probability theory – Understanding deterministic capacity of AVC

In the paper by Csiszar & Narayanan where they proved the deterministic capcity of an AVC, can someone please explain the decoder logic?

The second condition used by the decoder is
$$ I(XY;X’|S) leq eta $$
I can not understand the relevance of this term and why this is needed. Why doesn’t it work with only the first condition? An intuitive explanation is what I am seeking here.