There is the concept of Kolomogorov complexity, the size of the
smallest algorithm that can generate the message. A perfectly
compressed message would have Kolomogorov complexity
equal to itself.
Kolomogorov complexity does have a freedom in its definition,
but the exciting thing is that any two definitions will differ only
by a constant.
lcs Mixmaster Remailer wrote:
> "Perfect compression" doesn't make sense anyway. Perfection of
> compression (as with entropy) can be expressed only relative to a specific
> probability distribution of possible inputs. Once you have specified
> such a probability distribution, you can evaluate how well a particular
> compression algorithm works. But speaking of absolute compression or
> absolute entropy is meaningless.
