Chapter 3 Digital Transmission Fundamentals Chapter Figures

W H

Color image = H

W

W

W

Red component image

Green component image

Blue component image

+ H

+ H

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

Leon-Garcia/Widjaja

Communication Networks

Figure 3.1

(a) Original 7∆/2 waveform and 5∆/2 the sample 3∆/2 values ∆/2 -∆/2 -3∆/2 -5∆/2 -7∆/2 (b) Original waveform and the quantized values

7∆/2 5∆/2 3∆/2 ∆/2 -∆/2 -3∆/2 -5∆/2 -7∆/2

Leon-Garcia/Widjaja

Communication Networks

Figure 3.2

176 (a) QCIF videoconferencing

at 30 frames/sec =

144

760,000 pixels/sec

720 (b) Broadcast TV

480

at 30 frames/sec = 10.4 x 106 pixels/sec

1920 (c) HDTV

at 30 frames/sec = 67 x 106 pixels/sec

1080

Leon-Garcia/Widjaja

Communication Networks

Figure 3.3

Transmitter

Receiver Communication channel

Leon-Garcia/Widjaja

Communication Networks

Figure 3.4

(a) Sent

Received

Examples: AM, FM, TV transmission (b) Sent

Received

Examples: digital telephone, CD Audio

Leon-Garcia/Widjaja

Communication Networks

Figure 3.5

Transmission segment Source

Leon-Garcia/Widjaja

Repeater

Repeater

Communication Networks

Destination

Figure 3.6

Attenuated and distorted signal + noise

Recovered signal + residual noise

Amp

Equalizer

Repeater

Leon-Garcia/Widjaja

Communication Networks

Figure 3.7

Decision circuit and signal regenerator

Amplifier equalizer Timing recovery

Leon-Garcia/Widjaja

Communication Networks

Figure 3.8

0110101...

Leon-Garcia/Widjaja

d meters Communication channel

Communication Networks

0110101...

Figure 3.9

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

A(f)

1 f

f 0

0

W

W

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

Channel t

Leon-Garcia/Widjaja

t

Communication Networks

Figure 3.10

Signal

Signal + noise

Noise

High SNR

Noise

Signal

Signal + noise

Low SNR t

t

SNR =

t

t

t

t

Average signal power Average noise power SNR (dB) = 10 log10 SNR

Leon-Garcia/Widjaja

Communication Networks

Figure 3.11

Th e s p ee

Leon-Garcia/Widjaja

ch s

i

g n al l e

v el

Communication Networks

v a r ie s w i th

t

i

m(e)

Figure 3.12

Leon-Garcia/Widjaja

Communication Networks

Figure 3.13

1 01 01 01 0 (a)

...

... t

1 ms 11 1 1 0 000 (b)

...

... t

1 ms

Leon-Garcia/Widjaja

Communication Networks

Figure 3.14

Frequency components for 10101010

40

45

50

40

45

50

35

30

25

20

15

10

5

1.4 1.2 1 0.8 0.6 0.4 0.2 0

0

|am plitude|

(a)

frequency (kHz)

Frequency components for 11110000

35

30

25

20

15

10

5

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

|am plitude|

(b)

frequency (kHz)

Leon-Garcia/Widjaja

Communication Networks

Figure 3.15

s

(noisy )

Leon-Garcia/Widjaja

| p (air stopped)

| ee

(periodic)

Communication Networks

| t (stopped) | sh (noisy)

Figure 3.16

X(f)

f 0

Leon-Garcia/Widjaja

W

Communication Networks

Figure 3.17

x(t) x(nT) t T

Leon-Garcia/Widjaja

nT

Communication Networks

Figure 3.18

(a)

x(t)

x(nT) t

t

Sampler

(b) x(nT)

x(t) t

Leon-Garcia/Widjaja

Interpolation filter

Communication Networks

t

Figure 3.19

m bits / sample

2W samples / sec Analog source

Sampling (A/D)

Quantization

Original x(t) Bandwidth W

2W m bits/sec Transmission or storage

Approximation y(t) Display or playout

Interpolation filter

Pulse generator

2W samples / sec

Figure 3.20 Leon-Garcia/Widjaja

Communication Networks

Uniform quantizer

3.5∆

output y(nT) 2.5∆ 1.5∆ 0.5∆

−4∆ −3∆ −2∆ −∆ -0.5∆



2∆

-1.5∆

3∆

4∆

input x(nT)

-2.5∆ -3.5∆

3.5∆ 2.5∆ 1.5∆ 0.5∆ -0.5∆ -1.5∆ -2.5∆ -3.5∆ Leon-Garcia/Widjaja

t

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

Figure 3.21

M = 2m levels,

Dynamic Range ( -V, V),

∆ = 2V/M

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

-V

−2∆

∆ 2

∆ −

Mean Square Error:

Leon-Garcia/Widjaja



2∆

3∆

input

...

