16 research outputs found
On Error Decoding of Locally Repairable and Partial MDS Codes
We consider error decoding of locally repairable codes (LRC) and partial MDS
(PMDS) codes through interleaved decoding. For a specific class of LRCs we
investigate the success probability of interleaved decoding. For PMDS codes we
show that there is a wide range of parameters for which interleaved decoding
can increase their decoding radius beyond the minimum distance with the
probability of successful decoding approaching , when the code length goes
to infinity
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
Maximally Recoverable Codes with Hierarchical Locality
Maximally recoverable codes are a class of codes which recover from all
potentially recoverable erasure patterns given the locality constraints of the
code. In earlier works, these codes have been studied in the context of codes
with locality. The notion of locality has been extended to hierarchical
locality, which allows for locality to gradually increase in levels with the
increase in the number of erasures. We consider the locality constraints
imposed by codes with two-level hierarchical locality and define maximally
recoverable codes with data-local and local hierarchical locality. We derive
certain properties related to their punctured codes and minimum distance. We
give a procedure to construct hierarchical data-local MRCs from hierarchical
local MRCs. We provide a construction of hierarchical local MRCs for all
parameters. For the case of one global parity, we provide a different
construction of hierarchical local MRC over a lower field size.Comment: 6 pages, accepted to National Conference of Communications (NCC) 201
Generalized Simple Regenerating Codes: Trading Sub-packetization and Fault Tolerance
Maximum distance separable (MDS) codes have the optimal trade-off between
storage efficiency and fault tolerance, which are widely used in distributed
storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can
achieve both smaller repair bandwidth and smaller repair locality than
traditional MDS codes in repairing single-node erasure.
In this paper, we propose {\em generalized simple regenerating codes} (GSRCs)
that can support much more parameters than that of SRCs. We show that there is
a trade-off between sub-packetization and fault tolerance in our GSRCs, and
SRCs achieve a special point of the trade-off of GSRCs. We show that the fault
tolerance of our GSRCs increases when the sub-packetization increases linearly.
We also show that our GSRCs can locally repair any singe-symbol erasure and any
single-node erasure, and the repair bandwidth of our GSRCs is smaller than that
of the existing related codes