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Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Published: 01 August 2011 Publication History

Abstract

Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n=d+1 . In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d ≥ 2k-2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our 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. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n=d+1, k, d ≥ 2k-1].

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  • (2024)Repairing Reed-Solomon Codes Over Prime Fields via Exponential SumsIEEE Transactions on Information Theory10.1109/TIT.2024.344904170:12(8587-8594)Online publication date: 23-Aug-2024
  • (2024)Generalization of Minimum Storage Regenerating Codes for Heterogeneous Distributed Storage SystemsIEEE Transactions on Information Theory10.1109/TIT.2024.338315270:6(4022-4043)Online publication date: 29-Mar-2024
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cover image IEEE Transactions on Information Theory
IEEE Transactions on Information Theory  Volume 57, Issue 8
August 2011
717 pages

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IEEE Press

Publication History

Published: 01 August 2011

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  • (2024)Morph: Efficient File-Lifetime Redundancy Management for Cluster File SystemsProceedings of the ACM SIGOPS 30th Symposium on Operating Systems Principles10.1145/3694715.3695981(330-346)Online publication date: 4-Nov-2024
  • (2024)Repairing Reed-Solomon Codes Over Prime Fields via Exponential SumsIEEE Transactions on Information Theory10.1109/TIT.2024.344904170:12(8587-8594)Online publication date: 23-Aug-2024
  • (2024)Generalization of Minimum Storage Regenerating Codes for Heterogeneous Distributed Storage SystemsIEEE Transactions on Information Theory10.1109/TIT.2024.338315270:6(4022-4043)Online publication date: 29-Mar-2024
  • (2024)MDS array codes with efficient repair and small sub-packetization levelDesigns, Codes and Cryptography10.1007/s10623-024-01440-892:11(3783-3798)Online publication date: 1-Nov-2024
  • (2024)Accelerating erasure coding by exploiting multiple repair paths in distributed storage systemsCluster Computing10.1007/s10586-024-04438-y27:6(8621-8635)Online publication date: 1-Sep-2024
  • (2024)Towards Breaking the Half-Barrier of Local Leakage-Resilient Shamir’s Secret SharingAdvances in Cryptology – CRYPTO 202410.1007/978-3-031-68388-6_10(257-285)Online publication date: 18-Aug-2024
  • (2024)Constructing Leakage-Resilient Shamir’s Secret Sharing: Over Composite Order FieldsAdvances in Cryptology – EUROCRYPT 202410.1007/978-3-031-58737-5_11(286-315)Online publication date: 26-May-2024
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  • (2023)Cooperative Repair of Reed-Solomon Codes via Linearized Permutation PolynomialsIEEE Transactions on Information Theory10.1109/TIT.2023.334765470:7(4747-4758)Online publication date: 26-Dec-2023
  • (2023)Rack-Aware MSR Codes With Error Correction Capability for Multiple Erasure ToleranceIEEE Transactions on Information Theory10.1109/TIT.2023.328918769:10(6428-6442)Online publication date: 28-Jun-2023
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