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CSCD 433Network ProgrammingFall 2013

Lecture 5aDigital Line Coding and other ...

Physical Layer Topics

• Digital transmission of digital data• Physical limits of networks for data • Encoding data onto signals

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Summary so Far Analog Communication

– Objective is to transform waveform– Varies continuously with time– Distortions unavoidable– More difficult to reproduce signal at receiver

Digital Communication– Objective is to transmit a symbol– Binary is 0 or 1– Done by transmitting positive voltage for 1,

negative voltage for 0– Receiver interprets symbol– Can handle a lot of distortion and still discern

symbol

Purpose of Digital Transmission Transfer sequence of 0's and 1's from transmitter on left to receiver on right

Interested in bit rate in bits/s Can look at cross section of pipe, R Think of it as pipe diameter As R increases, volume of information flow/s

increases

0110101 0110101

d meters

Channel

transmit receive

R

Summary of Analog and Digital Conversions

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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? Also worry about errors ...

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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Fundamental Limits of Digital Transmission Quality measured by: 1. Transmission speed or bit rate 2. Bit error rate in fraction of bits received in error

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Noiseless Channel: Nyquist Bit Rate Defines theoretical maximum bit rate for

Noiseless Channel: Bit Rate = 2 X Bandwidth X log2 L 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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Capacity of a SystemThe bit rate of a system increases with an increase in the number of signal levels we use to denote a symbol.A symbol can consist of a single bit or “n” bits.The number of signal levels = 2n.As the number of levels goes up, the spacing between level decreases -> increasing the probability of an error occurring in the presence of transmission impairments.

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Increasing Levels In theory, can increase the bit rate by

increasing the number of levels Yet, random noise limits the bit rate in

practice Noise causes measurement system to

make mistakes

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What is Communication Channel Noise Noise

Interference from sources like radio waves

Electrical wires, and Bad connections that alter the data

Distortion Alteration in signal caused by

communication channel itself Noise generated by components is

categorized as thermal noise Also known as additive noise.

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Claude ShannonNoisy Channel

Claude Shannon developed mathematical theory in the 1940's for noisy channels

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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Result = B logResult = B log22 (1) = B (1) = B 0 = 0 0 = 0This means that the capacity of this channel is zero regardless of the bandwidth

In other words, we cannot receive any data through this channel !!!

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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 3000 bpsThe 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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Example continued Result C = 3000 C = 3000 11.62 = 34,860 bps 11.62 = 34,860 bps

This means that the highest bit rate for a telephone line is 34.860 kbps

If we want to send data faster than this, we can either increase the bandwidth of the line or improve the signal-to-noise ratio.

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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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The Shannon capacity gives us the upper limit; the Nyquist formula tells us

how many signal levels we need.

Note

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Digital Line Coding

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Digital Line Coding Method for converting digital binary

information sequence into digital signal Selecting coding technique involves several

considerations Previously we said ...

– Wanted to maximize bit rate over channels with limited bandwidth

Yet, LAN's have other concerns– Ease of bit timing recovery from signal – So, receiving sample clock can maintain its

synchronization with transmitting clock– Some methods better at noise and interference

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Line Coding Schemes

Unipolar: Uses one voltage level Polar: Uses two voltage levels Bipolar: Uses three or more voltage levels

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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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Reception ErrorsTiming mismatch between sending and receiving computers

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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• Looked at digital data over digital

channels• Theoretical maximum limits of

transmitting bits in presence of noise and without

• Line encoding makes it possible to send more data as efficiency of coding increases

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• New Assignment is up !!!