Strongly Cancellative and Recovering Sets On Lattices

We use information theory to study recovering sets ${\mathbb{R}}_L$ and strongly cancellative sets ${\text{C}}_L$ 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 ${\mathbb{R}}_{B_n}$, ${\text{C}}_{B_n}$, and ${\text{C}}_{D_l^k}$.