A storage code is an assignment of symbols to the vertices of a connected graph G(V, E) with the property that the value of each vertex is a function of the values of its neighbors, or more generally, of a certain neighborhood of the vertex in G. Under the name of recoverable systems, a class of storage codes on Z was recently studied relying on methods from constrained systems and ergodic theory. In this work, we address the question of the maximum capacity of recoverable systems on Z and Z2 from a combinatorial perspective. We establish a closed form formula for the capacity of several one- and two-dimensional systems, depending on their recovery set, using connections between storage codes, graphs, anticodes, and difference-avoiding sets.
|Number of pages||6|
|State||Published - 3 Aug 2022|
|Event||2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland|
Duration: 26 Jun 2022 → 1 Jul 2022
|Conference||2022 IEEE International Symposium on Information Theory, ISIT 2022|
|Period||26/06/22 → 1/07/22|