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