Recoverable systems on lines and grids.

Alexander Barg, Ohad Elishco, Ryan Gabrys, Eitan Yaakobi

Research output: Contribution to conferencePaperpeer-review


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.
Original languageEnglish
Number of pages6
StatePublished - 3 Aug 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022


Conference2022 IEEE International Symposium on Information Theory, ISIT 2022


  • Measurement
  • Symbols
  • Stacking
  • Additives
  • Codes


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