[Nurbek Sagynbaev]

Here is what you can try:

Export 16 bit AE project as 16 bit TIFF sequence. Add some noise (aaround 0.3 will do fine) to every frame in Photoshop. Convert 16 bit TIFFs to 8 bit TIFFs in Photoshop. Import new sequence into AE and render the project as H.264 movie.

PS: You can record an action for converting 16 bit TIFF files to 8 bit, add noise, save as new files.