In this paper, the storage-repair-bandwidth (SRB) trade-off curve of regenerating codes is reformulated to yield a tradeoff between two global parameters of practical relevance, namely information rate and repair rate. The new information-repair-rate (IRR) tradeoff provides a different and insightful perspective on regenerating codes. For example, it provides a new motivation for seeking to investigate constructions corresponding to the interior of the SRB tradeoff. Interestingly, each point on the SRB tradeoff corresponds to a curve in the IRR tradeoff setup. We characterize completely, functional repair under the IRR framework, while for exact repair, an achievable region is presented. In the second part of this paper, a rate-half regenerating code for the minimum storage regenerating point is constructed that draws upon the theory of invariant subspaces. While the parameters of this rate-half code are the same as those of the MISER code, the construction itself is quite different.
[1]
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.
[2]
Alexandros G. Dimakis,et al.
Network Coding for Distributed Storage Systems
,
2007,
IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.
[3]
Cheng Huang,et al.
Optimal Repair of MDS Codes in Distributed Storage via Subspace Interference Alignment
,
2011,
ArXiv.
[4]
Kannan Ramchandran,et al.
Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions
,
2010,
IEEE Transactions on Information Theory.