Hierarchical Erasure Correction of Linear Codes
Netanel Raviv, Moshe Schwartz, Rami Cohen, and Yuval Cassuto
TL;DR
This paper introduces a mathematical framework for hierarchical erasure correction in linear codes, with bounds and constructions relevant to distributed storage and flash memories, connecting to well-known code families.
Contribution
It develops a new framework for hierarchical erasures over extension fields, linking to existing codes and providing bounds and constructions.
Findings
Established bounds for hierarchical erasure correction
Connected hierarchical erasures to Reed-Solomon and Gabidulin codes
Discussed applications in distributed storage and flash memories
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.
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