TY - GEN
T1 - Recoverable systems on lines and grids
AU - Barg, Alexander
AU - Elishco, Ohad
AU - Gabrys, Ryan
AU - Yaakobi, Eitan
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85136284599&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834541
DO - 10.1109/ISIT50566.2022.9834541
M3 - Conference contribution
AN - SCOPUS:85136284599
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2637
EP - 2642
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -