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Line Codes

By

Amanjot Singh

On the channel, we might want to send binary numbers

directly.

The resulting bit patterns on the channel might create a

static voltage, which is not desired.

Use line code to eliminate the average static voltage.

- Save power

- Save bandwidth (possibly)

Line Code

0 volt

5 volt

average

static voltage

0 0000 0

1 1 1 1 1

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Unipolar signaling: 1 = +A volt, 0 = 0 volt

Polar signaling: 1 = +A volt, 0 = -A volt

Biopolar signaling: 1 = +A or A, 0 = 0 volt

(Also called the alternate mark inversion AMI)

Machester signaling:

1 = +A (half duration) followed by A (half duration)

0 = -A (half duration) followed by +A (half duration)

Additional combinations can be made along with RZ

(return to zero) and NRZ (non return to zero).

Types of Line Code

4.4

Line coding schemes

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Self synchronization

Low probability of bit error

Spectral efficiency

Low transmission speed

Error detection capability

Transparency

Desired Properties of Line Code

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Line Coder

The input to the line encoder is the outputof the A/D converter or a sequence of valuesanthat is a function of the data bit

The output of the line encoder is awaveform:

where f(t) is the pulse shape and Tbis the bit period (Tb=Ts/nfor nbitquantizer)

n This means that each line code is described by a symbol mappingfunction anand pulse shape f(t)

n Details of this operation are set by the type of line code that is being used

( ) ( )n b

n

s t a f t nT

=

=

7

Goals of Line Coding(qualit ies to look for)

A line code is designed to meet one or more of the following goals:

Self-synchronization

The ability to recover timing from the signal itself

That is, self-clocking (self-synchronization) - ease of clock lock orsignal recovery for symbol synchronization

Long series of ones and zeros could cause a problem

Low probability of bit error Receiver needs to be able to distinguish the waveform associated

with a markfrom the waveform associated with a space

BER performance

relative immunity to noise

Error detection capability

enhances low probability of error

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Spectrum Suitable for the channel

Spectrum matching of the channel

e.g. presence or absence of DC level

In some cases DC components should be avoided

The transmission bandwidth should be minimized

Power Spectral Density

Particularly its value at zero

PSD of code should be negligible at the frequency near zero

Transmission Bandwidth

Should be as small as possible

Transparency

The property that any arbit rary symbol or bit pattern can betransmitted and received, i.e., all possible data sequence shouldbe faithfully reproducible

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Summary of Major Line Codes

Categories of Line Codes Polar - Send pulse or negative of pulse Uni-polar - Send pulse or a 0 Bipolar (a.k.a. alternate mark inversion, pseudoternary)

Represent 1 by alternating signed pulses Generalized Pulse Shapes

NRZ-Pulse lasts entire bit period Polar NRZ Bipolar NRZ

RZ- Return to Zero - pulse lasts just half of bit period Polar RZ Bipolar RZ

Manchester Line Code Send a 2- pulse for either 1 (high low) or 0 (low high) Includes rising and falling edge in each pulse No DC component

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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 precious

Unipolar NRZ

Turn the pulse ON for a 1, leave the pulse OFF for a 0

Useful for noncoherentcommunication where receiver cantdecide the sign of a pulse

fiber optic communication often use this signaling format

Unipolar RZ

RZ signaling has both a rising and falling edge of the pulse

This can be useful for timing and synchronization purposes

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Bipolar RZ

A unipolar line code, except now we alternatebetween positive and negative pulses to send a 1

Alternating like this eliminates the DC componentThis is desirable for many channels that cannot

transmit the DC components

Note:There are many other variations of line codes (see Fig. 2.22,page 80 for more)

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Commonly Used Line Codes

Polar line codes use the antipodal mapping

Polar NRZ uses NRZ pulse shape

Polar RZ uses RZ pulse shape

, 1

, 0

n

n

n

A w h en Xa

A w h en X

+ == =

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Unipolar NRZ Line Code (on-off Signaling)

Unipolar non-return-to-zero (NRZ) line code is defined by unipolarmapping

In addition, the pulse shape for unipolar NRZ is:

where Tb

is the bit period

, 1

0, 0

n

n

n

A when Xa

when X

+ == =

Where Xn is the nth data bit

( ) , NRZ Pulse Shapeb

tf t

T

=

14

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Bipolar Line Codes

With bipolar line codesa space is mapped to zero and a

mark is alternately mapped to -A and +A

n It is also called pseudoternary signaling or alternate mark inversion (AMI)

nEither RZ or NRZ pulse shape can be used

, when 1 and last mark

, when 1 and last mark

0, when 0

n

n n

n

A X A

a A X A

X

+ = = = + =

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Manchester Line Codes

Manchester line codesuse the antipodal mapping andthe following split-phasepulse shape:

4 4( )

2 2

b b

b b

T Tt t

f tT T

+ =

16

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Figure 3.15Line 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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Comparison of Line Codes

Self-synchronization

Manchester codes have built in timing information because theyalways have a zero crossing in the center of the pulse

Polar RZ codes tend to be good because the signal level alwaysgoes 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 Uni-

polar or Bipolar codes

Channel characteristics

We need to find the power spectral density (PSD) of the line codesto compare the line codes in terms of the channel characteristics

