[snthpy]

I totally agree with your argument. However just to throw out an idea for a possible counterexample (as mathematicians like to do):

What if you used aperiodic Penrose tiles and could detect intensity? Would it be possible to encode anything in that? There would be no repetition but when would you hit limits of discernability with all the overwriting?

[snthpy]

I mean the number of tiles is finite but what if the alphabet was the encoded in the geometrical arrangement of the tiles?

[snthpy]

Ignore me. That's no different to having infinite length strings with a finite alphabet.