Cyclic Lowest Density MDS Array Codes

Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the new codes can be utilized for simplified impl...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 55; no. 4; pp. 1721 - 1729
Main Authors: Cassuto, Y., Bruck, J.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Array codes
Arrays
Codes
Coding, codes
Construction
cyclic codes
Data encryption
Decoding
Density
Exact sciences and technology
Information theory
Information, signal and communications theory
low-density parity-check codes
maximum-distance separable (MDS) codes
Memory
Optimization
Preserving
Protection
Signal and communications theory
Symmetry
systematically cyclic codes
Telecommunications and information theory
Transformations
Cyclic code
Redundancy
cyclic codes
Updating
Distance transformation
systematically cyclic codes
Implementation
Parity check codes
Error correcting code
Minimal distance
Array codes
maximum-distance separable (MDS) codes
low-density parity-check codes
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the new codes can be utilized for simplified implementation in storage applications. The proof of the code properties has an indirect structure: first MDS codes that are not cyclic are constructed, and then transformed to cyclic codes by a minimum-distance preserving transformation.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2009.2013024