There aren't very many (if any) direct commercial routes from East Asia to ANC. Most direct route is to connect thru SEA or SFO. Alaskan Air is the main airline in ANC. Look at their site. Perhaps look at Delta or Korean Air as they all are apart of the same airline alliance. Without looking at any ticket prices recently, I'd say the cheapest tickets are around $1800, but I really don't know. Check Kayak.
FYI, travel in Alaska is expensive! If you're planning on flying to anywhere else besides the Anchorage area, you're looking at several hundreds more. Alaska really isn't the place to try and budget travel.