35 research outputs found
MDS array codes for correcting a signle criss-cross error
We present a family of maximum-distance separable (MDS) array codes of size (p-1)×(p-1), p a prime number, and minimum criss-cross distance 3, i.e., the code is capable of correcting any row or column in error, without a priori knowledge of what type of error occurred. The complexity of the encoding and decoding algorithms is lower than that of known codes with the same error-correcting power, since our algorithms are based on exclusive-OR operations over lines of different slopes, as opposed to algebraic operations over a finite field. We also provide efficient encoding and decoding algorithms for errors and erasures
Codes for Graph Erasures
Motivated by systems where the information is represented by a graph, such as
neural networks, associative memories, and distributed systems, we present in
this work a new class of codes, called codes over graphs. Under this paradigm,
the information is stored on the edges of an undirected graph, and a code over
graphs is a set of graphs. A node failure is the event where all edges in the
neighborhood of the failed node have been erased. We say that a code over
graphs can tolerate node failures if it can correct the erased edges of
any failed nodes in the graph. While the construction of such codes can
be easily accomplished by MDS codes, their field size has to be at least
, when is the number of nodes in the graph. In this work we present
several constructions of codes over graphs with smaller field size. In
particular, we present optimal codes over graphs correcting two node failures
over the binary field, when the number of nodes in the graph is a prime number.
We also present a construction of codes over graphs correcting node
failures for all over a field of size at least , and show how
to improve this construction for optimal codes when .Comment: To appear in IEEE International Symposium on Information Theor
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
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
Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric
We speed up existing decoding algorithms for three code classes in different
metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved
Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in
the sum-rank metric. The speed-ups are achieved by reducing the core of the
underlying computational problems of the decoders to one common tool: computing
left and right approximant bases of matrices over skew polynomial rings. To
accomplish this, we describe a skew-analogue of the existing PM-Basis algorithm
for matrices over usual polynomials. This captures the bulk of the work in
multiplication of skew polynomials, and the complexity benefit comes from
existing algorithms performing this faster than in classical quadratic
complexity. The new faster algorithms for the various decoding-related
computational problems are interesting in their own and have further
applications, in particular parts of decoders of several other codes and
foundational problems related to the remainder-evaluation of skew polynomials
Intuition, expertise and judgement in the capture and assessment of photographic images
The aim of this thesis is to contribute to our theoretical and experiential understanding of the
exercise of multivariate, short time-slice photographic judgement. This research is grounded
in both the ontology and the psychology of nonconscious (intuitive) cognition and its
orthogonal interaction with conscious thought at the moment of capture or assessment of a
photographic image. My principal mode of empirical investigation uses a cross-sectional,
correlational design employing a testing instrument, the Intuitive Mastery Photography Test
(the IMP Test) originally developed to support Ryan (2017). The tests were conducted upon
a mixed sample of 106 amateur and professional photographers, twenty of whom also
participated in an unstructured intraspective interview. The testing and interviews establish:
(i) that ten constructs satisfactorily enclose the concept of expertise for this sample of
photographers in this domain, (ii) that partitioning on the basis of inter alia gender,
photographic qualification and genre produce significant differences in the engagement and
conjugation of the ten constructs in the intuitive moment of capture or assessment, and (iii)
that ‘style’ or ‘voice’ can be explained as an emergent property derived from the complexities
of the exercise of expert, intuitive, photographic judgement. I conclude that, notwithstanding
the sample size, there are grounds for strong confidence that the testing is of high external
validity as a tool for individual analysis and modest confidence that it is also valid for the
partitioned sub-groups