4 research outputs found
Hierarchical Hybrid Error Correction for Time-Sensitive Devices at the Edge
Computational storage, known as a solution to significantly reduce the
latency by moving data-processing down to the data storage, has received wide
attention because of its potential to accelerate data-driven devices at the
edge. To meet the insatiable appetite for complicated functionalities tailored
for intelligent devices such as autonomous vehicles, properties including
heterogeneity, scalability, and flexibility are becoming increasingly
important. Based on our prior work on hierarchical erasure coding that enables
scalability and flexibility in cloud storage, we develop an efficient decoding
algorithm that corrects a mixture of errors and erasures simultaneously. We
first extract the basic component code, the so-called extended Cauchy (EC)
codes, of the proposed coding solution. We prove that the class of EC codes is
strictly larger than that of relevant codes with known explicit decoding
algorithms. Motivated by this finding, we then develop an efficient decoding
method for the general class of EC codes, based on which we propose the local
and global decoding algorithms for the hierarchical codes. Our proposed hybrid
error correction not only enables the usage of hierarchical codes in
computational storage at the edge, but also applies to any Cauchy-like codes
and allows potentially wider applications of the EC codes.Comment: 29 pages (single column), 0 figures, to be submitted to IEEE
Transactions on Communication
Extended Integrated Interleaved Codes over any Field with Applications to Locally Recoverable Codes
Integrated Interleaved (II) and Extended Integrated Interleaved (EII) codes
are a versatile alternative for Locally Recoverable (LRC) codes, since they
require fields of relatively small size. II and EII codes are generally defined
over Reed-Solomon type of codes. A new comprehensive definition of EII codes is
presented, allowing for EII codes over any field, and in particular, over the
binary field . The traditional definition of II and EII codes is shown
to be a special case of the new definition. Improvements over previous
constructions of LRC codes, in particular, for binary codes, are given, as well
as cases meeting an upper bound on the minimum distance. Properties of the
codes are presented as well, in particular, an iterative decoding algorithm on
rows and columns generalizing the iterative decoding algorithm of product
codes. Two applications are also discussed: one is finding a systematic
encoding of EII codes such that the parity symbols have a balanced distribution
on rows, and the other is the problem of ordering the symbols of an EII code
such that the maximum length of a correctable burst is achieved.Comment: 25 page
Multiple-Layer Integrated Interleaved Codes: A Class of Hierarchical Locally Recoverable Codes
The traditional definition of Integrated Interleaved (II) codes generally
assumes that the component nested codes are either Reed-Solomon (RS) or
shortened Reed-Solomon codes. By taking general classes of codes, we present a
recursive construction of Extended Integrated Interleaved (EII) codes into
multiple layers, a problem that brought attention in literature for II codes.
The multiple layer approach allows for a hierarchical scheme where each layer
of the code provides for a different locality. In particular, we present the
erasure-correcting capability of the new codes and we show that they are
ideally suited as Locally Recoverable (LRC) codes due to their hierarchical
locality and the small finite field required by the construction. Properties of
the multiple layer EII codes, like their minimum distance and dimension, as
well as their erasure decoding algorithms, parity-check matrices and
performance analysis, are provided and illustrated with examples. Finally, we
will observe that the parity-check matrices of high layer EII codes have low
density.Comment: 21 pages, 1 tabl
Hierarchical Coding for Cloud Storage: Topology-Adaptivity, Scalability, and Flexibility
In order to accommodate the ever-growing data from various, possibly
independent, sources and the dynamic nature of data usage rates in practical
applications, modern cloud data storage systems are required to be scalable,
flexible, and heterogeneous. The recent rise of the blockchain technology is
also moving various information systems towards decentralization to achieve
high privacy at low costs. While codes with hierarchical locality have been
intensively studied in the context of centralized cloud storage due to their
effectiveness in reducing the average reading time, those for decentralized
storage networks (DSNs) have not yet been discussed. In this paper, we propose
a joint coding scheme where each node receives extra protection through the
cooperation with nodes in its neighborhood in a heterogeneous DSN with any
given topology. This work extends and subsumes our prior work on coding for
centralized cloud storage. In particular, our proposed construction not only
preserves desirable properties such as scalability and flexibility, which are
critical in dynamic networks, but also adapts to arbitrary topologies, a
property that is essential in DSNs but has been overlooked in existing works.Comment: 25 pages (single column), 19 figures, submitted to the IEEE
Transactions on Information Theory (TIT