Transcript William Stallings Data and Computer Communications

Data and Computer
Communications
Chapter 3
Data Transmission
Required Reading: Stallings chapter 3
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Physical Layer
Source node
Destination node
Application
Application
Presentation
Presentation
Session
Session
Intermediate node
transport
Network
Packets
transport
Network
Network
Data link
Data link
Physical
Physical
Frames
Data link
Physical
Bits
Signals
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Physical / Data Link Layer Interface
Sender
Receiver
NL
DLL
PL
HDR
Frame
ACK
HDR
Transmitted Bits
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Physical Layer
Communications and Information Theory are topics
of whole courses
We’ll cover some theoretical basics regarding
communications over a physical channel
We discover that there are physical limitations to
communications over a given channel
We’ll cover some fundamental theorems
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Terminology (1)
Transmitter
Receiver
Medium
Guided medium
e.g. twisted pair, optical fiber
Unguided medium
e.g. air, water, vacuum
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Terminology (2)
Direct link
No intermediate devices
Point-to-point
Direct link
Only 2 devices share link
Multi-point
More than two devices share the link
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Terminology (3)
Simplex
One direction (but in Europe means half duplex)
e.g. Television
Half duplex
Either direction, but only one way at a time
e.g. police radio
Full duplex
Both directions at the same time
e.g. telephone
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Electromagnetic Signals
Function of time
Analog (varies smoothly over time)
Digital (constant level over time, followed by a
change to another level)
Function of frequency
Spectrum (range of frequencies)
Bandwidth (width of the spectrum)
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Frequency, Spectrum and
Bandwidth
Time domain concepts
Continuous signal
Varies in a smooth way over time
Discrete signal
Maintains a constant level then changes to another constant
level
Periodic signal
Pattern repeated over time
Aperiodic signal
Pattern not repeated over time
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Periodic Signal Characteristics
Amplitude (A): signal value, measured in volts
Frequency (f ): repetition rate, cycles per second or
Hertz
Period (T): amount of time it takes for one repetition,
T=1/f
Phase (Φ): relative position in time, measured in
degrees or radians
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Analog Signaling
amplitude (volts)
represented by sine waves
1 cycle
phase
difference
time
(sec)
frequency (hertz)
= cycles per second
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Digital Signaling
amplitude (volts)
represented by square waves or pulses
1 cycle
time
(sec)
frequency (hertz)
= cycles per second
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Continuous & Discrete Signals
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Periodic
Signals
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Sine Wave
Peak Amplitude (A)
maximum strength of signal
volts
Frequency (f)
Rate of change of signal
Hertz (Hz) or cycles per second
Period = time for one repetition (T)
T = 1/f
Phase ()
Relative position in time
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Varying Sine Waves
Sin2πt
0.5Sin2πt
Sin 2
Phase Shift in
radians
Sin4πt
Sin (2t 
or

4
)
Sin2 (t  0.125)
Phase Shift in
seconds 16
Wavelength ()
Distance occupied by one cycle
Distance between two points of corresponding
phase in two consecutive cycles
Assuming signal velocity in space is equal to v
 = vT or
f = v
Here, V=c = 3*108 ms-1 (speed of light in free space)
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Frequency Domain Concepts
A Signal is usually made up of many frequencies
Components are sine waves
It Can be shown (Fourier analysis) that any
signal is made up of component sine waves
One can plot frequency domain functions
instead of/in addition to time domain functions
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Addition of
Frequency
Components
(a) Sin(2πft)
(b) (1/3)Sin(2π(3f)t)
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(c) (4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
Frequency
Domain
Note: For square waves,
only odd harmonics exist
(plus the fundamental
component of course).
Figure a is discrete because
the time domain function is
periodic. Figure b is
continuous because the time
domain function is aperiodic.
(a) Frequency domain function for s(t)=(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
See Figure 3.16 Page
103. Note that s(f) is
of the form SinX
X
(b) Frequency domain function for a single square pulse s(t)=1 for -X/2<t<X/2
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Communications Basics
 Represent a signal as a single-valued function of time,
g(t), to model behavior of a signal (may be voltage,
current or other change)
 Jean-Baptiste Fourier showed we can represent a
periodic signal (given some conditions) as the sum of a
possibly infinite number of sines and cosines
Period = T
g(t) = (1/2)c + n=1
S an sin(2nft) +n=1S bn cos(2nft)
f = 1/T is fundamental frequency
a & b coefficients are the amplitude of the nth harmonic
This is a Fourier Series
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Original
Time ->
Harmonic spectrum
As we add
more
harmonics
the signal
reproduces
the original
more closely
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Signal Transmission
No transmission facility can transmit signals
without losing some power
Usually this attenuation is frequency
dependent so the signal becomes distorted
Generally signal is completely attenuated
above some max frequency (due to medium
characteristics or intentional filtering)
The signal is bandwidth limited
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Signal Transmission
Time T necessary to transmit a character depends on
coding method and signalling speed
Signaling speed = number of times per second the
signal changes value and is measured in baud
Note that baud rate is not necessarily the same as
the bit rate
By limiting the bandwidth of the signal we also limit
the data rate even if a channel is perfect
Overcome this by encoding schemes
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Spectrum & Bandwidth
Spectrum
range of frequencies contained in signal
Absolute bandwidth
width of spectrum
Effective bandwidth
Often just bandwidth
Narrow band of frequencies containing most of the
energy
DC Component
Component of zero frequency
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Signal with DC Component
(a) s(t)=1+(4/π)[Sin(2πft)+(1/3)Sin(2π(3f)t)]
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Data Rate and Bandwidth
Any transmission system has a limited band of
frequencies
This limits the data rate that can be carried
See Figure 3.8 Page 79
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Bandwidth
Width of the spectrum of frequencies that can
be transmitted
if spectrum=300 to 3400Hz, bandwidth=3100Hz
Greater bandwidth leads to greater costs
Limited bandwidth leads to distortion
Analog measured in Hertz, digital measured in
baud
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BPS vs. Baud
BPS=bits per second
Baud=# of signal changes per second
Each signal change can represent more than
one bit, through variations on amplitude,
frequency, and/or phase
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Analog and Digital Data
Transmission
Data
Entities that convey meaning
Signals
Electric or electromagnetic representations of data
Transmission
Communication of data by propagation and
processing of signals
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Data
Analog
Continuous values within some interval
e.g. sound, video
Digital
Discrete values
e.g. text, integers
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Acoustic Spectrum (Analog)
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Signals
Means by which data are propagated
Analog
Continuously variable
Various media
wire, fiber optic, space
Speech bandwidth 100Hz to 7kHz
Telephone bandwidth 300Hz to 3400Hz
Video bandwidth 4MHz
Digital
Use two DC components
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Digital Text Signaling
Transmission of electronic pulses representing
the binary digits 1 and 0
How do we represent letters, numbers,
characters in binary form?
Earliest example: Morse code (dots and dashes)
Most common current form: ASCII
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ASCII Character Codes
Use 8 bits of data (1 byte) to transmit one
character
8 binary bits has 256 possible outcomes (0 to
255)
Represents alphanumeric characters, as well as
“special” characters
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Digital Image Signaling
 Pixelization and binary representation
Code:
00000000
00111100
01110110
01111110
01111000
01111110
00111100
00000000
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Data and Signals
Usually use digital signals for digital data and
analog signals for analog data
Can use analog signal to carry digital data
Modem
Can use digital signal to carry analog data
Compact Disc audio
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Why Study Analog?
Telephone system is primarily analog rather
than digital (designed to carry voice signals)
Low-cost, transmission medium (present almost
at all places at all times
If we can convert digital information (1s and 0s)
to analog form (audible tone), it can be
transmitted inexpensively
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Voice Signals
Easily converted from sound frequencies
(measured in loudness/db) to electromagnetic
frequencies, measured in voltage
Human voice has frequency components
ranging from 20Hz to 20kHz
For practical purposes, the telephone system
has a narrower bandwidth than human voice,
from 300 to 3400Hz
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Analog Signals Carrying Analog
and Digital Data
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Digital Signals Carrying Analog
and Digital Data
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Analog Transmission
Analog signal transmitted without regard to
content
May be analog or digital data
Attenuated over distance
Use amplifiers to boost signal
Also amplifies noise
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Digital Transmission
Concerned with content
Integrity endangered by noise, attenuation etc.