V

∆ 2

σ e2 ≈

x(nT)

∆ 12

Communication Networks

Figure 3.22

Aincos 2πft

Aoutcos (2πft + ϕ(f)) Channel

t

t A(f) =

Leon-Garcia/Widjaja

Aout Ain

Communication Networks

Figure 3.23

(b)

(a) 1

A(f) =

1 1+4π2f2

ϕ(f) = 0

tan-1 2πf

1/ 2π f

f -45o

-90o

Leon-Garcia/Widjaja

Communication Networks

Figure 3.24

1

1

0

0.875

0

0.75

0

0.625

0

0.5

0

0.375

0

0.25

1

0.125

0

1.5 1 0.5 0 -0.5 -1 -1.5

1 ms

Leon-Garcia/Widjaja

Communication Networks

Figure 3.25

Leon-Garcia/Widjaja

0.625

0.75

0.875

1

0.625

0.75

0.875

1

0.75

0.875

1

0.5

0.375

0.25

0.125

0

0.5

0.375

0.25

0.625

0.5

0.375

0.25

0.125

(c) 4 Harmonics

0

1.5 1 0.5 0 -0.5 -1 -1.5

(b) 2 Harmonics

0.125

1.5 1 0.5 0 -0.5 -1 -1.5

(a) 1 Harmonic

0

1.5 1 0.5 0 -0.5 -1 -1.5

Communication Networks

Figure 3.26

h(t) Channel 0

t

t t d

Leon-Garcia/Widjaja

Communication Networks

Figure 3.27

s(t) = sin(2πWt)/ 2πWt 1.2 1 0.8 0.6 0.4 0.2 0 -7T

-6T

-5T

-4T

-3T

-2T

t

-1-0.2 0 T

1T

2T

3T

4T

5T

6T

7T

-0.4

Leon-Garcia/Widjaja

Communication Networks

Figure 3.28

1

0

1

1

0

0

T

2T

3T

4T

1

+A

5T

t

-A

Transmitter Filter

Communication Medium

Receiver Filter

r(t) Receiver

Received signal Leon-Garcia/Widjaja

Communication Networks

Figure 3.29

1

(a)

0 -2 T

-1T

0

1T

2T

3T

4T

t

-1

(b)

2 1

t

0 -2T

-1T

0

1T

2T

3T

4T

-1

Leon-Garcia/Widjaja

-2 Communication Networks

Figure 3.30

0

Leon-Garcia/Widjaja

(1-α )W W

(1+α )W

Communication Networks

f

Figure 3.31

Typical noise

Four signal levels

Leon-Garcia/Widjaja

Eight signal levels

Communication Networks

Figure 3.32

1 2π σ

0

Leon-Garcia/Widjaja

Communication Networks

e

− x 2 2σ 2

x

Figure 3.33

1.00E+00 1.00E-01 1.00E-02 1.00E-03 1.00E-04 1.00E-05 1.00E-06 1.00E-07 1.00E-08 1.00E-09 1.00E-10 1.00E-11 1.00E-12

Leon-Garcia/Widjaja

0

2

4

Communication Networks

6

8

δ/2σ

Figure 3.34

1

0

1

0

1

1

1

0

0

Unipolar NRZ

Polar NRZ

NRZ-inverted (differential encoding) Bipolar encoding Manchester encoding Differential Manchester encoding Leon-Garcia/Widjaja

Communication Networks

Figure 3.35

1.2

NRZ

pow er density

1

Bipolar

0.8 0.6 0.4

Manchester

0.2 2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

-0.2

0.2

0

0

fT

Leon-Garcia/Widjaja

Communication Networks

Figure 3.36

A(f)

0

Leon-Garcia/Widjaja

f1

fc

Communication Networks

f2

f

Figure 3.37

Information (a) Amplitude Shift Keying

1

0

1

1

0

1

+1

-1

0

T

2T

3T

4T

5T

6 T

0

T

2T

3T

4T

5T

6 T

0

T

2T

3T

4T

5T

6 T

t

+1 (b) Frequency Shift Keying

(c)

