  Let $I=(a,b)\times(c,d)\subset {\mathbb R}_{+}^2$ be an index set and let
$\{G_{\alpha}(x) \}_{\alpha \in I}$ be a collection of Gaussian functions, i.e.
$G_{\alpha}(x) = \exp(-\alpha_1 x_1^2 - \alpha_2 x_2^2)$, where $\alpha =
(\alpha_1, \alpha_2) \in I, \, x = (x_1, x_2) \in {\mathbb R}^2$. We present a
complete description of the uniformly discrete sets $\Lambda \subset {\mathbb
R}^2$ such that every bandlimited signal $f$ admits a stable reconstruction
from the samples $\{f \ast G_{\alpha} (\lambda)\}_{\lambda \in \Lambda}$.
