Fractional Repetition Codes In Distributed Storage System

Distributed storage system plays an important role in the growing demand of large scale data storage.In DSS,one wants to provide security,reliability,reduced storage overhead and minimal bandwidth for repair by using network coding.Compared with the traditional replication strategy and the general erasure codes,regenerating codes can optimize these parameters.In the actual storage system,storage capacity and repair bandwidth are two important indicators to measure the system.For the two cases,regenerating codes are typically known for minimum storage regenerating(MSR)codes and minimum bandwidth regenerating(MBR)codes.DRESS(Distributed replication based exact simple storage)codes are a new class of codes at the minimum bandwidth regeneration point.The codes are obtained by the concatenation of an outer MDS code and an inner fractional repetition(FR)code.DRESS codes are characterized by an efficient and low-complexity uncoded repair process that can tolerate multiple node failures,which greatly increase the reliability of the system.MDS codes are well-studied,so the emphases are the constructions of FR codes and the calculation of rate.For these questions above,the material in this thesis is organized as follows.In Introduction,we give a brief introduction to the background and status of FR codes.In Chapter 1,we introduce the referent definitions of FR codes,and elaborate the encoding scheme for a DRESS code.In Chapter 2,we focus our attention on the constructions of FR codes based on graphs,such as -cube (,2),2-cube (2,2)and Johnson graph.In Chapter 3,we study the constructions of FR codes based on designs,such as affine plane of order 9).In Chapter 4,we present some other constructions of FR codes,such as symplectic space.For all types of codes mentioned above,we give the calculation process of the rate and the further analysis.