As others have stated, you must have some venting!
Deep bedding works on the principal of creating an environment for beneficial bacteria to break down your organic material into compost. The reason for the deepness of the bedding is to provide some moisture for the material to decompose.
Deep bedding requires at least 12" of material, and its usually better if its more like 24". It is not possible to get compost with less material. If it's not composting you just have poop and carbon and that's what is creating harmful bacteria that produce ammonia.
If you are concerned about thet smell you can always add a dusting of activated lime (while you build mass). There is tons of information on the web about composting, but essentially you want enough carbon to mix with your organic material, in the proper ratio. You can be really creative with finding sources of carbon: paper shredding places, cardboard, mulch, wood shavings, even straw. They all have different carbon ratios...
Deep bedding should never smell like ammonia! Good luck!
Here is a link with C:N ratios...
http://www.homecompostingmadeeasy.com/carbonnitrogenratio.html