Fractional repetition codes for repair in distributed storage systems

We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity, while a precise expression remains an open problem.

[1]  Richard M. Wilson,et al.  An Existence Theory for Pairwise Balanced Designs, III: Proof of the Existence Conjectures , 1975, J. Comb. Theory, Ser. A.

[2]  R. Brualdi.  Combinatorial Matrix Classes , 2006 .

[3]  N. Wormald,et al.  Models of the , 2010 .

[4]  Ben Y. Zhao,et al.  Maintenance-Free Global Data Storage , 2001, IEEE Internet Comput..

[5]  Van H. Vu,et al.  Generating Random Regular Graphs , 2003, STOC '03.

[6]  GhemawatSanjay,et al.  The Google file system , 2003 .

[7]  C. Colbourn,et al.  Handbook of Combinatorial Designs , 2006 .

[8]  Charles J. Colbourn,et al.  Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications) , 2006 .

[9]  Alexandros G. Dimakis,et al.  Network Coding for Distributed Storage Systems , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[10]  A. Dimakis,et al.  Deterministic Regenerating Codes for Distributed Storage Yunnan , 2007 .

[11]  C. Lindner,et al.  Design Theory, Second Edition , 2008 .

[12]  C. Lindner,et al.  Design Theory , 2008 .

[13]  Kannan Ramchandran,et al.  Explicit construction of optimal exact regenerating codes for distributed storage , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Yunnan Wu,et al.  Reducing repair traffic for erasure coding-based storage via interference alignment , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  Kannan Ramchandran,et al.  Exact Regenerating Codes for Distributed Storage , 2009, ArXiv.

[16]  Syed Ali Jafar,et al.  Distributed Data Storage with Minimum Storage Regenerating Codes - Exact and Functional Repair are Asymptotically Equally Efficient , 2010, ArXiv.

[17]  Alexandros G. Dimakis,et al.  Security in distributed storage systems by communicating a logarithmic number of bits , 2010, 2010 IEEE International Symposium on Information Theory.

[18]  Kannan Ramchandran,et al.  Explicit codes minimizing repair bandwidth for distributed storage , 2009, 2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo).

[19]  Kannan Ramchandran,et al.  Explicit and optimal exact-regenerating codes for the minimum-bandwidth point in distributed storage , 2010, 2010 IEEE International Symposium on Information Theory.

[20]  Kannan Ramchandran,et al.  On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage , 2010, ArXiv.

[21]  Kannan Ramchandran,et al.  On secure distributed data storage under repair dynamics , 2010, 2010 IEEE International Symposium on Information Theory.

[22]  N. Wormald.  Models of random regular graphs , 2010 .

[23]  Kannan Ramchandran,et al.  Exact Regeneration Codes for Distributed Storage Repair Using Interference Alignment , 2009, ArXiv.

[24]  Kannan Ramchandran,et al.  Securing Dynamic Distributed Storage Systems Against Eavesdropping and Adversarial Attacks , 2010, IEEE Transactions on Information Theory.

[25]  Nihar B. Shah,et al.  Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction , 2010, IEEE Transactions on Information Theory.

[26]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .