Class 10: Data-Link Basics

Held Monday, February 14, 2000

Overview

Today we return to networking issues at the lowest appropriate level by considering general issues for direct-link networks.

Notes

• A number of you have reported difficulty with Assignment 2. To give you a chance to talk to me about those difficulties, I am extending the due date until Friday.
  • Please do come talk to me.
  • In the C that I learned, it was dangerous to pass a struct to a function or return a struct from a function.
  • I'd strongly recommend that you write a wrapper class for your node class.
• Assignment 1 has been (mostly) graded.
  • Some notes are available.
  • We'll spend a few minutes on common errors.
• For Wednesday's class, find out something useful about an error-correcting code. That is, identify an error-correcting code and learn how it works.

Contents

• Direct-Link Networks
• Connecting Nodes
  • Encoding Bits
  • Physical Layer: Theory and Characteristics
  • Detour: Information Theory

Summary

• Introduction to direct-link networks
• Basics of information theory
• Representing bits
• The problem of framing
• Handouts:
  • Notes on assignment 1
  • A strategy for printing debugging messages

Direct-Link Networks

• In direct-link networks, the nodes are directly connected.
  • You may have two nodes on each end of a ``wire''.
  • You may have multiple nodes on some form of ``bus'' (physical or wireless)
• Like our textbook authors, I will emphasize the two-node version.
• The physical layer provides us with a semi-reliable stream of bits. But we clearly want more. We might also want
  • Error detection and correction.
  • Bytes or frames instead of bits.
  • Flow control.
  • Other services for the network layer.
• There are different services we can provide.
  • Simple frames: an unacknowledged connectionless service
  • Frames with error detection: ackonwledged connectionless service
  • Reliable frame streams: acknowledged connection-oriented services
• What are the issues we are concerned with for directly-connected nodes?
  • How do we connect the nodes?
  • How do we represent bits?
  • How do we multiplex the line?
  • How do we make chunks of bits (frames)?
  • How do we detect errors in those chunks?
  • How do we correct errors in those chunks?

Connecting Nodes

• Let the hardware people worry about it. We're software people.
• More realistically, we can use cables of some form (twisted pair, thin-net, thick-net, or fiber) or radio waves.
• We can also form virtual connections from existing infrastructure, such as the phone company's networks or the cable company's.
  • Yes, you get to pay for that privilege.
• What do we care about when selecting a medium?
  • Cost
  • Bandwidth (information/second)
  • Reliability
  • Speed (for getting initial pieces of information)
  • Distance-sensitivity
  • Maintainability
  • Support for topologies

Encoding Bits

• There are many different techniques you can use to encode a signal.
  • Change the amplitude of the wave
  • Change the frequency of the wave
  • Change the phase of the wave (not mentioned earlier)
• We can use one or more of these to increase our data rate.
• In constellation patterns, the possible values are indicated by points in a two-dimensional grid, with distance from origin signifying amplictude and rotation from 0 degrees indicating the phase shift.

Physical Layer: Theory and Characteristics

• Okay, we've got to get some (digital) information over an electrical/optical/radio/whatever connection. How do we do it?
• We need to encode each bit
  • Simple scheme: 1 = high power, 0 = low power
  • Yes, there are better schemes
• Problem: the sent signal (square wave) often looks little like the received signal (smoothed out).
  • It is affected by noise, delay, and attenuation.
  • Not a new realization: Morse code invented 1832, telegraph between Washington and Baltimore 1843 had this problem.
• Solution: Fourier (early 1800's) noted that any periodcc function (variation of quantity with time) can be represented as the sum of sine waves of different amplitudes, phases, and frequencies. These component waves are called harmonics.
• Why do we care? Because by understanding the effects of a circuit on the component sine waves, we can understand the effect of the circuit on more complex signals.
  • Particular application: higher-frequency signals are usually highly distorted. We can filter out higher frequencies or ignore them or virtually ignore them or ....
  • On phone lines, the signal is usally filtered at 3200 hz.
• The difference between the highest-frequency and minimum-frequency on a channel is called the bandwidth of the channel.
• The data rate is affected by
  • the bandwidth of the channel,
  • the number of changes per ser second (the baud), and
  • the number of bits encoded in each change to the signal.
  • The higher the baud, the fewer harmonics we can send.
• So, how much can we really send on a line? Harry Nyquist gave a sampling theorem, which says that any signal of bandwidth H can be reconstructed by no more than 2H samples per second.
  • Hence, if the signal has V distinct levels, the maximum data rate is 2H*log₂(V) bits/sec.
  • However, this ignores noisy channels. Shannon says that the actual rate is H*log₂(1 + S/N), where S/N is the signal to noise ratio.

Detour: Information Theory

• Shannon did more than talk about Nyquist's result. He developed a technique for analying information (that serves as the basis of what we call information theory).
• Shannon claimed that we can analyze information solely in terms of its statistical properties. He also suggested that sources are typically ergodic: the statistical properties of a single message tend to be the same as average properties over all messages.
  • For example, the frequencies of individual letters in English text are about the same for each document as for English in general.
  • The same holds true for pairs of letters and even triplets of letters.
• Shannon discussed entropy: uncertainty in a domain, which is resolved by messages.
  • It is a function of the number of possible messages and the probabililties of each possible message in the domain of all messages. Shannon's definition was that entropy is the negative of the sum over all messages of (the probability of the message times log₂(prob message)).
• As an example, consider a fair coin and an unfair coin.
  • For the fair coin, the probability of each message is 1/2. Hence the total entropy is
    • -1 * (1/2*log₂(1/2) + 1/2*log₂(1/2))
    • = -1 * (log₂(1/2))
    • = -1 * -1
    • = 1
  • For a somewhat unfair coin, let us say that the probablity of heads is 3/4 and the probability of tails is 1/4. The total entropy is
    • -1 * (3/4*log₂(3/4) + 1/4*log₂(1/4))
    • = -1 * (3/4*log₂(3) + 3/4*log₂(1/4) + 1/4*log₂(1/4))
    • = -1 * (3/4*log₂(3) + log₂(1/4))
    • ~= -1 * (3/4 * 1.6 + -2)
    • ~= 0.8
  • For a truly unfair coin, let us say that the probability of heads is 1 and the probability of tails is 0. The total entropy is
    • -1 * (1*log₂(1) + 0*log₂(0))
    • = -1 * (1*0 + 0)
    • = 0
  • The fair coin has the most entropy. The deterministic coin has no entropy. The somewhat biased coin is somewhere in the middle, just as we'd expect.
• Using entropy of noise and entropy of signals, Shannon came up with the results that the maximum rate is H*log₂(1 + S/N)
  • No, we won't derive that result.