1Cooperative Local Repair in Distributed Storage

Abstract—Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention re-cently for their application in distributed storage systems. This paper investigates a generalization of the usual locally recoverable codes. In particular, this paper studies a class of codes with the following property: any small set of codeword symbols is recoverable from a small number of other symbols. This is referred to as cooperative local repair. The main contribution of this paper is bounds on the trade-off of minimum distance and the dimension of such codes, as well as explicit constructions of families of codes that enable cooperative local repair. Some other results regarding cooperative local repair are also presented, including an analysis for the well-known Hadamard codes. Index Terms—Coding for distributed storage, locally re-pairable codes, codes on graphs, cooperative repair. I