Optimal fractional repetition codes and fractional repetition batch codes

Fractional repetition (FR) codes is a family of codes for distributed storage systems (DSS) that allow uncoded exact repairs with minimum repair bandwidth. In this work, we consider a bound on the maximum amount of data that can be stored using an FR code. Optimal FR codes which attain this bound are presented. The constructions of these FR codes are based on families of regular graphs, such as Turán graphs and graphs with large girth; and on combinatorial designs, such as transversal designs and generalized polygons. In addition, based on a connection between FR codes and batch codes, we propose a new family of codes for DSS, called fractional repetition batch codes, which allow uncoded efficient exact repairs and load balancing which can be performed by several users in parallel.