Phase Shift Keying

-1 +1

-1 Leon-Garcia/Widjaja

t

Communication Networks

Figure 3.38

t

1

(a) Information

0

1

1

0

1

+A (b) Baseband signal Xi(t)

T

0

2T

3T

4T

5T

t

6T

-A +A (c) Modulated signal Yi(t)

-A

0

2T

T

3T

4T

5T

6T

t

6T

t

+2A (d) 2Yi(t) cos(2πfct)

Leon-Garcia/Widjaja

-2A

0

T

2T

Communication Networks

3T

4T

5T

Figure 3.39

(a)

Ak

×

Yi(t) = Ak cos(2πfct)

cos(2πfct)

(b) Yi(t) = Akcos(2πfct)

Low-pass filter with cutoff W Hz

× 2cos(2πfct)

Leon-Garcia/Widjaja

Xi(t)

2Ak cos2(2πfct) = Ak {1 + cos(2π2fct)}

Communication Networks

Figure 3.40

Ak

×

Yi(t) = Ak cos(2πfc t)

cos(2πfc t) Bk

×

+

Y(t)

Yq(t) = Bk sin(2πfc t)

sin(2πfc t)

Leon-Garcia/Widjaja

Communication Networks

Figure 3.41

Y(t)

Low-pass filter with cutoff W/2 Hz

× 2cos(2πfc t)

× 2sin(2πfc t)

Leon-Garcia/Widjaja

Ak

2Akcos2(2πfct)+2Bk cos(2πfct)sin(2πfct) = Ak {1 + cos(4πfct)}+Bk {0 + sin(4πfct)} Low-pass filter with cutoff W/2 Hz

Bk

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

Communication Networks

Figure 3.42

2-D signal

2-D signal

Bk

Ak

Ak

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

Leon-Garcia/Widjaja

Bk

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

Communication Networks

Figure 3.43

Bk

Bk

Ak

Ak

4 “levels”/pulse 2 bits/pulse 2W bits/second

Leon-Garcia/Widjaja

16 “levels”/pulse 4 bits/pulse 4W bits/second

Communication Networks

Figure 3.44

Frequency (Hz)

Leon-Garcia/Widjaja

104

102

10

10-2 10-4 10-6 Wavelength (meters)

Communication Networks

Gamma rays

X-rays

Ultraviolet light

Visible light

1010 1012 1014 1016 1018 1020 1022 1024

Infrared light

Broadcast radio

Power and telephone

106

108

Microwave radio

106

102 104

10-8 10-10 10-12 10-14

Figure 3.45

d meters Communication channel t = d/v

t=0

Leon-Garcia/Widjaja

Communication Networks

Figure 3.46

26 gauge 30 24 gauge

Attenuation (dB/mi)

27 24

22 gauge

21 18

19 gauge

15 12 9 6 3 1

Leon-Garcia/Widjaja

10

100

Communication Networks

1000

f (kHz)

Figure 3.47

z z z

Leon-Garcia/Widjaja

z

z

z

Communication Networks

Figure 3.48

Center conductor

Leon-Garcia/Widjaja

Dielectric material

Braided outer conductor

Communication Networks

Outer cover

Figure 3.49

35 0.7/2.9 mm

Attenuation (dB/km)

30 25

1.2/4.4 mm

20 15

2.6/9.5 mm

10 5 0.01

Leon-Garcia/Widjaja

0.1

1.0

Communication Networks

10

100

f (MHz) Figure 3.50

Head end

= Unidirectional amplifier

Leon-Garcia/Widjaja

Communication Networks

Figure 3.51

Upstream fiber

Head end

Fiber node

Fiber

Fiber node

Fiber

Downstream fiber Coaxial distribution plant

= Bidirectional split-band amplifier

Leon-Garcia/Widjaja

Communication Networks

Figure 3.52

Downstream (a) Current allocation 500 MHz

54 MHz

Downstream

Upstream

Proposed downstream

(b)

750 MHz

550 MHz

Communication Networks

500 MHz

54 MHz

42 MHz

Leon-Garcia/Widjaja

5 MHz

Proposed hybrid fibercoaxial allocation

Figure 3.53

(a) Geometry of optical fiber Light

Cladding

Jacket

Core

(b) Reflection in optical fiber

θc

Leon-Garcia/Widjaja

Communication Networks

Figure 3.54

100 50

Loss (dB/km)

10 5

Infrared absorption

1 0.5

Rayleigh scattering

0.1 0.05 0.01

0.8

1.0

1.2

1.4

1.6

1.8

Wavelength (µm)

