Hi guys, I want to setup a HTPC. Appreciate if you can advise and correct me if I'm wrong.

Currently I have:
(1) Full HD LED TV with HDMI input
(2) Zotac Zbox nano AD10 with HDMI output

I'd like to get at least a 5.1 sound setup. I understand that I need to get a decoder or home theater system with HDMI input for audio/video and outputs HDMI video to my TV.

I've seen many home theater system on the market only with hdmi output so I guess that is out of question.

Some more expensive models have both hdmi in and out. They come with 5.1 speaker set. I wonder these are the models I should be looking for? Do they have the ability to decode 5.1 sound from my Zotac HDMI out to the respective speakers?

Please recommend a system with at least 5.1 speaker set if possible. Prefer budget models. Thank you.