Chapter 3 Digital Transmission Fundamentals Chapter Figures.

Chapter 3 Digital Transmission

Fundamentals

Chapter Figures

Leon-Garcia/Widjaja Communication Networks

H

W

= + +H

W

H

W

H

W

Color image

Red component

image

Green component

image

Blue component

image

Total bits before compression = 3 H W pixels B bits/pixel = 3HWB

Figure 3.1


/2

3/2

5/2

7/2

-/2

-3/2

-5/2

-7/2

(a) Original waveform and

the sample values

/2

3/2

5/2

7/2

-/2

-3/2

-5/2

-7/2

(b) Original waveform and the quantized

values

Figure 3.2


(b) Broadcast TV at 30 frames/sec =

10.4 x 106 pixels/sec

720

480

(c) HDTV at 30 frames/sec =

67 x 106 pixels/sec1080

1920

(a) QCIF videoconferencing at 30 frames/sec =

760,000 pixels/sec

144

176

Figure 3.3


Receiver

Communication channel

Transmitter

Figure 3.4


(a)

(b)

Sent

Sent

Received

Received

Examples: digital telephone, CD Audio

Examples: AM, FM, TV transmission

Figure 3.5


Source Repeater DestinationRepeater

Transmission segment

Figure 3.6


Attenuated and distorted signal

+ noise

Equalizer

Recovered signal+

residual noise

Repeater

Amp

Figure 3.7


Amplifierequalizer

Timingrecovery

Decision circuitand signal

regenerator

Figure 3.8



d meters

0110101... 0110101...

Figure 3.9


(a) Low-pass and idealized low-pass channel

f0 W

A(f)

0 Wf

A(f)1

Figure 3.10

Channel

tt

(b) Maximum pulse transmission rate is 2W pulses/second

Leon-Garcia/Widjaja Communication Networks Figure 3.11

SNR = Average signal power

Average noise power

SNR (dB) = 10 log10 SNR

Signal Noise Signal + noise

HighSNR

t t t

Signal Noise Signal + noise

LowSNR

t t t


Th e s p ee ch s i g n al l e v el v a r ie s w i th t i m(e)

Figure 3.12



1 0 1 0 1 0 1 0

. . . . . .

t

1 ms

(a)

1 ms

1 1 1 1 0 0 0 0

. . . . . .

t

(b)

Figure 3.14


00.20.40.60.8

11.21.4

0 5 10 15 20 25 30 35 40 45 50

frequency (kHz)

|am

plit

ud

e|

00.20.40.60.8

11.21.4

0 5 10 15 20 25 30 35 40 45 50

frequency (kHz)|a

mp

litu

de

|

(a) Frequency components for 10101010

(b) Frequency components for 11110000

Figure 3.15


s (noisy ) | p (air stopped) | ee (periodic) | t (stopped) | sh (noisy)


f

W

X(f)

0


T

x(t)

t

x(nT)

nT

Figure 3.18


Samplert

x(t)

t

x(nT)(a)

Interpolationfilter

t

x(t)

t

x(nT)

(b)

Figure 3.19


Interpolationfilter

Displayor

playout

2W samples / sec

2W m bits/secx(t)Bandwidth W

Sampling(A/D)

QuantizationAnalogsource

2W samples / sec m bits / sample

Pulsegenerator

y(t)

Original

Approximation

Transmissionor storage

Figure 3.20


x(t) and the corresponding quantizer approximations y(nT)

t

3.52.51.50.5

-0.5-1.5-2.5-3.5

Figure 3.21

input x(nT)

output y(nT)

0.51.5

2.5

3.5

-0.5

-1.5

-2.5

-3.5

Uniform quantizer


M = 2m levels, Dynamic Range ( -V, V), Δ = 2V/M

2

...

error = y(nT)-x(nT)=e(nT)

input...

2

x(nT) V-V

Mean Square Error: σe2 ≈

Δ 12


Channel

t t

Aincos 2ft Aoutcos (2ft + (f))

Aout

AinA(f) =

Figure 3.23


f

1A(f) = 1

1+42f2

(a)

f

0

(f) = tan-1 2f

-45o

-90o

1/ 2

(b)

Figure 3.24


-1.5-1

-0.50

0.51

1.5

0

0.12

5

0.25

0.37

5

0.5

0.62

5

0.75

0.87

5 1

1 0 0 0 0 0 0 1

1 ms


- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

0

0.125 0.2

5

0.375 0.5

0.625 0.7

5

0.875

1

( b ) 2 H a r m o n i c s

( c ) 4 H a r m o n i c s

( a ) 1 H a r m o n i c

Figure 3.26


Channel

t0t

h(t)

td

Figure 3.27


-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7t

s(t) = sin(2πWt)/ 2πWt

T T T T T T T T T T T T T T

Figure 3.28


+A

-A0 T 2T 3T 4T 5T

1 1 1 10 0

t

Transmitter Filter

Communication Medium

Receiver Filter Receiver

r(t)

