Theoretical Basis of Data Communication
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Transcript Theoretical Basis of Data Communication
CS 313 Introduction to
Computer Networking &
Telecommunication
Theoretical Basis of
Data Communication
Chi-Cheng Lin, Winona State University
Topics
Data Communication Performance
Measurements
Analog/Digital Signals
Time and Frequency Domains
Bandwidth and Channel Capacity
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Data Communication Performance
Measurements
Throughput
How fast data can pass through an entity
Number of bits passing through an imaginary wall in
a second
Bit time
Duration of a bit (time for a bit ejected into network)
1 / throughput
Propagation time (propagation delay)
Time required for one bit to travel from one point to
another
Propagation speed depends on medium and signal
frequency
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Message Transmission Delay
Total transmission delay
= (size_of_message / throughput) + propagation_time
Sender
01101…
Time
01101…
Receiver
t0
t1
first bit last bit
sent
sent
t2
t3
first bit last bit
arrived arrived
propagation_time
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Message Transmission Delay - Example
What is the transmission delay of a 2 KB message
transmitted over a 2 km cable that has a throughput
40 Mbps and a propagation delay of 8 µs/km?
Answer:
Total transmission delay
= (size_of_message / throughput) + propagation_time
= (2048 x 8 bits / 40x106 bits/sec) + 8 µs/km x 2 km
= 409.6 x 10-6 sec + 16 µs
= 425.6 µs
What is the bit time?
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Signals
Information must be transformed into
electromagnetic signals to be
transmitted
Signal forms
Analog or digital
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Analog/Digital Signals
Analog signal
Continuous waveform
Can have a infinite number of values in a
range
Digital signal
Discrete
Can have only a limited number of values
E.g., 0 and 1, i.e., two levels, for binary signal
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Time Vs. Frequency Domain
A signal can be represented in either
the time domain or the frequency
domain.
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Period (Time) and Frequency
Unit
Seconds (s)
Equivalent
1s
Unit
Hertz (Hz)
Equivalent
1 Hz
Milliseconds (ms)
10–3 s
Kilohertz (KHz)
103 Hz
Microseconds (ms)
10–6 s
Megahertz (MHz)
106 Hz
Nanoseconds (ns)
10–9 s
Gigahertz (GHz)
109 Hz
Picoseconds (ps)
10–12 s
Terahertz (THz)
1012 Hz
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Composite Signals
A composite signal can be decomposed
into component sine waves - harmonics
The decomposition is performed by
Fourier Analysis
DC component is the one with
frequency 0.
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Frequency Spectrum and Bandwidth
Frequency spectrum
Collection of all component frequencies it
contains
Bandwidth
Width of frequency spectrum
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Digital Signal - Decomposition
A digital signal can be decomposed into an
infinite number of simple sine waves
(harmonics)
A digital signal is a composite signal
with an infinite bandwidth.
More harmonics components
= better approximation
Animation
Significant spectrum
Components required to reconstruct the digital
signal
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Bandwidth-Limited Signals
(a) A binary signal and its root-meansquare Fourier amplitudes.
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Bandwidth-Limited Signals (2)
(b) – (e) Successive approximations
to the original signal.
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Channel Capacity
Channel capacity
Maximum bit rate a transmission medium can
transfer
Nyquist theorem for noiseless channels
C = 2H log2V
where C: channel capacity (bit per second)
H: bandwidth (Hz)
V: signal levels (2 for binary)
C is proportional to H
bandwidth puts a limit on channel capacity
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Channel Capacity
Shannon Capacity for noisy channels
C = H log2(1 + S/N)
where C: (noisy) channel capacity (bps)
H: bandwidth (Hz)
S/N: signal-to-noise ratio
dB = 10 log10 S/N
In practice, we have to apply both for
determining the channel capacity.
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Examples
Noiseless channel.
Consider a noiseless channel with a bandwidth of 3000 Hz
transmitting a signal with two signal levels. What is the
maximum bit rate of this channel?
Noiseless channel.
Consider the same noiseless channel, transmitting a signal with
four signal levels (for each level, we send two bits). What is the
maximum bit rate of this channel?
Extremely noisy channel.
Consider an extremely noisy channel in which the value of the
signal-to-noise ratio is almost zero. In other words, the noise is
so strong that the signal is faint. What is the channel capacity of
this channel?
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Examples
Theoretical highest bit rate of a regular telephone line.
A telephone line normally has a bandwidth of 3000 Hz (300 Hz
to 3300 Hz). The signal-to-noise ratio is usually 35dB, i.e.,
3162. What is the capacity of this channel?
Applying both theorems.
We have a channel with a 2 MHz bandwidth. The S/N for this
channel is 127; what is the appropriate bit rate and signal level?
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