Leon-Garcia/Widjaja

Communication Networks

Figure 3.55

(a) Multimode fiber: multiple rays follow different paths Reflected path Direct path

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

Leon-Garcia/Widjaja

Communication Networks

Figure 3.56

Electrical signal

Modulator

Optical fiber

Receiver

Electrical signal

Optical source

Leon-Garcia/Widjaja

Communication Networks

Figure 3.57

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

R

R

R

R

R

R

R

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



R

…R

R

…R

R

R

R

R

R

…R



…R

R

R

R

R

(c) DWDM composite signal with optical amplifiers R

OA

… R



Regenerator

Leon-Garcia/Widjaja

OA

…R

R

OA



OA

…R

R

R

R

R

OA Optical

amplifier Communication Networks

DWDM multiplexer Figure 3.58

Frequency (Hz) 105

104

106

108

107

109

1011

1010

1012

FM radio and TV Wireless cable

AM radio

Cellular and PCS

Satellite and terrestrial microwave LF 104

MF 103

HF 102

VHF 101

UHF 1

SHF 10-1

EHF 10-2

10-3

Wavelength (meters)

Leon-Garcia/Widjaja

Communication Networks

Figure 3.59

All inputs to channel satisfy pattern or condition User Encoder information

Leon-Garcia/Widjaja

Channel output

Channel

Communication Networks

Pattern checking

Deliver user information or set error alarm

Figure 3.60

Received information bits

Information bits

Recalculate check bits

Calculate check bits

Leon-Garcia/Widjaja

Channel Sent check bits

Received check bits

Communication Networks

Compare Information accepted if check bits match

Figure 3.61

(a)

A code with poor distance properties

o o o o x x x x x o o o x x o o o o o

o (b)

A code with good distance properties

x o o

x = codewords Leon-Garcia/Widjaja

o

x o

x

x o

o o

x

o o o x o x

o = noncodewords Communication Networks

Figure 3.62

1 0 0 1 0 0 0 1 0 0 0 1

Last column consists 1 0 0 1 0 0 of check bits for each 1 1 0 1 1 0 row 1 0 0 1 1 1 Bottom row consists of check bit for each column

Leon-Garcia/Widjaja

Communication Networks

Figure 3.63

1 0 0 1 0 0

1 0 0 1 0 0

0 0 0 0 0 1

0 0 0 0 0 1

1 1 0 1 1 0

Two 1 0 0 1 0 0 errors 1 0 0 1 1 0

1 0 0 1 1 1

1 0 0 1 1 1

1 0 0 1 0 0

1 0 0 1 0 0

0 0 0 1 0 1

0 0 0 1 0 1

1 0 0 1 0 0 Three errors 1 0 0 1 1 0

1 0 0 1 0 0

1 0 0 1 1 1

1 0 0 1 1 1

1 0 0 1 0 0

One error

Four errors

1 0 0 0 1 0

Arrows indicate failed check bits Leon-Garcia/Widjaja

Communication Networks

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++; coun t -=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) ; }

Leon-Garcia/Widjaja

return ~sum;

Communication Networks

Figure 3.65

(x 7 + x 6 +1) + (x 6 + x 5 ) = x 7 + (1 +1)x 6 + x 5 +1

Addition:

= x 7 + x 5 +1 Multiplication:

2

3

x3 + x2 + x Division: divisor 3 35 ) 122 105 17

Leon-Garcia/Widjaja

2

2

3

(x + 1)(x + x + 1) = x + x + x + x + x + 1 = x + 1

x3 + x + 1 ) x6 + x5 x6 +

= q(x) quotient dividend

x4 + x3 x5 + x4 + x3 x5 + x3 + x2 x4 + x4 +

x2 x2 + x x

Communication Networks

= r(x) remainder Figure 3.66

Steps: 1. Multiply i(x) by xn-k (puts zeros in (n-k) low order positions) Quotient Remainder xn-ki(x) = g(x) q(x) + r(x)

2. Divide xn-k i(x) by g(x) b(x) = xn-ki(x) + r(x)

Transmitted codeword

3. Add remainder r(x) to xn-k i(x) (puts check bits in the n-k low order positions):

Leon-Garcia/Widjaja

Communication Networks

Figure 3.67

Generator polynomial: g(x)= x3 + x + 1 Information: (1,1,0,0) i(x) = x3 + x2 Encoding: x3i(x) = x6 + x5 x3 + x2 + x

