Battlefield 4 enters beta later this year and word from Origin Russia is that all Battlefield 3 Premium subscribers will receive access. Swallow some salt and judge the evidence for yourself.
Russian Battlefield fan site MyBattlefield grabbed the above screen from Origin Russia. Note the timeline of unlocks on the right side. It goes through all subscription goodies, starting with all Battlefield 3 DLC and ending on Battlefield 4 beta access.