Compact composition operators on model spaces

Let $\phi :B_d\to \mathbb{D}$, $d\ge 1$, be a holomorphic function, where $B_d$ denotes the open unit ball of ${\mathbb{C}}^d$ and $\mathbb{D}=B_1$. Let $\mathrm{\Theta }:\mathbb{D}\to \mathbb{D}$ be an inner function and let $K_{\mathrm{\Theta }}^p$ denote the corresponding model space. For $p>1$, we characterize the compact composition operators $C_{\phi }:K_{\mathrm{\Theta }}^p\to H^p(B_d)$, where $H^p(B_d)$ denotes the Hardy space.