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Register a new userCodes for Distributed Storage
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Added by
Vinayak Ramkumar
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of ensuring reliability against data loss while minimizing storage overhead. More recently, a third concern has surfaced, namely of the need to efficiently recover from the failure of a single storage unit, corresponding to recovery from the erasure of a single code symbol. We explain here, how coding theory has evolved to tackle this fresh challenge.
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This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding stored information. Second, the paper focuses on coding schemes that enable optimal local repairs. It further brings these two concepts together, to develop locally repairable coding schemes for DSS that are secure against eavesdroppers. The main results of this paper include: a. An improved bound on the secrecy capacity for minimum storage regenerating codes, b. secure coding schemes that achieve the bound for some special cases, c. a new bound on minimum distance for locally repairable codes, d. code construction for locally repairable codes that attain the minimum distance bound, and e. repair-bandwidth-efficient locally repairable codes with and without security constraints.
In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a failed node can only be reconstructed from the available live nodes belonging to the available blocks. To analyze the resilience of the system against such block failures, this work introduces the framework of Block Failure Resilient (BFR) codes, wherein the data (e.g., a file in DSS) can be decoded by reading out from a same number of codeword symbols (nodes) from a subset of available blocks of the underlying codeword. Further, repairable BFR codes are introduced, wherein any codeword symbol in a failed block can be repaired by contacting a subset of remaining blocks in the system. File size bounds for repairable BFR codes are derived, and the trade-off between per node storage and repair bandwidth is analyzed, and the corresponding minimum storage regenerating (BFR-MSR) and minimum bandwidth regenerating (BFR-MBR) points are derived. Explicit codes achieving the two operating points for a special case of parameters are constructed, wherein the underlying regenerating codewords are distributed to BFR codeword symbols according to combinatorial designs. Finally, BFR locally repairable codes (BFR-LRC) are introduced, an upper bound on the resilience is derived and optimal code construction are provided by a concatenation of Gabidulin and MDS codes. Repair efficiency of BFR-LRC is further studied via the use of BFR-MSR/MBR codes as local codes. Code constructions achieving optimal resilience for BFR-MSR/MBR-LRCs are provided for certain parameter regimes. Overall, this work introduces the framework of block failures along with optimal code constructions, and the study of architecture-aware coding for distributed storage systems.
We study the secrecy of a distributed storage system for passwords. The encoder, Alice, observes a length-n password and describes it using two hints, which she then stores in different locations. The legitimate receiver, Bob, observes both hints. The eavesdropper, Eve, sees only one of the hints; Alice cannot control which. We characterize the largest normalized (by n) exponent that we can guarantee for the number of guesses it takes Eve to guess the password subject to the constraint that either the number of guesses it takes Bob to guess the password or the size of the list that Bob must form to guarantee that it contain the password approach 1 as n tends to infinity.
Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular workaround to the well known ``straggling nodes problem, in particular, by matching linear coding for linear computation tasks. It was observed that decoding tends to amplify the computation ``noise, i.e., the numerical errors at the computation nodes. We propose taking advantage of the case that more nodes return than minimally required. We show how a clever construction of a polynomial code, inspired by recent results on robust frames, can significantly reduce the amplification of noise, and achieves graceful degradation with the number of straggler nodes.
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node. Efficient repair calls for erasure codes that in the face of node failure, are efficient in terms of minimizing the amount of repair data transferred over the network, the amount of data accessed at a helper node as well as the number of helper nodes contacted. Coding theory has evolved to handle these challenges by introducing two new classes of erasure codes, namely regenerating codes and locally recoverable codes as well as by coming up with novel ways to repair the ubiquitous Reed-Solomon code. This survey provides an overview of the efforts in this direction that have taken place over the past decade.
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