# 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
2
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
3
Message Transmission Delay
Total transmission delay
= (size_of_message / throughput) + propagation_time
Sender
01101…
Time
01101…
t0
t1
first bit last bit
sent
sent
t2
t3
first bit last bit
arrived arrived
propagation_time
4
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?
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?
5
Signals
Information must be transformed into
electromagnetic signals to be
transmitted
 Signal forms

Analog or digital
6
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
7
Time Vs. Frequency Domain

A signal can be represented in either
the time domain or the frequency
domain.
8
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
9
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.
10
Frequency Spectrum and Bandwidth

Frequency spectrum
Collection of all component frequencies it
contains

Bandwidth
Width of frequency spectrum
11
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
12
Bandwidth-Limited Signals

(a) A binary signal and its root-meansquare Fourier amplitudes.
13
Bandwidth-Limited Signals (2)

(b) – (e) Successive approximations
to the original signal.
14
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
15
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.
16
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?
17
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?
18
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