A Family of Optimal Locally Recoverable Codes
By Itzhak Tamo, Alexander Barg. IEEE Transactions on Information Theory, 2013
620 citations recorded by the source corpus.
A code over a finite alphabet is called locally recoverable (LRC) 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 codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to a Reed-Solomon code if the locality parameter r is set to be equal to the code dimension. The size of the code alphabet for most parameters is only slightly greater than the code length. 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 (“hot data”).
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Networks and Communications
View Paper: https://www.semanticscholar.org/paper/d276d3a2a5fbc81ab4358b5e6a356496de4c4ff8
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Citations in the corpus
- Centralized Repair of Multiple Node Failures With Applications to Communication Efficient Secret Sharing (2016, background): “Various minimum distance bounds and constructions achieving trade-offs are presented in [17]–[20] and the references therein.”
- Arcs in finite projective spaces (2019, background): “MDS codes are the codes of choice for codes over large alphabets and there has been a recent resurgence of interest in MDS codes and locally recoverable codes (see [7] and [27]) due to their applications to distributed storage systems.”
- Locality and Availability in Distributed Storage (2014, background): “recently constructed codes with good locality and availability properties [27].”