TY - CONF
T1 - Recoverable systems on lines and grids.
AU - Barg, Alexander
AU - Elishco, Ohad
AU - Gabrys, Ryan
AU - Yaakobi, Eitan
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2022/8/3
Y1 - 2022/8/3
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.
KW - Measurement
KW - Symbols
KW - Stacking
KW - Additives
KW - Codes
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 - Paper
SP - 2637
EP - 2642
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -