Hierarchical Erasure Correction of Linear Codes
Information Theory
2019-10-23 v3 math.IT
Abstract
Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we develop a mathematical framework for hierarchical erasures over extension fields, provide several bounds and constructions, and discuss potential applications in distributed storage and flash memories. Our results show intimate connection to Universally Decodable Matrices, as well as to Reed-Solomon and Gabidulin codes.
Cite
@article{arxiv.1802.02265,
title = {Hierarchical Erasure Correction of Linear Codes},
author = {Netanel Raviv and Moshe Schwartz and Rami Cohen and Yuval Cassuto},
journal= {arXiv preprint arXiv:1802.02265},
year = {2019}
}