UNLIMITED COMPRESSION WORKS

Takes any file. proceed with this algorithm
1.try to compress it with ZIP if it reduces size proceed to step 1. if not step.2. Pick a short random string and XOR the file with it. proceed to step 1 until you reduce file size.
3.record all random strings and result file.

3.record all random strings and result file.

The problem is that the size of the random strings will be at least as big as the amount you reduced from the ZIP file.  Making the whole exercise pointless.