Roland Of Gilead :
itzdanielp :
Yep, you should be good to go
think your jumping the gun a little. @ OP what res are you gaming at? the 7770 is barely a midrange card, it's more entry level than anything else.
This will give you an idea of your card at 1680 x 1050 high settings.
http://www.tomshardware.com/reviews/battlefield-4-graphics-card-performance,3634-6.html
it's touching 30 + fps or thereabouts. Not stellar performance. It may feel stuttery when playing.
Your CPU is weaker than the I5 2550k in this article, so most likely will not attain exactly those frame rates. I'd say a mix of med-high settings, getting up to the low 30's FPS, but prob with dips on larger maps (if your playing multi). Prob slightly better performance on single player.
keep in mind that that article was written using beta graphics drivers on a beta game. Both the game and the drivers have drastically matured since that was written, and I am getting about a 20-30fps jump using the same hardware since the beta.
So, I would expect that card to be in the 30-40 range on medium settings, depending on the resolution.
Also, even though it's not an Intel processor, it has a higher thread count than the 2500k, which BF4 will use, since it is very well optimized for multi-threading.