ENGS 4 - Lecture 12 Technology of Cyberspace

Winter 2004 Thayer School of Engineering Dartmouth College Instructor: George Cybenko, x6-3843 Assistant: [email protected]

Sharon Cooper (“Shay”), x6-3546 Course webpage: http://thayer.dartmouth.edu/~engs004/ ENGS4 2004 Lecture 12

Today’s Class

• Sarah (social inequality/digital divide) • Ryan (internet dating) • Noah R. (nanotechnology) • Leo • Break • Lempel-Ziv Coding • Digitalization of analog signals • Wireless networking basics ENGS4 2004 Lecture 12

Future mini-lectures

• Feb 24 – Dason (pornography), En Young (persistence), Rob (GPS), Simon (online games) ENGS4 2004 Lecture 12

Break

ENGS4 2004 Lecture 12

Models of a source

We can easily measure the probability of each symbol in English. How?

How about the probabilities of each pair of symbols?

Triples?

Sentences?

True model of English = model of language = model of thought This is very hard.

ENGS4 2004 Lecture 12

Lempel-Ziv Coding (zip codes, etc)

Want to encode a string: aaabcababcaaa into 0’s and 1’s.

Step 1: Convert to 0’s and 1’s by any prefix substitution.

a=00 b=01 c=11 00000001110001000111000000 ENGS4 2004 Lecture 12

Lempel-Ziv Coding (zip codes, etc)

Step 2: Parse the string into “never before seen” strings.

00000001110001000111000000 0,00,000,01,1,10,001,0001,11,0000,00 ENGS4 2004 Lecture 12

Lempel-Ziv Coding (zip codes, etc)

Step 3: Assign binary numbers to each.

0,00,000,01,1,10,001,0001,11,0000,00 0001,0010,0011,0100,0101,0110,0111,1000,1001,1010,1011 Step 4: To each string, assign number of substring plus last bit.

00000,00010,00100,00011,00001,01010,00101, 00000000100010000011000010101000101...

ENGS4 2004 Lecture 12

Lempel-Ziv Coding (zip codes, etc)

Step 5: Store this string plus length of labels in bits.

00000,00010,00100, 1111000000001000100....

This may be inefficient for small examples but for very long inputs, it achieves the entropy for the best model.

LZW = Lempel-Ziv-Welsch, GIF image interchange standard ENGS4 2004 Lecture 12

Example

What is the Lempel Ziv encoding of 00000...0000 (N 0’s)?

What is the entropy of the source?

How many bits per symbol will be used in the encoded data as N goes to infinity?

Let’s work out the details.

How about 010010001000010000010000001.... ?

ENGS4 2004 Lecture 12

Properties of Lempel-Ziv

For most sources (alphabets+probabilities), the Lempel-Ziv algorithm will result in average number of bits per symbol entropy of the source (any order model) if the string/data to be compressed is long enough.

How about compressing the compressed string?

That is, applying Lempel-Ziv again and again?

Answer: The compressed bit string will look completely random: 0 or 1 with probability 1/2.

Entropy = 1 means 1 bit per symbol on average.

No improvement is possible.

ENGS4 2004 Lecture 12

Analog vs Digital

• Most “real world” phenomena is continuous: • images • vision • sound • touch • To transmit it, we must convert continuous signals into digital signals.

• Important note: • There is a fundamental shift from continuous to digital representation of the real world.

ENGS4 2004 Lecture 12

The Fundamental Shift

The telephone system is designed to carry analog voice signals using circuit switching. The whole infrastructure is based on that.

When a modem connects your computer to the network over a telephone line, the modem must disguise the computer data as a speech/voice signal.

The infrastructure of the internet is totally digital.

Sending voice over the internet requires disguising voice as digital data!!!

This is a fundamental turnaround....same will hold for TV, cable TV, audio, etc.

