Compression of random binary data

[Ian Kelly]

On Tue, Jul 12, 2016 at 11:35 AM,  <jonas.thornvall at gmail.com> wrote:
>
> No it is only compressible down to a limit given by the algorithm.

Then your algorithm does not compress random data as you claimed.

For some input, determine the limiting output that it ultimately
compresses down to. Take that output and feed it through your
algorithm as if it were the original input. If the data are to be
considered random, then this input is just as probable as the
original. What output does the algorithm now create? If it just
returns the input unchanged, then how do you discern the original
input from this input when decompressing? If it returns a different
output of the same size, then repeat the process with the new output.
Now there are *two* outputs of that size that can't be repeated. There
are only finitely many possible outputs of that size, so eventually
you're going to have to get to one that either repeats an output -- in
which case your algorithm produces the same output for two different
inputs and is therefore incorrect -- or you will get to an input that
produces an output *larger* in size than the original.