Fundamental Insights

• Digital Representation of Data
• Source Coding
• Channel Coding
• Packet Switching
• Project 1: Web server

Analog Representation of Data

• The world as we experience it is continuous
• Records
• Audio Tapes
• Telephones
• Radio
• TV
• Analog amplification
• Voltages, physical position

Analog Representation of Data:
Problems

• Amplification cannot restore what is no longer there
• Noise is amplified with the signal
• Compare with handwriting (digital):
  • limited number of symbols aids in recognition
  • redundancy in shapes, words, and prose, also aids in recognition
  • reconstructed (unreadable) signal is just as good as original.

Digital representation of data

• represent analog values (quantities) as numbers
• represent numbers as sequences of bits, each with value 0 or 1
• can sample a continuous analog signal into a stream of digital values
• even in the presence of noise, can often correctly distinguish a 0 from a 1
• if circuitry can work in the presence of noise, can be cheaper
• circuitry can be general-purpose (eg DSPs), leading to even cheaper implementation

Source Coding

• Shannon (Bell Labs, 1940s)
• Meaning and quantification of "information"
• How do you measure information?

Shannon Information Theory

• information means we are learning something we didn't know before
• information = uncertainty
• uncertainty modeled using random variables
• number of bits per symbol required to encode the output of a source is the entropy rate of a source
• no compression algorithm can do better than the Shannon limit

Distortion

• use fewer bits than the limit
• "lose" \epsilon$ of the data
• average number of bits H(\epsilon)$ is less than limit
• if \epsilon is small, H(\epsilon)$ is close to the entropy rate
• this is lossy compression
• try to keep the losses to where they are not easily detected (by humans)

Channel Coding

• Send bits over a real channel, e.g. telephone line
• In the real world there is no guarantee -- might always get an error (noise is due to quantum randomness)
• How fast can we go?
  • Rate R0 gives us bit error rate \epsilon0$
  • Rate R1 > R0 gives us BER \epsilon1 > \epsilon0$

Shannon: Channel Coding

• what is maximum rate R$ at which bits can be sent with arbitrarily low error rate \epsilon$?
• call that maximum rate C$
• for any R < C and any given 0 < \epsilon <= 1$, we can transmit at R and have \epsilon$ or fewer errors.
• actually getting such a rate can be complicated!

Packet Switching

• different from telephone communication (circuit switching)
• package some data with control information and send it out
• analogous to post office
• circuit switching implies resource reservation, which may be wasteful
• circuit switching requires more overhead to set up, maintain, and tear down the connection

Statistical Multiplexing

• how many bits per second do you need?
  • averaged over a minute
  • averaged over an hour
  • averaged over a day (40bps at Berkeley in 1995)
• with packet switching, idle resources can be used by others
• examples:
  • email (up to 10^3$ bytes)
  • files (up to 10^6$ bytes)
• overhead of connection setup might be worth it for files, might not for email

Cost estimation
Circuit Switching

• connection setup time TC = 0.1s$
• data rate R = 64Kb/s$
• message size M = 8Kb$
• time to transmit message TM = M/R = 0.125s$
• total time T = TC + TM = 0.225s$
• effective rate RE = M / T = 36Kb/s$
• this is a waste of bandwidth!

Packet switching

• data rate R = 64Kb/s$
• message size M = 8Kb$
• header size H = 200b$
• time to transmit message TM = M/R = 0.125s$
• time to transmit header TH = H/R = 0.003125s$
• total time T = TH + TM = 0.128125$
• effective rate RE = M / T = 62Kb/s$
• statistical multiplexing gain: e.g. internet phone might only use 30% of the bandwidth of a regular phone call

Project 1

• http://www.ics.hawaii.edu/~esb/1998fall.ics451/proj1.html
• build a simple web server
• individual programming only
• "automatic" grading (TBD)
• serve files from /home/1/esb/451 on uhunix2
• URL: http://host:port/path

Web Servers

• accept a connection
• read a request from the connection
  • Single-line request, or
  • Multi-line request with "HTTP/1.0" in first line
• parse the request
• determine correctness of request
• write header to connection
• if request is correct, read data from file, write to connection