1110

x3 + x + 1 ) x6 + x5 x4 + x3 x6 +

1011 ) 1100000 1011

x5 + x4 + x3 x5 +

x3 + x2 x4 + x4 +

x2 x2 + x

Transmitted codeword: b(x) = x6 + x5 + x b = (1,1,0,0,0,1,0) Leon-Garcia/Widjaja

1110 1011

x

Communication Networks

1010 1011 010

Figure 3.68

Encoder for g (x ) = x

i (x ) = x

3

+x

i (x ) Clock 0 1 2 3 4 5 6 7

+

Input 1 = i3 1 = i2 0 = i1 0 = i0 0 0 0 Check bits:

+ x +1

g1 =1

g0 = 1

2

3

Reg 0

Reg 0 0 1 1 0 1 1 1 0 r0 = 0

+

g3 = 1 Reg 1

Reg 1 0 0 1 1 1 0 0 1 r1 = 1

Reg 2

Reg 2 0 0 0 1 1 1 0 0 r2 = 0

r(x) = x Leon-Garcia/Widjaja

Communication Networks

Figure 3.69

(Transmitter)b(x)

+

R(x) (Receiver)

e(x) Error pattern

Leon-Garcia/Widjaja

Communication Networks

Figure 3.70

1. Single errors:

0 ≤ i ≤ n-1

e(x) = xi

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-k−1

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.

Leon-Garcia/Widjaja

Communication Networks

Figure 3.71

ith position

4. Error bursts of length b: e(x) = xi d(x)

L 0000110• • •0001101100 • • • 0 error pattern 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)) z z

z

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

Leon-Garcia/Widjaja

Communication Networks

Figure 3.72

(a) Single bit input (Transmitter) b

+

r (Receiver)

e Error pattern (b) Vector input (Transmitter) b

+

r (Receiver)

e Error pattern

Leon-Garcia/Widjaja

Communication Networks

Figure 3.73

1011100 s=He= 1101010 0111001

1011100 s=He= 1101010 0111001

1011100 s=He= 1101010 0111001

Leon-Garcia/Widjaja

0 0 1 0 0 0 0 0 1 0 0 1 0 0

1

Single error detected

= 0 1

0 1 = 1 + 0 = 1 0

1 1 1 1 0 = 1 + 0 0 0 0

0 1 + 1

Communication Networks

1 1 1

1 0 = 0 1

Double error detected

Triple error not detected

Figure 3.74

s = H r = He 7p s=0

s=0

No errors in transmission (1–p)7

Leon-Garcia/Widjaja

1–3p

Undetectable errors 7p3

Correctable errors 7p(1–3p)

Communication Networks

3p Uncorrectable errors 21p2

Figure 3.75

b1

o

o

o

o

b2

Set of all n-tuples within distance t

Set of all n-tuples within distance t

t=2

Leon-Garcia/Widjaja

Communication Networks

Figure 3.76

L codewords written vertically in array; then transmitted row by row

b1

b2

b3

b4

b1

b2

b3

b4

A long error burst produces errors in two adjacent rows

Leon-Garcia/Widjaja

...

bL-3 bL-2 bL-1 bL

bL-3 bL-2 bL-1 bL

...

Communication Networks

Figure 3.77

13

1

(a)

• • • • • • • • • • • • • • • • • • • • • • • • • 14

(b)

DTE

Leon-Garcia/Widjaja

25

1

Protective Ground (PGND)

1

2

Transmit Data (TXD)

2

3

Receive Data (RXD)

3

4

Request to Send (RTS)

4

5

Clear to Send (CTS)

5

6

Data Set Ready (DSR)

6

7

Ground (G)

7

8

Carrier Detect (CD)

8

20

Data Terminal Ready (DTR)

20

22

Ring Indicator (RI)

22

Communication Networks

DCE

Figure 3.78

Data bits Line idle

Start bit

1

3T/2

2

T

3

T

4

T

5

T

6

T

7

T

8

Stop bit

T

Receiver samples the bits

Leon-Garcia/Widjaja

Communication Networks

Figure 3.79

X(f)

0

-W

f

W

X(f)

X(f + 1/T)

X(f – 1/T)



… –1 T

–W

0

W X(f)

X(f + 1/T)

f

X(f – 1/T)



… –W

Leon-Garcia/Widjaja

1 T

0

Communication Networks

W

f

Figure 3.80

Chapter 3 Figures - Higher Ed

Leon-Garcia/Widjaja. Communication Networks. (a) QCIF videoconferencing at 30 frames/sec = 760,000 pixels/sec. 144. 176. (b) Broadcast TV at 30 frames/sec ...

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