888 research outputs found
Locally recoverable J-affine variety codes
A locally recoverable (LRC) code is a code over a finite eld Fq such that
any erased coordinate of a codeword can be recovered from a small number of other
coordinates in that codeword. We construct LRC codes correcting more than one erasure,
which are sub eld-subcodes of some J-affine variety codes. For these LRC codes, we
compute localities (r; )) that determine the minimum size of a set R of positions so that
any - 1 erasures in R can be recovered from the remaining r coordinates in this set.
We also show that some of these LRC codes with lengths n >> q are ( - 1)-optimal
Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems
Cloud systems have become the backbone of many applications such as multimedia
streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture
lies a large-scale, distributed, data storage system. To accommodate the massive
amount of data being stored on the cloud, these distributed storage systems (DSS) have
been scaled to contain hundreds to thousands of nodes that are connected through a networking
infrastructure. Such data-centers are usually built out of commodity components,
which make failures the norm rather than the exception.
In order to combat node failures, data is typically stored in a redundant fashion. Due to
the exponential data growth rate, many DSS are beginning to resort to error control coding
over conventional replication methods, as coding offers high storage space efficiency. This
paradigm shift from replication to coding, along with the need to guarantee reliability, efficiency,
and security in DSS, has created a new set of challenges and opportunities, opening
up a new area of research. This thesis addresses several of these challenges and opportunities
by broadly making the following contributions. (i) We design practically amenable,
low-complexity coding schemes that guarantee security of cloud systems, ensure quick
recovery from failures, and provide high availability for retrieving partial information; and
(ii) We analyze fundamental performance limits and optimal trade-offs between the key
performance metrics of these coding schemes.
More specifically, we first consider the problem of achieving information-theoretic
security in DSS against an eavesdropper that can observe a limited number of nodes. We
present a framework that enables design of secure repair-efficient codes through a joint
construction of inner and outer codes. Then, we consider a practically appealing notion
of weakly secure coding, and construct coset codes that can weakly secure a wide class of regenerating codes that reduce the amount of data downloaded during node repair.
Second, we consider the problem of meeting repair locality constraints, which specify
the number of nodes participating in the repair process. We propose a notion of unequal
locality, which enables different locality values for different nodes, ensuring quick recovery
for nodes storing important data. We establish tight upper bounds on the minimum
distance of linear codes with unequal locality, and present optimal code constructions.
Next, we extend the notion of locality from the Hamming metric to the rank and subspace
metrics, with the goal of designing codes for efficient data recovery from special types of
correlated failures in DSS.We construct a family of locally recoverable rank-metric codes
with optimal data recovery properties.
Finally, we consider the problem of providing high availability, which is ensured by
enabling node repair from multiple disjoint subsets of nodes of small size. We study
codes with availability from a queuing-theoretical perspective by analyzing the average
time necessary to download a block of data under the Poisson request arrival model when
each node takes a random amount of time to fetch its contents. We compare the delay
performance of the availability codes with several alternatives such as conventional erasure
codes and replication schemes
Asymptotic construction of locally repairable codes with multiple recovering sets
Locally repairable codes have been extensively investigated due to practical
applications in distributed and cloud storage systems in recent years. However,
not much work on asymptotic behavior of locally repairable codes has been done.
In particular, there is few result on constructive lower bound of asymptotic
behavior of locally repairable codes with multiple recovering sets. In this
paper, we construct some families of asymptotically good locally repairable
codes with multiple recovering sets via automorphism groups of function fields
of the Garcia-Stichtenoth towers. The main advantage of our construction is to
allow more flexibility of localities
Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems
Cloud systems have become the backbone of many applications such as multimedia
streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture
lies a large-scale, distributed, data storage system. To accommodate the massive
amount of data being stored on the cloud, these distributed storage systems (DSS) have
been scaled to contain hundreds to thousands of nodes that are connected through a networking
infrastructure. Such data-centers are usually built out of commodity components,
which make failures the norm rather than the exception.
