I've fixed it twice on my PS4 following the below process - but it will crash again and this process takes too long to keep doing.
1. Delete the corrupt save file
2. Delete BF4
3. Turn PS4 off/back on
4. Enter the disc into PS4
5. Start BF4 – update will start downloading in the background
6. Exit BF4, close the application
7. Wait for 607MB update to download and install
8. AFter update is installed, restart BF4
9. DON’T PLAY THE GAME UNTIL THE FULL GAME IS INSTALLED 100%!
10. Once the game is 100%, you should be able to start the game and play.
However it will crash again – if the save data is corrupt (System -> Application Data -> Delete -> Battlefield 4) you’re pretty much screwed. Even deleting the file and re-starting doesn’t fix it. However if the save IS NOT corrupted, shut down the PS4 and turn it back on. You should be OK to play.
I’m NOT doing the above procedure again – it takes way too long, I’ll just play CoD or Killzone until they fix it. Hard to believe deleting the file and rebooting doesn’t fix it, but it don’t!