Hierarchical Erasure Correction of Linear Codes

Netanel Raviv; Moshe Schwartz; Rami Cohen; Yuval Cassuto

Hierarchical Erasure Correction of Linear Codes

Netanel Raviv, Moshe Schwartz, Rami Cohen, Yuval Cassuto

Technion - Israel Institute of Technology

Research output: Working paper › Preprint

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.

Original language	English
State	Published - 6 Feb 2018

Keywords

cs.IT
math.IT

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1802.02265v3

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AU - Raviv, Netanel

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AU - Cohen, Rami

AU - Cassuto, Yuval

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N2 - 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.

AB - 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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KW - math.IT

M3 - نسخة اولية

BT - Hierarchical Erasure Correction of Linear Codes

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Hierarchical Erasure Correction of Linear Codes

Abstract

Keywords

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