a friend of mine emailed me this advice....
"You don't want the deck directly on the slab, because every rainstorm will trap water there which will sit there and rot the wood, and even pressure treated wood won't last long that way. At the very least you want it up a couple inches, but personally I would "lift" it to the height of the back door anyway. That will let you get a leaf blower under it and blow the crap (leaves, twigs, hot dog bun pieces) that will inevitably fall between the boards and clean it out once in a while. I'd try to run the joists side to side so you can "blow" the stuff out, if you run them front to back you can only blow the stuff against the house, which you really don't want.
You might not have enough height to use those piers from earlier in the thread (add that height to a 2x6 or preferably 2x8 joist) and you might be too high. But using a few pavers and then the joists might give you the right height. Run the back joist into and fastened to the back wall of the house, that will give you stability from having it "drift." I'd try to run the joists side to side so you can "blow" the stuff out, if you run them front to back you can only blow the stuff against the house, which you really don't want.
My neighbor concocted an awning out of canvas (I think he told me he got it at a marine store: sailcloth, maybe?) and PVC pipes. It's about 5' x 20', with a triangular frame built from heavy duty PVC. Gorgeous blue color canvas. He put grommets in the canvas, then looped rope through the grommets and around the pipe, which attached to the house. Looks good, actually. Only covers about half the porch, but he says that's all he wanted; enough coverage for the grill and the doghouse.
Looks kind of like this without the curvature:
Attached kind of like this, with one continuous rope:
Using one of these will give you a 4x4 anchor from which you can run a "stub" to lift the deck. And these will keep the end of the 4x4 off any pooled water as well.
link broken "