bk

x t a p t kT

Line Coderka

DigitalData

PhysicalWaveform

( ) ( )k bk

x t a p t kT

ak

Types of Line Codes

• Each line code is described by a symbol mapping function ak and a pulse shape p(t):

• Categories of line codes:– Symbol mapping functions (ak).

• Unipolar• Polar• Bipolar (a.k.a. alternate mark inversion, pseudoternary)

– Pulse shapes p(t).• NRZ (Nonreturn-to-zero)• RZ (Return to Zero)• Manchester (split phase)

( ) ( )k bk

x t a p t kT

Unipolar NRZ Line Code• The unipolar nonreturn-to-zero line code is defined by the

unipolar mapping:

– where Xk is the kth data bit.

– In addition, the pulse shape for unipolar NRZ is:

– Where Tb is the bit period.

0when

1 when

0

k

kk X

XAa

( ) NRZ pulse shapeb

tp t

T

• Advantages:– Simplicity in implementation.– Doesn’t require a lot of bandwidth for transmission.

• Disadvantages:– Presence of DC level (indicated by spectral line at 0 Hz).– Contains low frequency components. Causes “Signal Droop”.– Does not have any error correction capability.– Does not posses any clocking component for ease of synchronisation.– Is not Transparent. Long string of zeros causes loss of

synchronisation.

Unipolar NRZ Line Code

Unipolar RZ Line Code

• The unipolar return-to-zero line code has the same symbol mapping but a different pulse shape than unipolar NRZ:

0when

1 when

0

k

kk X

XAa

( ) RZ pulse shape/ 2b

tp t

T

Unipolar RZ Line Code

• Advantages:– Simplicity in implementation.– Presence of a spectral line at symbol rate which can be used

as symbol timing clock signal.

• Disadvantages:– Presence of DC level (indicated by spectral line at 0 Hz).– Continuous part is non-zero at 0 Hz. Causes “Signal Droop”.– Does not have any error correction capability.– Occupies twice as much bandwidth as Unipolar NRZ.– Is not Transparent

Polar Line Codes• Polar line codes use the antipodal mapping:

– Polar NRZ uses NRZ pulse shape.– Polar RZ uses RZ pulse shape.

0when

1 when

k

kk X

X

A

Aa

Polar Non-Return to Zero (NRZ):•Advantages:

– Simplicity in implementation.– No DC component.

•Disadvantages:– Continuous part is non-zero at 0 Hz. Causes “Signal Droop”.– Does not have any error correction capability.– Does not posses any clocking component for ease of synchronisation.– Is not transparent.

Polar Signalling

Polar Signalling

Polar Return to Zero (RZ):•Advantages:

– Simplicity in implementation.– No DC component.

•Disadvantages:– Continuous part is non-zero at 0 Hz. Causes “Signal Droop”.– Does not have any error correction capability.– Does not posses any clocking component for easy synchronisation.

However, clock can be extracted by rectifying the received signal.– Occupies twice as much bandwidth as Polar NRZ.

Manchester Line Codes• Manchester line codes use the antipodal mapping and the

following split-phase pulse shape:• Transition in the middle of each bit period• Transition provides clocking and data• Low-to-high=1 , high-to-low=0• Used in Ethernet

/ 4 / 4( )

/ 2 / 2b b

b b

t T t Tp t

T T

Polar biphase: Manchester and differential Manchester schemes

Comparison of Line Codes

• Self-synchronization:– Manchester codes have built in timing information because they

always have a zero crossing in the center of the pulse.– Polar RZ codes tend to be good because the signal level always

goes to zero for the second half of the pulse.– NRZ signals are not good for self-synchronization.

• Error probability:– Polar codes perform better (are more energy efficient) than

Unipolar or Bipolar codes.

• Channel characteristics:– We need to find the PSD of the line codes to answer this ...

PSD for line codes

22

Uni. NRZ

sin 1( ) 1 ( )

4b b

b b

A T fTP f f

fT T

2

2Polar NRZ

sin( ) b

bb

fTP f A T

fT

Bit rate: R=1/Tb

Unipolar NRZ

Polar NRZ

PSD for line codesUnipolar RZ

Bipolar RZ

ManchesterNRZ

Uni. R

2

Z

2sin / 2 1

( ) 1 ( )16 / 2

b b

nb b b

A T fT nP f f

fT T T

Bipolar

2

RZ

2

2sin( ) sin

4b b

bb

A T fTP f fT

fT

Manch. NR

2

Z2 2sin / 2

( ) sin / 2/ 2b

b bb

fTP f A T fT

fT

Bit rate: R=1/Tb

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