The Constructions Of Fractional Repetition Codes Based On Designs And Graphs

Data storage in Distributed Storage Systems is a multidimensional optimization problem.In order to provide fault-tolerance and guarantee reliability,Dimakis et al.introduced regenerating codes,which could optimize storage overhead and repair band-width.However,these codes usually involve a large number of finite field operations,with high computational complexity in their repair processes.Therefore,Rouayheb et al.proposed Fractional Repetition(FR)codes that allowed uncoded exact repairs with minimum repair bandwidth.Based on the work focusing on FR codes,Bing Zhu et al.extended the construction of FR codes and presented a new coding scheme,termed Gen-eral Fractional Repetition(GFR)codes.The proposed codes can be applied to storage systems in which the storage capacities of nodes may be different.The problems of how to construct the codes and how to find the maximum value of the reconfiguration files(i.e.code rate DC(k))are some hot topics in the researches.In this paper,we mainly study the above two problems.In Introduction,we mainly introduce the related background and status of FR codes.In Chapter 1,we mainly introduce the relevant definitions of' FR and GFR codes.In Chapter 2,we use t-designs,triangular association schemes as well as association schemes of Latin-square type to construct three kinds of universally good FR codes,and calculate their code rate Dc(k)respectively.In Chapter 3,we use Partially Balanced Incomplete Block(PBIB)designs and par-tial regular graphs to construct GFR codes.What's more,we figure out the code rate Dc(k)of these codes.