Received signal

Leon-Garcia/Widjaja Communication Networks-2

-1

0

1

2

-2 -1 0 1 2 3 4

-1

0

1

-2 -1 0 1 2 3 4

(a)

(b)

t

tT T T T TT

T T T T TT

Figure 3.30


W (1+)W(1-)W0 f

Figure 3.31


Four signal levels Eight signal levels

Typical noise

Figure 3.32


x

222

2

1

xe

0

Figure 3.33


1.00E-121.00E-111.00E-101.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00

0 2 4 6 8 /2

Figure 3.34


1 0 1 0 1 1 0 01

UnipolarNRZ

NRZ-inverted(differentialencoding)

Bipolarencoding

Manchesterencoding

DifferentialManchesterencoding

Polar NRZ

Figure 3.35


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8 1

1.2

1.4

1.6

1.8 2

fT

pow

er d

ensi

ty

NRZ

Bipolar

Manchester

Figure 3.36


f f2 f1 fc

0

A(f)


Information 1 1 1 10 0

+1

-10 T 2T 3T 4T 5T 6

T

AmplitudeShift

Keying

+1

-1

FrequencyShift

Keying

+1

-1

PhaseShift

Keying

(a)

(b)

(c)

0 T 2T 3T 4T 5T 6T

0 T 2T 3T 4T 5T 6T

t

t

t

Figure 3.38


1 1 1 10 0(a) Information

(d) 2Yi(t) cos(2fct)

+2A

-2A

+A

-A

(c) Modulated signal Yi(t)

0 T 2T 3T 4T 5T 6T

+A

-A

(b) Baseband signal Xi(t)

0 2T 3T 6T

0 T 2T 3T 4T 5T 6T

T 4T 5T

t

t

t

Figure 3.39


(a) Ak

cos(2fct)

Yi(t) = Ak cos(2fct)

(b)

2cos(2fct)2Ak cos2(2fct) = Ak {1 + cos(2fct)}

Low-passfilter withcutoff W Hz

Xi(t)Yi(t) = Akcos(2fct)

Figure 3.40


Ak

cos(2fc t)

Yi(t) = Ak cos(2fc t)

Bk

sin(2fc t)

Yq(t) = Bk sin(2fc t)

+ Y(t)

Figure 3.41


Y(t)

2cos(2fc t)2Akcos2(2fct)+2Bk cos(2fct)sin(2fct) = Ak {1 + cos(4fct)}+Bk {0 + sin(4fct)}

Low-passfilter withcutoff W/2 Hz

Ak

2sin(2fc t)2Bk sin2(2fct)+2Ak cos(2fct)sin(2fct) = Bk {1 - cos(4fct)}+Ak {0 + sin(4fct)}

Low-passfilter withcutoff W/2 Hz

Bk

Figure 3.42


Ak

Bk

(a) 4 “levels”/pulse 2 bits/pulse 2W bits/second

2-D signal

Ak

Bk

(b) 16 “levels”/ pulse 4 bits/pulse 4W bits/second

2-D signal

Figure 3.43


Ak

Bk

4 “levels”/pulse2 bits/pulse2W bits/second

Ak

Bk

16 “levels”/pulse4 bits/pulse4W bits/second

Figure 3.44


102 104 106 108 1010 1012 1014 1016 1018 1020 1022 1024

Frequency (Hz)

Wavelength (meters)

106 104 102 10 10-2 10-4 10-6 10-8 10-10 10-12 10-14

Pow

er a

nd te

leph

one

Bro

adca

stra

dio

Mic

row

ave

radi

o

Infr

ared

ligh

t

Vis

ible

ligh

t

Ultr

avio

let l

ight

X-r

ays

Gam

ma

rays

Figure 3.45


t = 0t = d/v


d meters

Figure 3.46


Att

enua

tion

(dB

/mi)

f (kHz)

19 gauge

22 gauge

24 gauge

26 gauge

6

12

3

9

15

18

21

24

27

30

1 10 100 1000

Figure 3.47


Figure 3.48


Dielectricmaterial Braided

outer conducto

r

Outercover

Centerconductor

Figure 3.49


35

30

10

25

20

5

15Att

enua

tion

(dB

/km

)

0.01 0.1 1.0 10 100 f (MHz)

