CSCD 433 Network Programming

Fall 2012

Lecture 4a

Physical Layer Line Coding 1

Physical Layer Topics

• •

Physical limits of networks for data Encoding data onto signals

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Physical Layer

    Looked at physical media for networks Many types of wired and wireless connections All have different capacities and purposes with regards to network creation Next, look at some theoretical limits of networks, encoding schemes for digital modulation and several multiplexing methods

Data Rate Limits

 Important consideration in data communications is  How fast we can send data, in bits per second, over a channel?

 Data rate depends on three factors: 1. The available bandwidth 2. The number of levels used to represent signals 3. The quality of the channel (the level of noise) 4

Nyquist Maximum

  1924, Henry Nyquist of AT&T developed an equation for a perfect channel with finite capacity His equation expresses – Maximum data rate for a finite bandwidth

noiseless

channel 5

Noiseless Channel: Nyquist Bit Rate

 Defines theoretical maximum bit rate for Noiseless Channel:   Bit Rate=2 X Bandwidth X log 2 L L = number of signal levels 6

Example

Have a noiseless channel Bandwidth of 3000 Hz transmitting a signal with two signal levels The maximum bit rate can be calculated as Bit Rate = 2  3000  log 2 2 = 6000 bps 7

Example

Consider the same noiseless channel Transmitting a signal with four signal levels – For each level, we send two bits The maximum bit rate can be calculated as: Bit Rate = 2 x 3000 x log 2 4 = 12,000 bps 8

Note

Increasing the levels of a signal may reduce the reliability of the system

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Claude Shannon Noisy Channel

 Claude Shannon developed mathematical theory in the 1940's for noisy channels  He used Entropy in his equation, which is the amount of randomness for a channel  Then, defined the amount of information that a message could carry  This allowed networks to plan for capacity of information 10

Noisy Channel: Shannon Capacity

 Defines theoretical maximum bit rate for Noisy Channel:  Capacity=Bandwidth X log 2 (1+SNR) 11

Example

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 For this channel the capacity is calculated as C = B log 2 (1 + SNR) = B log 2 (1 + 0) = B log 2 (1) = B  0 = 0 12

Example

We can calculate the theoretical highest bit rate of a regular telephone line A telephone line normally has a bandwidth of 4KHz The signal-to-noise ratio is usually 3162 For this channel the capacity is calculated as C = B log 2 (1 + SNR) = 3000 log 2 (1 + 3162) = 3000 log 2 C = 3000  (3163) 11.62 = 34,860 bps 13

Example

We have a channel with a 1 MHz bandwidth The SNR for this channel is 63, What is the appropriate bit rate and signal level?

Solution

First, we use the Shannon formula to find our upper limit

C = B log 2 (1 + SNR) = 10 6 log 2 (1 + 63) = 10 6 log 2 (64) = 6 Mbps

Then we use the Nyquist formula to find the number of signal levels.

6 Mbps = 2



1 MHz



log 2

L



L = 8

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Digital Modulation 15

Digital Modulation

   Process of converting between bits and signals is called digital modulation Convert voltages into bits  Mostly for wired media Other schemes regulate the phase or frequency of a carrier signal  Mostly for wireless media 16

Line Coding Schemes

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Note

In unipolar encoding, we use only one voltage level, positive

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Unipolar Encoding

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Note

In polar encoding, we use two voltage levels: positive & negative

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Polar: NRZ-L and NRZ-I Encoding

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Note

In NRZ-L, level of voltage determines value of the bit In NRZ-I, inversion or lack of inversion determines value of the bit

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Polar: RZ Encoding

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Polar: Manchester Encoding

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Note

In Manchester and differential Manchester encoding, the transition at the middle of the bit is used for synchronization.

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Note

In bipolar encoding, we use three levels: positive, zero, and negative.

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Bipolar: AMI (Alternative Mark Inversion) Encoding 27

Summary

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Summary

• • • Many types of encoding for sending data over analog types of lines Multiplexing allows sharing – More on this later ….

There are actually limits to how much data can be sent within a network

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