Storage codes and recoverable systems on lines and grids
Information Theory
2023-08-29 v1 Combinatorics
math.IT
Abstract
A storage code is an assignment of symbols to the vertices of a connected graph 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 . In this work we introduce a new construction method of storage codes, enabling one to construct new codes from known ones via an interleaving procedure driven by resolvable designs. We also study storage codes on and (lines and grids), finding closed-form expressions 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.
Cite
@article{arxiv.2308.14558,
title = {Storage codes and recoverable systems on lines and grids},
author = {Alexander Barg and Ohad Elishco and Ryan Gabrys and Geyang Wang and Eitan Yaakobi},
journal= {arXiv preprint arXiv:2308.14558},
year = {2023}
}