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Comparisons of Line Codes

Different pulse shapes are used

to control the spectrum of the transmitted signal (no DC value, bandwidth,etc.)

guarantee transitions every symbol interval to assist in symbol t imingrecovery

1. Power Spectral Densit y of Line Codes (see Fig. 2.23, Page 90)

After line coding, the pulses may be filtered or shaped to further improvethere propert ies such as

Spectral efficiency

Immunity to Intersymbol Interference

Distinction between Line Coding and Pulse Shaping is not easy

2. DC Component and Bandwidth DC Components

Unipolar NRZ, polar NRZ, and unipolar RZ all have DC components

Bipolar RZ and Manchester NRZ do not have DC components

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Differential Encoding

(a) Original binary data. (b) Differentially encoded data, assuming

reference bit 1. (c) Waveform of differentially encoded data using

unipolar NRZ signaling.

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Differential Coding Encoding

encoded(k) = encoded(k 1) XOR original(k)

where k starts from 0

Encoded(-1) is called the reference bit which can beeither 1 or 0

Decoding original(k) = encoded (k 1) XOR encoded(k)

where k starts from 0

Reference bit remains same for both encoding anddecoding process

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Sources of Corruption in the sampled,quantized and transmitted pulses

Channel Effects Channel Noise (AWGN, White Noise, Thermal etc)

Intersymbol Interference (ISI)

Sampling and Quantization Effects Quantization (Granularity) Noise

Quantizer Saturation or Overload Noise

Timing Jitter

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Section 2.8.4: Bits per PCM Word and Bits per Symbol L=2l

Section 2.8.5: M-ary Pulse Modulation Waveforms M = 2k

Problem 2.14: The information in an analog waveform, whosemaximum frequency fm=4000Hz, is to be transmit ted using a 16-levelPAM system. The quantization must not exceed 1% of the peak-to-peak analog signal.(a) What is the minimum number of bits per sample or bits per PCMword that should be used in this system?(b) What is the minimum required sampling rate, and what is theresulting bit rate?(c) What is the 16-ary PAM symbol Transmission rate?

Bits per PCM word and M-ary Modulation

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On the channel, we might want to send binary numbers

directly.

The resulting bit patterns on the channel might create a

static voltage, which is not desired.

Use line code to eliminate the average static voltage.

- Save power

- Save bandwidth (possibly)

Line Code

0 volt

5 volt

average

static voltage

0 0000 0

1 1 1 1 1

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Unipolar signaling: 1 = +A volt, 0 = 0 volt

Polar signaling: 1 = +A volt, 0 = -A volt

Biopolar signaling: 1 = +A or A, 0 = 0 volt

(Also called the alternate mark inversion AMI)

Machester signaling:

1 = +A (half duration) followed by A (half duration)

0 = -A (half duration) followed by +A (half duration)

Additional combinations can be made along with RZ

(return to zero) and NRZ (non return to zero).

Types of Line Code

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Self synchronization

Low probability of bit error

Spectral efficiency

Low transmission speed

Error detection capability

Transparency

Desired Properties of Line Code

Power Spectral Density for Line Code

(We will not follow the details in the book.)

)(1lim)(

symbol.for thevaluedatais

).(0forobservedsignaltheis)(

pulse.symbolais)(where

)()(source,At the

2

th

1

twT

f

na

NTTTttw

tf

nTtfatw

TTs

n

bT

N

n

bnT

=

=

=

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Eye Pattern

Seen in oscilloscopeThe Cleaner, the betterGood indication of transmission quality

Regenerative Repeater

( )

( )=

==

=

=

m

i

ie

im

e

i

eme

i

im

e

i

ei

mPPPi

mmP

mi

PPPi

mP

mP

oddis

1

e

1repeatersveregeneratiaftererrorinbitayprobabilit

place.takeerrorsofnumberoddanif

error,inbebit willthisrepeaters,veregeneratiAfterrepeaters.veregeneratiby

dregeneratelyincorrecteisbitsy that thiprobabilittheiswhere1

repeaters,veregeneratiofseriesathroughgotobit werethisIfrepeater.veregeneratiabydregenerateyincorrectlisbitsy that thiprobabilitbit,givenanyforSuppose

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Bit Synchronization

To accurately detect received signals,

synchronization timing is needed.

- derived from received data

- separate signal sent from source

Synchronization

- bit level

- frame level

- carrier level

Binary-to-Mult ilevel Conversion

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Spectral Efficiency

+==

=

N

S

B

C

B

R

1log:ShannonBy

second.perbitsefficiencySpectral.Definition

2max

Line Code First Null Bandwidth Spectral Efficiency

(Hz) =R/B bits/s

Unipolar NRZ R 1

Polar NRZ R 1

Unipolar RZ 2R 0.5

Bipolar RZ R 1Manchester NRZ 2R 0.5

Multilevel polar NRZ R/l l

No channel has infinite bandwidth

Most transmission schemes require higher bandwidth than available in the

channel.

- Square wave requires infinite bandwidth.

- Synch function is not possible due to causality violation.

- Modified synch function to satisfy the causality requires higher bandwidth.

Each symbol may be smeared into adjacent time slots.

Intersymbol Interference (ISI) is the spreading of symbol pulses from

one slot into adjacent slots.

Intersymbol Interference