Optimal Fractional Repetition Codes and Fractional Repetition Batch Codes

摘要

Fractional repetition (FR) codes is a family of codes for distributed storagesystems (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 bestored using an FR code. Optimal FR codes which attain this bound arepresented. The constructions of these FR codes are based on families of regulargraphs, such as Tur\'an graphs and graphs with large girth; and oncombinatorial designs, such as transversal designs and generalized polygons. Inaddition, based on a connection between FR codes and batch codes, we propose anew family of codes for DSS, called fractional repetition batch codes, whichallow uncoded efficient exact repairs and load balancing which can be performedby several users in parallel.