The standard Doppelblock rules apply. In addition, numbers outside the grid are encrypted into a set of letters. The set of the numbers corresponding to the letters is given.
Side Note: Happy Birthday Ivan a.k.a chaotic_iak! Here is my simple gift for you. I really want to make it small, but deadly enough...
Another Side Note: Yes, this is uniquely solvable despite having no logical path HAHAHA *evil laugh*. Thus, here is an additional important clue for other puzzlers (except Ivan): [{I,A,K} = {0,0,0}]. The clue above will make the puzzle solvable with a logical path, of course Ivan doesn't need this.
Solution code: The numbers for "CHAOTIK", Row 1, and Column 1. Use X for shaded cells.