Nair–Wang information inequality for the binary skew-symmetric broadcast channel

We consider the binary skew-symmetric broadcast channel with input $X$ and outputs $Y_1,Y_2$. Let $U,V$ be random variables such that

$$(U,V)-X-(Y_1,Y_2)$$

forms a Markov chain. Nair–Wang information inequality. For all such $(U,V,X)$,

$$I(U;Y_1)+I(V;Y_2)-I(U;V)\leq \max\bigl(I(X;Y_1),I(X;Y_2)\bigr).$$

The inequality is relevant to determining the capacity region of the binary skew-symmetric broadcast channel: if it holds, a sum-rate line segment on Marton's inner bound lies on its boundary. The source does not provide evidence that the conjecture has been resolved.