According to the blog "Starting tomorrow (March 13th), you can re-download a new, patched version of Battlefield 3: Back to Karkand on PS3. This will fix the weapon animation bug that some of you have experienced. This download is free of charge if you have already bought Back to Karkand. Note that changes made on our back end will make this re-download mandatory in the near future. If you buy Back to Karkand for the first time after tomorrow, no additional action is necessary.":
The Back of Karkand DLC was released on PlayStation Network on the 6th December, 2011.