16 research outputs found
On Distributed Storage Codes
Distributed storage systems are studied. The interest in such system has become relatively wide due to the increasing amount of information needed to be stored in data centers or different kinds of cloud systems. There are many kinds of solutions for storing the information into distributed devices regarding the needs of the system designer. This thesis studies the questions of designing such storage systems and also fundamental limits of such systems. Namely, the subjects of interest of this thesis include heterogeneous distributed storage systems, distributed storage systems with the exact repair property, and locally repairable codes. For distributed storage systems with either functional or exact repair, capacity results are proved. In the case of locally repairable codes, the minimum distance is studied.
Constructions for exact-repairing codes between minimum bandwidth regeneration (MBR) and minimum storage regeneration (MSR) points are given. These codes exceed the time-sharing line of the extremal points in many cases. Other properties of exact-regenerating codes are also studied. For the heterogeneous setup, the main result is that the capacity of such systems is always smaller than or equal to the capacity of a homogeneous system with symmetric repair with average node size and average repair bandwidth. A randomized construction for a locally repairable code with good minimum distance is given. It is shown that a random linear code of certain natural type has a good minimum distance with high probability. Other properties of locally repairable codes are also studied.Siirretty Doriast
Constructions of Optimal and Almost Optimal Locally Repairable Codes
Constructions of optimal locally repairable codes (LRCs) in the case of
and over small finite fields were stated as open problems for
LRCs in [I. Tamo \emph{et al.}, "Optimal locally repairable codes and
connections to matroid theory", \emph{2013 IEEE ISIT}]. In this paper, these
problems are studied by constructing almost optimal linear LRCs, which are
proven to be optimal for certain parameters, including cases for which . More precisely, linear codes for given length, dimension, and
all-symbol locality are constructed with almost optimal minimum distance.
`Almost optimal' refers to the fact that their minimum distance differs by at
most one from the optimal value given by a known bound for LRCs. In addition to
these linear LRCs, optimal LRCs which do not require a large field are
constructed for certain classes of parameters.Comment: 5 pages, conferenc
Exact-Regenerating Codes between MBR and MSR Points
In this paper we study distributed storage systems with exact repair. We give
a construction for regenerating codes between the minimum storage regenerating
(MSR) and the minimum bandwidth regenerating (MBR) points and show that in the
case that the parameters n, k, and d are close to each other our constructions
are close to optimal when comparing to the known capacity when only functional
repair is required. We do this by showing that when the distances of the
parameters n, k, and d are fixed but the actual values approach to infinity,
the fraction of the performance of our codes with exact repair and the known
capacity of codes with functional repair approaches to one.Comment: 5 pages, 2 figures, submitted to ITW 201
Construction of MIMO MAC Codes Achieving the Pigeon Hole Bound
This paper provides a general construction method for multiple-input
multiple-output multiple access channel codes (MIMO MAC codes) that have so
called generalized full rank property. The achieved constructions give a
positive answer to the question whether it is generally possible to reach the
so called pigeon hole bound, that is an upper bound for the decay of
determinants of MIMO-MAC channel codes.Comment: 5 pages, nofigures, conferenc
On the Combinatorics of Locally Repairable Codes via Matroid Theory
This paper provides a link between matroid theory and locally repairable
codes (LRCs) that are either linear or more generally almost affine. Using this
link, new results on both LRCs and matroid theory are derived. The parameters
of LRCs are generalized to matroids, and the matroid
analogue of the generalized Singleton bound in [P. Gopalan et al., "On the
locality of codeword symbols," IEEE Trans. Inf. Theory] for linear LRCs is
given for matroids. It is shown that the given bound is not tight for certain
classes of parameters, implying a nonexistence result for the corresponding
locally repairable almost affine codes, that are coined perfect in this paper.
Constructions of classes of matroids with a large span of the parameters
and the corresponding local repair sets are given. Using
these matroid constructions, new LRCs are constructed with prescribed
parameters. The existence results on linear LRCs and the nonexistence results
on almost affine LRCs given in this paper strengthen the nonexistence and
existence results on perfect linear LRCs given in [W. Song et al., "Optimal
locally repairable codes," IEEE J. Sel. Areas Comm.].Comment: 48 pages. Submitted for publication. In this version: The text has
been edited to improve the readability. Parameter d for matroids is now
defined by the use of the rank function instead of the dual matroid. Typos
are corrected. Section III is divided into two parts, and some numberings of
theorems etc. have been change
Capacity and Security of Heterogeneous Distributed Storage Systems
We study the capacity of heterogeneous distributed storage systems under
repair dynamics. Examples of these systems include peer-to-peer storage clouds,
wireless, and Internet caching systems. Nodes in a heterogeneous system can
have different storage capacities and different repair bandwidths. We give
lower and upper bounds on the system capacity. These bounds depend on either
the average resources per node, or on a detailed knowledge of the node
characteristics. Moreover, we study the case in which nodes may be compromised
by an eavesdropper, and give bounds on the system secrecy capacity. One
implication of our results is that symmetric repair maximizes the capacity of a
homogeneous system, which justifies the model widely used in the literature.Comment: 7 pages, 2 figure