Given an alphabet $\mathbb{A}$ and a lattice $L = \{Y : Y = Hx, X \in \mathbb{A}^n\}$, the lattice decoding problem is to find: $$ \hat{x} = \text{argmin } \| Z - Hx \| $$
Where Z is some vector $\in \mathcal{R}^n$. I read that it is NP-hard to solve for the ML solution. Can someone explain why? Can one not simply find $x_1 = H^{-1}Z $ and quantize the result, coordinate by coordinate onto the alphabet $\mathbb{A}$?