Communication is a discrete, finite process
Assume a continuously valued random variable x
- Cannot assign an entropy to x because the number of possible events x( ) is uncountable
- We approximate x by a discrete rv x?
- We sample x
- ? is a measure of roundoff noise
- If ? << physical noise in the system, then the approximation causes vanishingly small error
- Discrete symbols can represent real signals with arbitrarily small error
- We can only differentiate among a finite number of messages in a finite time