 is optimal, and a distortion pair $(D_0, D_0)$ is achievable if $$\begin{aligned} R^{RC}_{S_0| Z}(D_0)&< I(X_0; Y|X_0, Q) \label{eq:commonr0}\\ R^{RC}_{S_0| Z}(D_0)&< I(X_0; Y|X_0, Q) \label{eq:commonr0}\\ R^{RC}_{S_0| Z}(D_0)