59 research outputs found
Partial MDS Codes with Local Regeneration
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes
that combine locality with strong erasure correction capabilities. We construct
PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS
code. The constructions require significantly smaller field size than the only
other construction known in literature
Explicit Construction of Minimum Bandwidth Rack-Aware Regenerating Codes
In large data centers, storage nodes are organized in racks, and the
cross-rack communication dominates the system bandwidth. We explicitly
construct codes for exact repair of single node failures that achieve the
optimal tradeoff between the storage redundancy and cross-rack repair bandwidth
at the minimum bandwidth point (i.e., the cross-rack bandwidth equals the
storage size per node). Moreover, we explore the node repair when only a few
number of helper racks are connected. Thus we provide explicit constructions of
codes for rack-aware storage with the minimum cross-rack repair bandwidth,
lowest possible redundancy, and small repair degree (i.e., the number of helper
racks connected for repair).Comment: 4 pages, 1 figure. arXiv admin note: text overlap with
arXiv:2101.0873
Error correction based on partial information
We consider the decoding of linear and array codes from errors when we are
only allowed to download a part of the codeword. More specifically, suppose
that we have encoded data symbols using an code with code length
and dimension During storage, some of the codeword coordinates might
be corrupted by errors. We aim to recover the original data by reading the
corrupted codeword with a limit on the transmitting bandwidth, namely, we can
only download an proportion of the corrupted codeword. For a given
our objective is to design a code and a decoding scheme such that we
can recover the original data from the largest possible number of errors. A
naive scheme is to read coordinates of the codeword. This method
used in conjunction with MDS codes guarantees recovery from any errors. In this paper we show that we can instead read an
proportion from each of the codeword's coordinates. For a
well-designed MDS code, this method can guarantee recovery from errors, which is times more than the naive
method, and is also the maximum number of errors that an code can
correct by downloading only an proportion of the codeword. We present
two families of such optimal constructions and decoding schemes. One is a
Reed-Solomon code with evaluation points in a subfield and the other is based
on Folded Reed-Solomon codes. We further show that both code constructions
attain asymptotically optimal list decoding radius when downloading only a part
of the corrupted codeword. We also construct an ensemble of random codes that
with high probability approaches the upper bound on the number of correctable
errors when the decoder downloads an proportion of the corrupted
codeword.Comment: Extended version of the conference paper in ISIT 201
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