Optimality of the pre-coding for broadcast channels with receiver message side information

Consider a two-receiver memoryless broadcast channel with states and receiver message side information (RMSI), together with the corresponding channel without RMSI. Let a transmission scheme for the channel without RMSI be transformed by the pre-coding described in the paper, treating the common message as $M_\text{m}=(M_0,M_3,M_4)$ and the private messages as $M_1$ and $M_2$. Optimal pre-coding conjecture. If the original scheme achieves the capacity region of the channel without RMSI, then the scheme obtained by applying this pre-coding achieves the capacity region of the same channel with RMSI. The conjecture asserts that this pre-coding preserves optimality when receiver message side information is introduced; whether this holds for every such capacity-achieving scheme remains open.