I have two concrete walls on either side of a proposed deck area.  In the middle of the span I have some concrete columns that will support a beam for a deck.  My proposed deck design has 2x12s sitting on the concrete walls and attached with 2x12 joists to the center beam that rests on the columns.  The height of the walls is ~6" lower than the columns.  

How should I build up the concrete wall to support the 2x12s at the same height as the center columns?

If it was 1.5" lower than the columns then I would put down a sill gasket, epoxy in some anchor bolts and put a plate down and have 2x12s sit on it.  With it 6" lower I have to build up 5.5 inches.  

Ideas?

Maybe I put down a plate, anchor bolt it, add two 2x members cut to 4" high, top it with another plate to make a box for the 2x12s to sit on and have the anchor bolt high enough that I bolt the top of the box to the concrete. 

Concrete walls are level and flat.  I'll plan for a 2% slope from the top of the plan view to the bottom - away from the house.  This deck is self supported and does not tie into the house.

Attached a sketch of the plan view of the structure.  Ignore the first level deck

[![deck structure plan view][1]][1]

    _______________________________________________________________________


    _______________________________________________________________________
                                   |  |  |
          6" gap                   |  |  |
          ______                   |  |  |                       ______
         |      | <-- concrete     |  |  |<-- 2x12 beam         |      |
         |      |     wall         |  |  |                      |      |
         |      |                  |__|__|                      |      |

  [1]: https://i.sstatic.net/JxR4U.jpg