why compression doesn't perfectly even out entropy

[Perry E. Metzger]

Jon asked why it is that I contend that a compression algorithm won't
in the general case even out the entropy of a semi-random stream.

The answer can be obtained by simply trying to run gzip over an image,
preferably one that hasn't been compressed. The results are, in
general, very bad, even though images are highly compressable (even
losslessly). I leave the why up as an exercise to the reader.

I have said before and I will say again that the only reliable way of
dealing with a stream that has some amount of randomness mixed in with
it that you wish to distil down into pure random bits is to use solid
reasoning to figure out how many bits of entropy per unit of input you
can actually expect to see, add a large fudge factor to cover your
ass, and then distil down using a cryptographic hash. Anything else
makes me highly nervous. If you can't estimate the amount of entropy
in an input stream from first principles, then you are probably in
trouble and should seek an input stream that you have a better handle
on.

Perry