Could super compression(compression which is not linear, e.g as the data to be compressed increases, so also does the ratio of compression. A kind of logarithmic growth.) through recursive compression algorithms. The binary file is first scanned, to identify patterns. After this, the file is rewritten such that the patterns are encoded. E.g if there is a sequence of 100 $0$'s, It could be represented as $xxx 0$ where $xxx$ represents that the 0 occurs 100 times. 

After this is done, the algorithm is then called on the generated compression file, until a file with no patterns is produced. The header of the file will contain how many times the algorithm was run, so the file can be decompressed.


Apologies if this is the wrong SE site.