2.6/9.5 mm

1.2/4.4 mm

0.7/2.9 mm

Figure 3.50


Headend

= Unidirectionalamplifier

Figure 3.51


Headend

Upstream fiber

Downstream fiber

Fibernode

Coaxialdistribution

plant

Fibernode

= Bidirectionalsplit-bandamplifier

Fiber Fiber

Figure 3.52


Downstream

54 MH

z

500 MH

z

(a) Current allocation

550 MH

z

750 M

Hz

UpstreamDownstream

5 MH

z

42 MH

z

54 MH

z

500 MH

z

(b) Proposed hybrid fiber-coaxial allocation

Proposed downstream

Figure 3.53


Core

Cladding Jacket

Light

(a) Geometry of optical fiber

c

(b) Reflection in optical fiber

Figure 3.54


100

50

10

5

1

0.5

0.1

0.05

0.010.8 1.0 1.2 1.4 1.6 1.8

Wavelength (m)

Loss

(dB

/km

)

Infrared absorption

Rayleigh scattering

Figure 3.55


(a) Multimode fiber: multiple rays follow different paths

Direct path

Reflected path

(b) Single-mode fiber: only direct path propagates in fiber

Figure 3.56


Optical fiber

Opticalsource

ModulatorElectricalsignal

ReceiverElectrical

signal

Figure 3.57


R R R R R R R R

(a) Single signal per fiber with 1 regenerator per span

… …R

R

R

R

…R

R

R

R

…R

R

R

R

…R

R

R

R…

(b) DWDM composite signal per fiber with 1 regenerator per span

Opticalamplifier

R Regenerator OA DWDMmultiplexer

…

(c) DWDM composite signal with optical amplifiers

…R

R

R

R

…R

R

R

ROA OA OA OA… …

Figure 3.58


104 106 107 108 109 1010 1011 1012

Frequency (Hz)

Wavelength (meters)

103 102 101 1 10-1 10-2 10-3

105

Satellite and terrestrial microwave

AM radio

FM radio and TV

LF MF HF VHF UHF SHF EHF104

Cellularand PCS

Wireless cable

Figure 3.59


ChannelEncoderUserinformation

Patternchecking

All inputs to channel satisfy pattern or condition

Channeloutput

Deliver user information orset error alarm

Figure 3.60


Calculate check bits

Channel

Recalculate check bits

Compare

Information bits Received information bits

Sent checkbits

Information accepted if check bits match

Received check bits

Figure 3.61


o

x = codewords o = noncodewords

x

x x

x

x

x

x

o

oo

oo

oo

o

oo

o

o

xx x

x

xx

x

oo

oo

ooooo

o

o

A code with poordistance properties

A code with gooddistance properties

(a)

(b)

Figure 3.62


1 0 0 1 0 0

0 1 0 0 0 1

1 0 0 1 0 0

1 1 0 1 1 0

1 0 0 1 1 1

Bottom row consists of check bit for each column

Last column consists of check bits for each row

Figure 3.63


1 0 0 1 0 0

0 0 0 1 0 1

1 0 0 1 0 0

1 0 0 0 1 0

1 0 0 1 1 1

1 0 0 1 0 0

0 0 0 0 0 1

1 0 0 1 0 0

1 0 0 1 1 0

1 0 0 1 1 1

1 0 0 1 0 0

0 0 0 1 0 1

1 0 0 1 0 0

1 0 0 1 1 0

1 0 0 1 1 1

1 0 0 1 0 0

0 0 0 0 0 1

1 0 0 1 0 0

1 1 0 1 1 0

1 0 0 1 1 1

Arrows indicate failed check bits

Two errorsOne error

Three errors Four errors

Figure 3.64


unsigned short cksum(unsigned short *addr, int count){

/*Compute Internet Checksum for “count” bytes * beginning at location “addr”.*/

register long sum = 0;while ( count > 1 ) {

/* This is the inner loop*/ sum += *addr++; count -=2;}

/* Add left-over byte, if any */if ( count > 0 )

sum += *addr;

/* Fold 32-bit sum to 16 bits */while (sum >>16)sum = (sum & 0xffff) + (sum >> 16) ;

return ~sum;}

Figure 3.65


(x7 x6 1) (x6 x5 ) x7 (1 1)x6 x 5 1

x7 x5 1

(x 1)(x2 x 1) x3 x 2 x x2 x 1 x3 1

Addition:

Multiplication:

Division: x3 + x + 1 ) x6 + x5

x3 + x2 + x

x6 + x4 + x3

x5 + x4 + x3

x5 + x3 + x2

x4 + x2

x4 + x2 + x

x

= q(x) quotient

= r(x) remainder

divisordividend

35 ) 1223

10517

Figure 3.66


Steps:

1. Multiply i(x) by xn-k (puts zeros in (n-k) low order positions)

2. Divide xn-k i(x) by g(x)

3. Add remainder r(x) to xn-k i(x)

(puts check bits in the n-k low order positions):

Quotient Remainder

Transmitted codewordb(x) = xn-ki(x) + r(x)

xn-ki(x) = g(x) q(x) + r(x)

