38 research outputs found
Optimal Linear and Cyclic Locally Repairable Codes over Small Fields
We consider locally repairable codes over small fields and propose
constructions of optimal cyclic and linear codes in terms of the dimension for
a given distance and length. Four new constructions of optimal linear codes
over small fields with locality properties are developed. The first two
approaches give binary cyclic codes with locality two. While the first
construction has availability one, the second binary code is characterized by
multiple available repair sets based on a binary Simplex code. The third
approach extends the first one to q-ary cyclic codes including (binary)
extension fields, where the locality property is determined by the properties
of a shortened first-order Reed-Muller code. Non-cyclic optimal binary linear
codes with locality greater than two are obtained by the fourth construction.Comment: IEEE Information Theory Workshop (ITW) 2015, Apr 2015, Jerusalem,
Israe
Constructions of Batch Codes via Finite Geometry
A primitive -batch code encodes a string of length into string
of length , such that each multiset of symbols from has mutually
disjoint recovering sets from . We develop new explicit and random coding
constructions of linear primitive batch codes based on finite geometry. In some
parameter regimes, our proposed codes have lower redundancy than previously
known batch codes.Comment: 7 pages, 1 figure, 1 tabl
Optimal Binary Locally Repairable Codes via Anticodes
This paper presents a construction for several families of optimal binary
locally repairable codes (LRCs) with small locality (2 and 3). This
construction is based on various anticodes. It provides binary LRCs which
attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal
with respect to the Griesmer bound
Network Traffic Driven Storage Repair
Recently we constructed an explicit family of locally repairable and locally
regenerating codes. Their existence was proven by Kamath et al. but no explicit
construction was given. Our design is based on HashTag codes that can have
different sub-packetization levels. In this work we emphasize the importance of
having two ways to repair a node: repair only with local parity nodes or repair
with both local and global parity nodes. We say that the repair strategy is
network traffic driven since it is in connection with the concrete system and
code parameters: the repair bandwidth of the code, the number of I/O
operations, the access time for the contacted parts and the size of the stored
file. We show the benefits of having repair duality in one practical example
implemented in Hadoop. We also give algorithms for efficient repair of the
global parity nodes.Comment: arXiv admin note: text overlap with arXiv:1701.0666
HFR Code: A Flexible Replication Scheme for Cloud Storage Systems
Fractional repetition (FR) codes are a family of repair-efficient storage
codes that provide exact and uncoded node repair at the minimum bandwidth
regenerating point. The advantageous repair properties are achieved by a
tailor-made two-layer encoding scheme which concatenates an outer
maximum-distance-separable (MDS) code and an inner repetition code. In this
paper, we generalize the application of FR codes and propose heterogeneous
fractional repetition (HFR) code, which is adaptable to the scenario where the
repetition degrees of coded packets are different. We provide explicit code
constructions by utilizing group divisible designs, which allow the design of
HFR codes over a large range of parameters. The constructed codes achieve the
system storage capacity under random access repair and have multiple repair
alternatives for node failures. Further, we take advantage of the systematic
feature of MDS codes and present a novel design framework of HFR codes, in
which storage nodes can be wisely partitioned into clusters such that data
reconstruction time can be reduced when contacting nodes in the same cluster.Comment: Accepted for publication in IET Communications, Jul. 201