Chi-Cheng Lin, Winona State University

CS 313 Introduction to Computer Networking &

Telecommunication

Theoretical Basis of Data Communication

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Topics Data Communication Performance

Measurements

Analog/Digital Signals

Time and Frequency Domains

Bandwidth and Channel Capacity

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Data Communication Performance Measurements

ThroughputHow fast data can pass through an entityNumber 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 DelayTotal transmission delay = (size_of_message / throughput) + propagation_time

Sender

Receivert0 t1 t2 t3

first bit sent

last bit sent

first bit arrived

last bit arrived

Time

propagation_time

01101…

01101…

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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 formsAnalog or digital

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Analog/Digital Signals Analog signal

Continuous waveformCan have a infinite number of values in

a range Digital signal

DiscreteCan have only a limited number of

valuesE.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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Unit Equivalent Unit Equivalen

tSeconds (s) 1 s Hertz (Hz) 1 Hz

Milliseconds (ms) 10–3 s Kilohertz (KHz) 103 Hz

Microseconds (ms) 10–6 s Megahertz (MHz) 106 HzNanoseconds (ns) 10–9 s Gigahertz (GHz) 109 HzPicoseconds (ps) 10–12 s Terahertz (THz) 1012 Hz

Period (Time) and Frequency

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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 spectrumCollection 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 A digital signal is a composite signal with an infinite bandwidth.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-

mean-square 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 channelsC = 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 ratiodB = 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?