Figure 3.67


Generator polynomial: g(x)= x3 + x + 1

Information: (1,1,0,0) i(x) = x3 + x2

Encoding: x3i(x) = x6 + x5

Transmitted codeword:b(x) = x6 + x5 + xb = (1,1,0,0,0,1,0)

1011 ) 1100000

1110

1011

1110

1011

1010

1011

010

x3 + x + 1 ) x6 + x5

x3 + x2 + x

x6 + x4 + x3

x5 + x4 + x3

x5 + x3 + x2

x4 + x2

x4 + x2 + x

x

Figure 3.68


Clock Input Reg 0 Reg 1 Reg 2

0 - 0 0 0

1 1 = i3 1 0 0

2 1 = i2 1 1 0

3 0 = i1 0 1 1

4 0 = i0 1 1 1

5 0 1 0 1

6 0 1 0 0

7 0 0 1 0Check bits:r0 = 0 r1 = 1 r2 = 0

r(x) = x

g (x ) x 3 x 1

Reg 0 ++

g3 1

i (x )

g0 1 g1 1 i (x ) x 3 x 2

Encoder for

Reg 1 Reg 2

Figure 3.69


b(x)

e(x)

R(x)+ (Receiver)(Transmitter)

Error pattern

Figure 3.70


1. Single errors:e(x) = xi 0 i n-1

If g(x) has more than 1 term, it cannot divide e(x)

2. Double errors: e(x) = xi + xj 0 i < j n-1

= xi (1 + xj-i )

If g(x) is primitive, it will not divide (1 + xj-i ) for j-i 2n-k1

3. Odd number of errors: e(1) =1 if number of errors is odd.

If g(x) has (x+1) as a factor, then g(1) = 0 and all codewords have an even number of 1s.

Figure 3.71


4. Error bursts of length b: 0000110• • •0001101100 • • • 0

e(x) = xi d(x) where deg(d(x)) = L-1

g(x) has degree n-k;

g(x) cannot divide d(x) if deg(g(x))> deg(d(x))

L = (n-k) or less: all will be detected L = (n-k+1): deg(d(x)) = deg(g(x))

i.e. d(x) = g(x) is the only undetectable error pattern,

fraction of bursts which are undetectable = 1/2L-2 L > (n-k+1): fraction of bursts which are undetectable = 1/2n-k

L

ithposition

error pattern d(x)

Figure 3.72


b

e

r+ (Receiver)(Transmitter)

Error pattern

b

e

r+ (Receiver)(Transmitter)

Error pattern

(a) Single bit input

(b) Vector input

Figure 3.73


0010000

s = H e = =101

Single error detected

0100100

s = H e = = + =011

Double error detected100

1 0 1 1 1 0 01 1 0 1 0 1 00 1 1 1 0 0 1

1110000

s = H e = = + + = 0 110

Triple error not detected

011

101

1 0 1 1 1 0 01 1 0 1 0 1 00 1 1 1 0 0 1

1 0 1 1 1 0 01 1 0 1 0 1 00 1 1 1 0 0 1

111

Figure 3.74


s = H r = He

s = 0 s = 0

No errors intransmission

Undetectableerrors

Correctableerrors

Uncorrectableerrors

(1–p)7 7p3

1–3p 3p

7p

7p(1–3p) 21p2

Figure 3.75


t = 2

b1 b2o o o o

Set of all n-tupleswithin distance t

Set of all n-tupleswithin distance t

Figure 3.76


b1 b2 b3 b4 bL-3 bL-2 bL-1 bL. . .

L codewordswritten verticallyin array; thentransmitted rowby row

b1 b2 b3 b4 bL-3 bL-2 bL-1 bL

. . .

A long error burst produceserrors in two adjacent rows

Figure 3.77


DTE DCE

Protective Ground (PGND)

Transmit Data (TXD)

Receive Data (RXD)

Request to Send (RTS)

Clear to Send (CTS)

Data Set Ready (DSR)

Ground (G)

Carrier Detect (CD)

Data Terminal Ready (DTR)

Ring Indicator (RI)

1

2

3

4

5

6

7

8

20

22

1

2

3

4

5

6

7

8

20

22

(b)

13

(a)

1

2514

Figure 3.78


Startbit

Stopbit1 2 3 4 5 6 7 8

Data bits

Lineidle

3T/2 T T T T T T T

Receiver samples the bits

Figure 3.79


f0 W

X(f)

-W

1 T

…

f0 W

X(f) X(f – 1/T)X(f + 1/T)

–W

…

1 T–

…

f0 W

X(f) X(f – 1/T)

–W

…

X(f + 1/T)

Figure 3.80

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Chapter 3 Digital Transmission Fundamentals Chapter Figures.

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