Coding for locality in reconstructing permutations

• Main Authors: Raviv, Netanel (Author), Yaakobi, Eitan (Author), Medard, Muriel (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2018-02-14T19:28:25Z.
• Subjects: Article
• Online Access: Get fulltext

 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.