412 research outputs found
When and By How Much Can Helper Node Selection Improve Regenerating Codes?
Regenerating codes (RCs) can significantly reduce the repair-bandwidth of
distributed storage networks. Initially, the analysis of RCs was based on the
assumption that during the repair process, the newcomer does not distinguish
(among all surviving nodes) which nodes to access, i.e., the newcomer is
oblivious to the set of helpers being used. Such a scheme is termed the blind
repair (BR) scheme. Nonetheless, it is intuitive in practice that the newcomer
should choose to access only those "good" helpers. In this paper, a new
characterization of the effect of choosing the helper nodes in terms of the
storage-bandwidth tradeoff is given. Specifically, answers to the following
fundamental questions are given: Under what conditions does proactively
choosing the helper nodes improve the storage-bandwidth tradeoff? Can this
improvement be analytically quantified?
This paper answers the former question by providing a necessary and
sufficient condition under which optimally choosing good helpers strictly
improves the storage-bandwidth tradeoff. To answer the latter question, a
low-complexity helper selection solution, termed the family repair (FR) scheme,
is proposed and the corresponding storage/repair-bandwidth curve is
characterized. For example, consider a distributed storage network with 60
total number of nodes and the network is resilient against 50 node failures. If
the number of helper nodes is 10, then the FR scheme and its variant
demonstrate 27% reduction in the repair-bandwidth when compared to the BR
solution. This paper also proves that under some design parameters, the FR
scheme is indeed optimal among all helper selection schemes. An explicit
construction of an exact-repair code is also proposed that can achieve the
minimum-bandwidth-regenerating point of the FR scheme. The new exact-repair
code can be viewed as a generalization of the existing fractional repetition
code.Comment: 35 pages, 10 figures, submitted to IEEE Transactions on Information
Theory on September 04, 201
Optimal Rebuilding of Multiple Erasures in MDS Codes
MDS array codes are widely used in storage systems due to their
computationally efficient encoding and decoding procedures. An MDS code with
redundancy nodes can correct any node erasures by accessing all the
remaining information in the surviving nodes. However, in practice,
erasures is a more likely failure event, for . Hence, a natural
question is how much information do we need to access in order to rebuild
storage nodes? We define the rebuilding ratio as the fraction of remaining
information accessed during the rebuilding of erasures. In our previous
work we constructed MDS codes, called zigzag codes, that achieve the optimal
rebuilding ratio of for the rebuilding of any systematic node when ,
however, all the information needs to be accessed for the rebuilding of the
parity node erasure.
The (normalized) repair bandwidth is defined as the fraction of information
transmitted from the remaining nodes during the rebuilding process. For codes
that are not necessarily MDS, Dimakis et al. proposed the regenerating codes
framework where any erasures can be corrected by accessing some of the
remaining information, and any erasure can be rebuilt from some subsets
of surviving nodes with optimal repair bandwidth.
In this work, we study 3 questions on rebuilding of codes: (i) We show a
fundamental trade-off between the storage size of the node and the repair
bandwidth similar to the regenerating codes framework, and show that zigzag
codes achieve the optimal rebuilding ratio of for MDS codes, for any
. (ii) We construct systematic codes that achieve optimal
rebuilding ratio of , for any systematic or parity node erasure. (iii) We
present error correction algorithms for zigzag codes, and in particular
demonstrate how these codes can be corrected beyond their minimum Hamming
distances.Comment: There is an overlap of this work with our two previous submissions:
Zigzag Codes: MDS Array Codes with Optimal Rebuilding; On Codes for Optimal
Rebuilding Access. arXiv admin note: text overlap with arXiv:1112.037
- …