Repeaters used
Repeater receives signal
Extracts bit pattern
Retransmits
Attenuation is overcome
Noise is not amplified
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Advantages of Digital
Transmission
 Digital technology
Low cost LSI/VLSI technology
 Data integrity
Longer distances over lower quality lines
 Capacity utilization
Economical high bandwidth links
High degree of multiplexing easier with digital
techniques
 Security & Privacy
Encryption
 Integration
Can treat analog and digital data similarly
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Transmission Media
the physical path between transmitter and
receiver
design factors
bandwidth
attenuation: weakening of signal over distances
interference
number of receivers
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Impairments and Capacity
Impairments exist in all forms of data
transmission
Analog signal impairments result in random
modifications that impair signal quality
Digital signal impairments result in bit errors (1s
and 0s transposed)
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Transmission Impairments
Signal received may differ from signal
transmitted
Analog - degradation of signal quality
Digital - bit errors
Caused by
Attenuation and attenuation distortion
Delay distortion
Noise
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Transmission Impairments
Attenuation
loss of signal strength over distance
Attenuation Distortion
different losses at different frequencies
Delay Distortion
different speeds for different frequencies
Noise
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Attenuation
P1 watts
transmitter
P2 watts
receiver
Attenuation
10 log10 (P1/P2) dB
Amplification
10 log10 (P2/P1) dB
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Attenuation
Signal strength falls off with distance
Depends on medium
Received signal strength:
must be enough to be detected
must be sufficiently higher than noise to be received
without error
Attenuation is an increasing function of
frequency
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Delay Distortion
Only in guided media
Propagation velocity varies with frequency
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Noise (1)
Additional signals inserted between transmitter
and receiver
Types of Noise:
Thermal
Due to thermal excitement of electrons
Uniformly distributed, cannot be eliminated
White noise
Intermodulation
Signals that are the sum and difference of original
frequencies sharing a medium
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Noise (2)
Crosstalk
A signal from one line is picked up by another
 NEXT (near-end crosstalk
)
interference in a wire at the transmitting end of a signal
sent on a different wire
 FEXT (far-end crosstalk)
interference in a wire at the receiving end of a signal
sent on a different wire
Impulse
Irregular pulses or spikes
e.g. External electromagnetic interference
Short duration
High amplitude
Less predictable
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Noise
 Effect
distorts a transmitted signal
attenuates a transmitted signal
 signal-to-noise ratio to quantify noise
S/Ndb =
10 log S
N
S= average signal power
N= noise power
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Effect of noise
Signal
Noise
Logic
Threshold
Signal+Noise
Sampling times
0 1
0 1
1
0
1 1 0
1 1 0
0
0
0
1
0 1
0 1
Data Received
Original data
Bit error
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Channel Capacity
Data rate
In bits per second
Rate at which data can be communicated
Bandwidth
In cycles per second of Hertz
Constrained by transmitter and medium
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Maximum Data Rate
In 1920s Nyquist (of the Nyquist Theorem)
developed an equation for the maximum data rate of
a noiseless channel
For low pass filtered signal of bandwidth B
Sampling at exactly 2B samples per sec allows
reconstruction of the signal
More samples are useless since the frequencies
above B are filtered out
C=Capacity=max data rate = 2B log2 M bits/sec
for M discrete levels
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Nyquist theorem
“ In a perfectly noiseless channel, if f is the
maxmimum frequency the medium can transmit, the
receiver can completely reconstruct a signal by
sampling it 2*f times per second”
Nyquist, 1920
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Nyquist formula
C=
2B log2 M
B = bandwidth
M = number of discrete signal levels
Theoretical capacity for Noiseless channel
Example: Channel capacity calculation for voice bandwidth (~3100 Hz):
M
2
4
8
16
Max data rate (C)
6200 bps
12400 bps
18600 bps
24800 bps
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Shannon’s Law
In the ‘40s Shannon (of Shannon’s Law) extended the
equation to a channel subject to thermodynamic
(thermal) noise
Thermal noise measured by ratio of signal (S) power to
noise (N) power (signal-to-noise ratio - S/N)
But represented as: 10 log10 S/N
These units are called decibels (dB)
Now, for a channel with signal to noise of S/N
Capacity=C=max bits/sec = B log2 (1 + S/N)
Here, C=Theoretical Maximum capacity with noise
Note: Only much lower rates are achieved since the equation
assumes zero impulse noise and no attenuation and delay
distortion.
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Bit rate and Baud rate
 Bit rate
number of bits that are transmitted in a second
 Baud rate
number of line signal changes (variations) per second
If a modem transmits 1 bit for every signal
change
bit rate = baud rate
If a signal change represents 2 or more or n
bits
bit rate = baud rate *n
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