Transcript Document 7580403
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