  We use information theory to study recovering sets $\R_L$ and strongly
cancellative sets $\C_L$ on different lattices. These sets are special classes
of recovering pairs and cancellative sets previously discussed in [1], [3] and
[5]. We mainly focus on the lattices $B_n$ and $D_{l}^{k}$. Specifically, we
find upper bounds and constructions for the sets $\R_{B_n}$, $\C_{B_n}$, and
$\C_{D_{l}^{k}}$.
