TY - GEN

T1 - A family of optimal locally recoverable codes

AU - Tamo, Itzhak

AU - Barg, Alexander

PY - 2014

Y1 - 2014

N2 - A code over a finite alphabet is called locally recoverable code (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. We present a family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality. The codes can be constructed over a finite field alphabet of any size that exceeds the code length. The codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to Reed-Solomon codes if the locality parameter r is set to be equal to the code dimension. The recovery procedure is performed by polynomial interpolation over r points. We also construct codes with several disjoint recovering sets for every symbol. This construction enables the system to conduct several independent and simultaneous recovery processes of a specific symbol by accessing different parts of the codeword. This property enables high availability of frequently accessed data.

AB - A code over a finite alphabet is called locally recoverable code (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. We present a family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality. The codes can be constructed over a finite field alphabet of any size that exceeds the code length. The codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to Reed-Solomon codes if the locality parameter r is set to be equal to the code dimension. The recovery procedure is performed by polynomial interpolation over r points. We also construct codes with several disjoint recovering sets for every symbol. This construction enables the system to conduct several independent and simultaneous recovery processes of a specific symbol by accessing different parts of the codeword. This property enables high availability of frequently accessed data.

UR - http://www.scopus.com/inward/record.url?scp=84906542937&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2014.6874920

DO - 10.1109/ISIT.2014.6874920

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AN - SCOPUS:84906542937

SN - 9781479951864

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 686

EP - 690

BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 IEEE International Symposium on Information Theory, ISIT 2014

Y2 - 29 June 2014 through 4 July 2014

ER -