Cascade Codes for Distributed Storage Systems

@article{Elyasi2020CascadeCF,
title={Cascade Codes for Distributed Storage Systems},
author={Mehran Elyasi and Soheil Mohajer},
journal={IEEE Transactions on Information Theory},
year={2020},
volume={66},
pages={7490-7527}
}
• Published 3 January 2019
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair process) and the required storage overhead of the system. These codes work for general system parameters <inline-formula> <tex-math notation="LaTeX">$(n,k,d)$ </tex-math></inline-formula>, which are the total number of nodes, the number of nodes suffice for data… Expand
10 Citations

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References

SHOWING 1-10 OF 63 REFERENCES
Distributed Storage Codes With Repair-by-Transfer and Nonachievability of Interior Points on the Storage-Bandwidth Tradeoff
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2012
An explicit, exact-repair code for the point on the storage-bandwidth tradeoff corresponding to the minimum possible repair bandwidth, and an ability of the code to perform repair through mere transfer of data as repair by transfer are named. Expand
Product Matrix MSR Codes With Bandwidth Adaptive Exact Repair
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2018
This paper introduces a class of MSR codes that realize the optimal repair bandwidth simultaneously with a set of different choices for the number of helpers, namely PM MSR code, which could be considered as a generalization of the product matrix (PM) framework. Expand
A Cascade Code Construction for (n, k, d) Distributed Storage Systems
• Computer Science, Mathematics
• 2018 IEEE International Symposium on Information Theory (ISIT)
• 2018
A novel class of exact-repair regenerating codes is introduced for a distributed storage system with arbitrary parameters, which meets the optimum trade-off at the MBR and MSR points and improves all the previously known bounds for interior points. Expand
Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2011
To the best of the knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. Expand
Determinant Coding: A Novel Framework for Exact-Repair Regenerating Codes
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2016
It is shown that the proposed codes are optimum, in the sense that any operating point satisfying the lower bound for the storage-bandwidth trade-off can be achieved with the proposed construction. Expand
Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2012
The constructions presented in this paper are the first explicit constructions of regenerating codes that achieve the cut-set bound, and Interference alignment is a theme that runs throughout the paper. Expand
Minimum storage regenerating codes for all parameters
• Computer Science, Mathematics
• 2016 IEEE International Symposium on Information Theory (ISIT)
• 2016
The main result in this paper is an explicit construction of systematic-repair MSR codes of high rate k/n > 0.5 and low repair connectivity k ≤ d ≤ n - 1, not previously known to exist. Expand
Determinant Codes With Helper-Independent Repair for Single and Multiple Failures
• Computer Science, Mathematics
• IEEE Transactions on Information Theory
• 2019
A new repair mechanism is proposed for determinant code, which relaxes this dependency, while preserving all other properties of the code, and it is shown that the determinant codes are capable of repairing multiple failures, with a per-node repair-bandwidth which scales sub-linearly with the number of failures. Expand
Bandwidth Adaptive & Error Resilient MBR Exact Repair Regenerating Codes
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2019
This paper considers two simultaneous extensions to the original regenerating codes framework, and provides a more natural extension of the well-known product matrix MBR codes, modified to provide flexibility in choosing the number of helpers in each repair, and simultaneously be robust to erroneous nodes in the network. Expand
Existence and construction of capacity-achieving network codes for distributed storage
• Yunnan Wu
• Computer Science
• 2009 IEEE International Symposium on Information Theory
• 2009
It is shown in this paper that optimal codes can be constructed over a finite field whose size depends only on the maximum number of nodes at any instant, but independent of how many failures/repairs can happen. Expand