In order to combat node failures, data is typically stored in a redundant fashion. Due to
the exponential data growth rate, many DSS are beginning to resort to error control coding
over conventional replication methods, as coding offers high storage space efficiency. This
paradigm shift from replication to coding, along with the need to guarantee reliability, efficiency,
and security in DSS, has created a new set of challenges and opportunities, opening
up a new area of research. This thesis addresses several of these challenges and opportunities
by broadly making the following contributions. (i) We design practically amenable,
low-complexity coding schemes that guarantee security of cloud systems, ensure quick
recovery from failures, and provide high availability for retrieving partial information; and
(ii) We analyze fundamental performance limits and optimal trade-offs between the key
performance metrics of these coding schemes.
More specifically, we first consider the problem of achieving information-theoretic
security in DSS against an eavesdropper that can observe a limited number of nodes. We
present a framework that enables design of secure repair-efficient codes through a joint
construction of inner and outer codes. Then, we consider a practically appealing notion
of weakly secure coding, and construct coset codes that can weakly secure a wide class of regenerating codes that reduce the amount of data downloaded during node repair.
Second, we consider the problem of meeting repair locality constraints, which specify
the number of nodes participating in the repair process. We propose a notion of unequal
locality, which enables different locality values for different nodes, ensuring quick recovery
for nodes storing important data. We establish tight upper bounds on the minimum
distance of linear codes with unequal locality, and present optimal code constructions.
Next, we extend the notion of locality from the Hamming metric to the rank and subspace
metrics, with the goal of designing codes for efficient data recovery from special types of
correlated failures in DSS.We construct a family of locally recoverable rank-metric codes
with optimal data recovery properties.
Finally, we consider the problem of providing high availability, which is ensured by
enabling node repair from multiple disjoint subsets of nodes of small size. We study
codes with availability from a queuing-theoretical perspective by analyzing the average
time necessary to download a block of data under the Poisson request arrival model when
each node takes a random amount of time to fetch its contents. We compare the delay
performance of the availability codes with several alternatives such as conventional erasure
codes and replication schemes
Locally recoverable codes from the matrix-product construction
Matrix-product constructions giving rise to locally recoverable codes are
considered, both the classical and localities. We study the
recovery advantages offered by the constituent codes and also by the defining
matrices of the matrix product codes. Finally, we extend these methods to a
particular variation of matrix-product codes and quasi-cyclic codes.
Singleton-optimal locally recoverable codes and almost Singleton-optimal codes,
with length larger than the finite field size, are obtained, some of them with
superlinear length
Locally repairable convertible codes with optimal access costs
Modern large-scale distributed storage systems use erasure codes to protect
against node failures with low storage overhead. In practice, the failure rate
and other factors of storage devices in the system may vary significantly over
time, and leads to changes of the ideal code parameters. To maintain the
storage efficiency, this requires the system to adjust parameters of the
currently used codes. The changing process of code parameters on encoded data
is called code conversion.
As an important class of storage codes, locally repairable codes (LRCs) can
repair any codeword symbol using a small number of other symbols. This feature
makes LRCs highly efficient for addressing single node failures in the storage
systems. In this paper, we investigate the code conversions for locally
repairable codes in the merge regime. We establish a lower bound on the access
cost of code conversion for general LRCs and propose a general construction of
LRCs that can perform code conversions with access cost matching this bound.
This construction provides a family of LRCs together with optimal conversion
process over the field of size linear in the code length.Comment: 25 page
Maori Education: The Politics of Reconciliation and Citizenship
The meaning of citizenship for many Indigenous peoples has historically entailed assimilation into the nation-state through colonizing education policies and practices. Several democratic nation-states are now seeking reconciliation with Indigenous peoples and redefining the meaning of citizenship within their borders. Using recent multicultural education and the politics of reconciliation research, this paper examines the possibility of reconciliation between nation-states and Indigenous peoples, focusing on the Maori of New Zealand and their quest for full inclusion and citizen rights. The paper illustrates why the politics of reconciliation is viewed as necessary to construct a political partnership that fosters a new meaning of citizenship. This analysis suggests that a new meaning of citizenship is emerging in New Zealand because the voices of the Maori are being recognized by the dominant group and historical injustices are being acknowledged through the Waitangi Tribunal process
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