Generalized entropy-ratio conjecture for the delayed-CSIT X-channel

Consider the 2-transmitter 2-receiver network setting of the paper's linear-subspace-ratio lemma. Let $n\in\mathbb N$, let $\{f_1^{(n)},f_2^{(n)}\}$ be arbitrary encoding functions, let $\vec{\bf y}_1^n$ and $\vec{\bf y}_2^n$ be the corresponding received signals, and let $\bm{\mathcal{G}}^n$ denote the channel-state information. Generalized entropy-ratio conjecture. For every $n\in\mathbb N$ and every coding strategy,

$$h(\vec{\bf y}_1^n\mid\bm{\mathcal{G}}^n)\leq\frac{3}{2}h(\vec{\bf y}_2^n\mid\bm{\mathcal{G}}^n)+n\times o(\log(P)).$$

This conjecture extends the linear entropy or received-subspace dimension ratio to arbitrary encoding strategies and is proposed as the information-theoretic basis for the claimed total degrees-of-freedom value.