Coding for locality in reconstructing permutations
Author(s)Raviv, Netanel; Yaakobi, Eitan; Medard, Muriel
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The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding approach. The former approach boils down to presenting large sets of permutations with locality, that is, any symbol of the permutation can be computed from a small set of other symbols. In the latter approach, a permutation may be coded in order to achieve locality. This paper focuses on the combinatorial approach. We provide upper and lower bounds for the maximal size of a set of permutations with locality, and provide several simple constructions which attain the upper bound. In cases where the upper bound is not attained, we provide alternative constructions using Reed-Solomon codes, permutation polynomials, and multi-permutations.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2016 IEEE International Symposium on Information Theory (ISIT)
Institute of Electrical and Electronics Engineers (IEEE)
Raviv, Netanel, Eitan Yaakobi, and Muriel Médard. "Coding for Locality in Reconstructing Permutations." 2016 IEEE International Symposium on Information Theory (ISIT), 10-15 July 2016, Barcelona, Spain, IEEE, 2016, pp. 450–54.