Communication

• "[...] reproducing at one point either exactly or approximately a message selected at another point."

  • "These semantic aspects of communication are irrelevant to the engineering problem."

• "The significant aspect is that the actual message is one itl(selected from a set) of possible messages."

  • The sender and receiver have to know the same set of messages.

Communicating

• What is communicating under these circumstances?

  • Selecting a message from a common set of messages.

  • Message meaning doesn't matter.

• How can we do communication?

A Simple Mapping

• Map the set { 1 .. size(message set) } to the set message set.

  • The particular mapping is called a codebook.

• To send a message, send the appropriate number.

• Properties:

  • Message-set independent, but not set-size independent.

  • Both sides need the same codebook.

Communicating Numbers

• How to communicate a value itl(i) between 1 and itl(N) inclusive?

• Just send itl(i) down the wire.

• This takes one time instant.

  • But it requires distinguishing one of itl(N) possible values.

The Playing Field

• The source picks one of itl(N).

• The transmitter encodes the message and sends it.

• The medium carries the encoded message (signal).

• The receiver receives the signal and decodes it.

• The destination gets the message.

Communicating Numbers

• The medium's ability to transmit different signals strongly influences communication.

  • This ability is not bandwidth because there's no time.

  • It's better thought of as frequency response (which is sometimes called bandwidth).

• In general, large frequency response media are more expensive than small frequency response media.

  • They're also more finicky and less reliable.

Alternative Approaches

• Sending one of itl(N) would work, but is there a better way?

  • The problem is the cost and reliability of the medium, which is directly related to frequency response.

  • This, in turn, effects the message set.

• Reduce the frequency response to reduce costs and increase reliability.

  • But how?

A New Encoding

• How can I reduce the number of signals I need to send?

• Break each number into its constituent digits, and send the digits one at a time.

  • Now I only need a constant 10 signals for any message set.

  • But sending and receiving a message now takes longer.

• This is your basic time-complexity trade-off.

An Extreme Encoding

• What is the smallest number of signals I need to send a message?

  • Zero or one doesn't work; how about two?

• Recognizing two signals (something and not something) is the easiest possible task.

  • It's cheap, reliable, durable.

A Binary Encoding

• How do you use two signals to encode itl(N) numbers?

  • Hint: let's play twenty questions.

• Is the message in this half or that half of the set?

• Is the message in this half half or that half half of the set?

• Is the message...

This page last modified on 14 i2m(11) 2004.