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CSCD 433Network ProgrammingFall 2012

Lecture 4aPhysical Layer Line Coding

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

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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 bandwidth2. The number of levels used to represent

signals3. The quality of the channel (the level of noise)

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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

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Noiseless Channel: Nyquist Bit Rate

Defines theoretical maximum bit rate for Noiseless Channel:

Bit Rate=2 X Bandwidth X log2L L = number of signal levels

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ExampleExample

Have a noiseless channel Bandwidth of 3000 Hz transmitting a signal with two signal levelsThe maximum bit rate can be calculated as

Bit Rate = 2 Bit Rate = 2 3000 3000 log log22 2 = 6000 bps 2 = 6000 bps

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Example Example

Consider the same noiseless channelTransmitting a signal with four signal levels

– For each level, we send two bitsThe maximum bit rate can be calculated as: Bit Rate = 2 x 3000 x logBit Rate = 2 x 3000 x log22 4 = 12,000 bps 4 = 12,000 bps

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

Note

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Claude ShannonNoisy 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

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Noisy Channel: Shannon Capacity Defines theoretical maximum bit rate for

Noisy Channel:

Capacity=Bandwidth X log2(1+SNR)

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ExampleExample

Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zeroIn other words, the noise is so strong that the signal is faint For this channel the capacity is calculated as

C = B logC = B log22 (1 + SNR) = B log (1 + SNR) = B log22 (1 + 0) (1 + 0)

= B log= B log22 (1) = B (1) = B 0 = 0 0 = 0

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ExampleExample

We can calculate the theoretical highest bit rate of a regular telephone lineA telephone line normally has a bandwidth of 4KHzThe signal-to-noise ratio is usually 3162For this channel the capacity is calculated as

C = B logC = B log22 (1 + SNR) = 3000 log (1 + SNR) = 3000 log22 (1 + 3162) (1 + 3162) = 3000 log= 3000 log22 (3163) (3163)

C = 3000 C = 3000 11.62 = 34,860 bps 11.62 = 34,860 bps

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

SolutionSolution

C = B logC = B log22 (1 + SNR) = 10 (1 + SNR) = 1066 log log22 (1 + 63) = 10 (1 + 63) = 1066 log log22 (64) = 6 Mbps (64) = 6 Mbps

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

6 Mbps = 2 6 Mbps = 2 1 MHz 1 MHz log log22 L L L = 8 L = 8

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

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Digital Modulation

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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

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Line Coding Schemes

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

Note

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Unipolar Encoding

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

Note

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Polar: NRZ-L and NRZ-I Encoding

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In NRZ-L, level of voltage determines value of the bit

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

Note

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Polar: RZ Encoding

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Polar: Manchester Encoding

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In Manchester and differential Manchester encoding, the transition

at the middle of the bit is used for synchronization.

Note

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

Note

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Bipolar: AMI (Alternative Mark Inversion) Encoding

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Summary

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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