Combine sugar and salt in a bowl. Rub over pork loin, wrap in plastic wrap, and refrigerate over night.
Place the pork loin in a slow cooker and turn on low heat.
In a medium bowl combine the ginger, rice vinegar, chicken stock, garlic cloves, chili paste, soy sauce, BBQ sauce, and black pepper. Mix well and pour over top of the pork.
Cook on low heat for 8 hours.
After 8 hours remove the lid and shred the pork.
Spoon pork into lettuce leaves and top with radishes.