Codes Between MBR and MSR Points With Exact Repair Property

In this paper, distributed storage systems with exact repair are studied. Constructions for exact-regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points are given. To the best of our knowledge, no previous construction of exact-regenerating codes between MBR and MSR points is done except in the works by Tian et al. and Sasidharan et al. In contrast to their works, the methods used here are elementary. In this paper, it is shown that in the case that the parameters \(n\) , \(k\) , and \(d\) are close to each other, the given construction is close to optimal when comparing with the known functional repair capacity. This is done by showing that when the distances of the parameters \(n\) , \(k\) , and \(d\) are fixed but the actual values approach to infinity, the fraction of the performance of constructed codes with exact repair and the known capacity of codes with functional repair, approaches to one. Also, a simple variation of the constructed codes with almost the same performance is given. Also some bounds for the capacity of exact-repairing codes are given. These bounds illustrate the relationships between storage codes with different parameters.

[1]  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).

[2]  Dimitris S. Papailiopoulos,et al.  Repair Optimal Erasure Codes Through Hadamard Designs , 2011, IEEE Transactions on Information Theory.

[3]  Jehoshua Bruck,et al.  Zigzag Codes: MDS Array Codes With Optimal Rebuilding , 2011, IEEE Transactions on Information Theory.

[4]  RamchandranKannan,et al.  Asymptotic Interference Alignment for Optimal Repair of MDS Codes in Distributed Storage , 2013 .

[5]  Alexandros G. Dimakis,et al.  Searching for Minimum Storage Regenerating Codes , 2009, ArXiv.

[6]  Dimitris S. Papailiopoulos,et al.  Locally Repairable Codes , 2012, IEEE Transactions on Information Theory.

[7]  Kannan Ramchandran,et al.  Distributed Storage Codes With Repair-by-Transfer and Nonachievability of Interior Points on the Storage-Bandwidth Tradeoff , 2010, IEEE Transactions on Information Theory.

[8]  Chao Tian.  Rate region of the (4, 3, 3) exact-repair regenerating codes , 2013, 2013 IEEE International Symposium on Information Theory.

[9]  Cheng Huang,et al.  Optimal Repair of MDS Codes in Distributed Storage via Subspace Interference Alignment , 2011, ArXiv.

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

[11]  P. Vijay Kumar,et al.  An improved outer bound on the storage-repair-bandwidth tradeoff of exact-repair regenerating codes , 2013, 2014 IEEE International Symposium on Information Theory.

[12]  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.

[13]  Camilla Hollanti,et al.  Capacity and Security of Heterogeneous Distributed Storage Systems , 2013, IEEE Journal on Selected Areas in Communications.

[14]  Cheng Huang,et al.  Permutation code: Optimal exact-repair of a single failed node in MDS code based distributed storage systems , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[15]  Kannan Ramchandran,et al.  Asymptotic Interference Alignment for Optimal Repair of MDS Codes in Distributed Storage , 2013, IEEE Transactions on Information Theory.

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

[18]  P. Vijay Kumar,et al.  High-rate regenerating codes through layering , 2013, 2013 IEEE International Symposium on Information Theory.

[19]  P. Vijay Kumar,et al.  Codes with local regeneration , 2012, 2013 IEEE International Symposium on Information Theory.

[20]  Chao Tian,et al.  Exact-repair regenerating codes via layered erasure correction and block designs , 2013, 2013 IEEE International Symposium on Information Theory.

[21]  Toni Ernvall,et al.  Exact-regenerating codes between MBR and MSR points , 2013, 2013 IEEE Information Theory Workshop (ITW).

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