ENGS4 2004 Lecture 12

111 110 101 100 011 010 001 000

Analog to Digital Conversion

are samples d 2d 3d 4d 5d 6d 7d 8d 9d 10d 11d 12d time ENGS4 2004 Lecture 12

111 110 101 100 011 010 001 000

Analog to Digital Conversion

are samples d 2d 3d 4d 5d 6d 7d 8d 9d 10d 11d 12d time d is the “sampling interval”, 1/d is the sampling “rate” ENGS4 2004 Lecture 12

Sampling and quantization

In this example, we are using 8 quantization levels which requires 3 bits per sample. Using 8 bits per sample would lead to 256 quantization levels, etc.

If the sampling interval is 1/1000000 second (a microsecond), the sampling rate is 1000000 samples per second or 1 megaHertz.

Hertz means “number per second” so 20,000 Hertz means 20,000 per second.

So sampling at 20 kiloHertz means “20,000 samples per second” ENGS4 2004 Lecture 12

Analog frequencies

All real world signals can be represented as a sum or superposition of sine waves with different frequencies - Fourier representation theorem.

The frequency of a sine wave is the number of times it oscillates in a second.

Sine wave with frequency 20 will complete a cycle or period once every 1/20th of a second so 20 times a second, etc.

We say that a sine wave with frequency 20 is a 20 Hertz signal.....oscillates 20 times a second.

ENGS4 2004 Lecture 12

Fourier Java Applet

http://www.falstad.com/fourier/ ENGS4 2004 Lecture 12

Nyquist Sampling Theorem

• If an analog signal is “bandlimited” (ie consists of frequencies in a finite range [0, F]), then sampling must be at or above the twice the highest frequency to reconstruct the signal perfectly.

• Does not take quantization into account.

• Sampling at lower than the Nyquist rate will lead to “aliasing”.

ENGS4 2004 Lecture 12

Sampling for Digital Voice

• High quality human voice is 4000 Hz • Sampling rate is 8000 Hz • 8 bit quantization means 64,000 bits per second • Phone system built around such a specification • Computer communications over voice telephone lines is limited to about 56kbps ENGS4 2004 Lecture 12

Implications for Digital Audio

• Human ear can hear up to 20 kHz • Sampling at twice that rate means 40 kHz • Quantization at 8 bits (256 levels) • 40,000 samples/second x 8 bits/ sample translates to 320,000 bits per second or 40,000 bytes per second.

• 60 seconds of music: 2,400,000 Bytes • 80 minutes: about 190 Mbytes • Audio CD??

ENGS4 2004 Lecture 12

Some Digital Audio Links

• • http://www.musiq.com/recording/mp3/index.html

http://www.musiq.com/recording/digaudio/bitrates.html

• Aliasing in Images http://www.telacommunications.com/nutshell/pixelation.ht

m#enlargement • Other http://www.physics.nyu.edu/faculty/sokal/#papers ENGS4 2004 Lecture 12

Introduction to Wireless Networks

Radio frequency constraints Current standards Current limitations ENGS4 2004 Lecture 12

Atmospheric Propagation of RF

F 2 F 1 E D EARTH 400km 250km 220km 200km 150km 90km 50km F 2 Layers in the ionosphere F 1 E D Electron Density ENGS4 2004 Lecture 12

F 2 F 1 E D

Refraction of Radiowaves

30 MHz 20 MHz 30 MHz 20 MHz 10 MHz

EARTH

ENGS4 2004 Lecture 12

Resulting Classes of RF Waves

Space Wave 30-3000 MHz Sky Wave 3-30 MHz Ground Wave 10-3000 kHz ENGS4 2004 Lecture 12 Communications satellite > 3GHz

Interior Path Loss Function

(Frequency dependent) d Power transmitted - Power received = L p = L + 10n log 10 (d) +lognorm(v) Experimentally and statistically determined - n is signal decay exponent, L is path loss at d=1m, lognorm is log-normal distribution with variance v.

ENGS4 2004 Lecture 12

Ambient Noise and Absorption

Power required for constant signal/(ambient noise) Sweet Spot Power for constant received signal power 1GHz 2GHz ENGS4 2004 Lecture 12 Frequency

Digital bps vs Analog Hz

Digital bandwidth of B bits per second can be encoded into an analog signal of roughly B Hertz. The B Hz signal is attached to a C Hz carrier resulting in a signal that lives in the interval [C,C+B] Hz.

Example: 2.4 - 2.45 GHz can carry 50 Mbps.

ENGS4 2004 Lecture 12

Current Standards

Cellular Digital Packet Data (CDPD) 19.2 kbps extension of cellular telephone network

Wireless LAN’s

1-2 Mbps using 2.4 GHz ISM (Industrial, Scientific Medical) band. Range 30-250 meters. IEEE 802.11

standard in place. Products by Lucent, Digital, etc.

$500 PCMCIA radio transceiver. > $1000 for base.

Wireless WAN’s

Metricom Richocet technology (US only). 28.8 kbps with a range of about 1 km.

ENGS4 2004 Lecture 12

Architecture

Access point (base station) Multihop not implemented Wired network ENGS4 2004 Lecture 12 Handoffs between access points in the same subnet - else need mobile IP

Name

Satellite Communications Upswing

Speed Cost Receiver Start Date Satellites Planet 1 9.6kbps $3/min Notebook ICO Globalcom 64kbps $1.50/min Dual-mode (Inmarsat) Now 2000 5 GEO’s 10 MEO’s Iridium (Motorola) 2.4kpbs $3/min Handset 1998 66 LEO’s Globalstar Cyberstar (Loral) 9.6kbps <$1/min Dual-mode 1998 48 GEO’s 6mbps ?? Home dish 2000 3 GEO’s Odyssey 9.6kbps $0.95/min Handset 2001 (TRW) 64kbps $0.65/min Dish Teledesic 2mbps $100’s Dish (Gates/McCaw) /month ENGS4 2004 Lecture 12 2002 12 MEO’s 288 LEO’s

Glossary

LEO’s

- Low Earth Orbit about 1,000 kms above earth

MEO’s

- Medium Earth Orbit about 10,000 kms

GEO’s

- Geostationary/Geosynchronous Earth Orbit about 36,000 kms

Dual-mode

handset supports both satellite and cellular communications.

ENGS4 2004 Lecture 12

Cellular Technology

• Frequencies used in cell phones have limited spatial propagation - this is good....we can reuse them.

• But adjacent “cells” cannot use the same frequencies if the phones are frequency multiplexed • So must multiplex based on space as well.

is a cell in which certain frequencies are allowed to be used.

Cells of different colors use different frequencies.

ENGS4 2004 Lecture 12

Freq 1 Freq 2 Freq 3

Frequency Division Multiple Access (FDMA)

User A User B User C Time Within a “cell” users are allocated a single frequency.

ENGS4 2004 Lecture 12

Time Division Multiple Access (TDMA)

Freq 1 User A User B User C Time Within a “cell” users are allocated time slots within a single frequency.

ENGS4 2004 Lecture 12

Code Division Multiple Access (CDMA)

Freq 1 Freq 2 Freq 3 User A User B User C Time Within a “cell” users are allocated different frequencies at different times.

ENGS4 2004 Lecture 12

Different Multiple Access Concepts

TDMA - examples??

FDMA - examples??

CDMA - examples??

SDMA - examples??

ENGS4 2004 Lecture 12

Implications for Wireless Networking

• Mobile users will experience varying delivered bandwidth.

• Connections will be intermittent, unreliable.

• Spatial multiplexing (cellular architecture) is required.

• Bandwidth will be a precious resource.

• Battery technology is very important.

• Antenna size and type is a factor.

• Security - eavesdropping, jamming.

ENGS4 2004 Lecture 12