SFG on Cement

Hi!
I'm in the middle of reading Square Foot Gardening and have a question. In my backyard, I have an ideal spot to garden, however, it's on top of cement. There use to be a small one-car garage there, and the previous owner knocked it down but left the cement.
I was thinking of building a 4x4 box to garden in on top of the cement. Will this work? How deep would I have to make it?
One of my concerns is about drainage. If I build it on top of the cement, then the water probably won't drain well. I'm also concerned about the hot/cold of the cement. I think dirt regulates heat/cold a little better than cement. BTW, I also live in Chicago.
My other idea is to build it in the yard. I'd rather not do it because the cement area gets the most sun, and my yard is pretty small. However, if it will affect my yield, then I can spare some room. ;-)
I would also like to plant (if it matters) broccoli, parsley, onions, peppers, tomatoes, muskmelons, peas, carrots, beans (pole), and corn....if possible.
Thanks in advanced for any suggestions!
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No problem. A lot of us do container gardening on decks and patios. As long as you have a foot or maybe more dirt, you can grow these things. If you are worried about water logging, unless your frame is water tight, excess should leak out, or as I do in some of my pots, put drain holes. If garden is only 4X4, you are best to plant higher value things like tomatos and peppers.
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