For every possible input 0 to X you need to map to a different 'compressed' format. So, if you want to handle every possibility then some of your compressed versions need to be as long if not longer than the original version. That's not a problem if their is some bias in how your generating the data. Just map the more common versions to shorter encoding and you get a useful compression even if sometimes it makes things worse on average their is an improvement. But, with unbiased random data you can't chose which subset is more likely because every version is equally likely. Which is why it does not work.