33 research outputs found
Convertible Codes: New Class of Codes for Efficient Conversion of Coded Data in Distributed Storage
Erasure codes are typically used in large-scale distributed storage systems to provide durability of data in the face of failures. In this setting, a set of k blocks to be stored is encoded using an [n, k] code to generate n blocks that are then stored on different storage nodes. A recent work by Kadekodi et al. [Kadekodi et al., 2019] shows that the failure rate of storage devices vary significantly over time, and that changing the rate of the code (via a change in the parameters n and k) in response to such variations provides significant reduction in storage space requirement. However, the resource overhead of realizing such a change in the code rate on already encoded data in traditional codes is prohibitively high.
Motivated by this application, in this work we first present a new framework to formalize the notion of code conversion - the process of converting data encoded with an [n^I, k^I] code into data encoded with an [n^F, k^F] code while maintaining desired decodability properties, such as the maximum-distance-separable (MDS) property. We then introduce convertible codes, a new class of code pairs that allow for code conversions in a resource-efficient manner. For an important parameter regime (which we call the merge regime) along with the widely used linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit low-field-size constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to the default approach of re-encoding
MDS Array Codes With (Near) Optimal Repair Bandwidth for All Admissible Repair Degrees
Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been
reported in the literature. However, most of them require contacting all the
surviving nodes during a node repair process, resulting in a repair degree of
d=n-1. In practical systems, it may not always be feasible to connect and
download data from all surviving nodes, as some nodes may be unavailable.
Therefore, there is a need for MSR code constructions with a repair degree of
d<n-1. Up to now, only a few (n, k) MSR code constructions with repair degree
d<n-1 have been reported, some have a large sub-packetization level, a large
finite field, or restrictions on the repair degree d. In this paper, we propose
a new (n, k) MSR code construction that works for any repair degree d>k, and
has a smaller sub-packetization level or finite field than some existing
constructions. Additionally, in conjunction with a previous generic
transformation to reduce the sub-packetization level, we obtain an MDS array
code with a small sub-packetization level and -optimal repair
bandwidth (i.e., times the optimal repair bandwidth) for repair
degree d=n-1. This code outperforms some existing ones in terms of either the
sub-packetization level or the field size.Comment: Submitted to the IEEE Transactions on Communication
New Centralized MSR Codes With Small Sub-packetization
Centralized repair refers to repairing node failures using
helper nodes in a centralized way, where the repair bandwidth is counted by the
total amount of data downloaded from the helper nodes. A centralized MSR code
is an MDS array code with -optimal repair for some and . In this
paper, we present several classes of centralized MSR codes with small
sub-packetization. At first, we construct an alternative MSR code with
-optimal repair for multiple repair degrees simultaneously.
Based on the code structure, we are able to construct a centralized MSR code
with -optimal repair property for all possible with
simultaneously. The sub-packetization is no more than , which is much smaller than a previous work given
by Ye and Barg (). Moreover, for general
parameters and , we further give a
centralized MSR code enabling -optimal repair with sub-packetization
smaller than all previous works