Compression of random binary data

[danceswithnumbers at gmail.com]

Thomas Jollans

On 2017-10-25 23:22, danceswi... at gmail.com wrote: 
> With every transform the entropy changes, 

That's only true if the "transform" loses or adds information. 

If it loses information, that's lossy compression, which is only useful 
in very specific (but also extremely common) circumstances. 

If it adds information, that's poetry, not compression. 



Not true! You can transform a stream lossless, and change its entropy without adding to or taking away. These two streams 16 bits are the same but one is reversed.

1111000010101011
This equals
61611
This can be represented using
0-6 log2(7)*5= 14.0367746103 bits


1101010100001111
This equals 
54543
This can be represented using
0-5 log2(6)*5= 12.9248125036 bits

In reality you can express 54543 with 10 bits.