1,247 research outputs found
All or Nothing at All
We continue a study of unconditionally secure all-or-nothing transforms
(AONT) begun in \cite{St}. An AONT is a bijective mapping that constructs s
outputs from s inputs. We consider the security of t inputs, when s-t outputs
are known. Previous work concerned the case t=1; here we consider the problem
for general t, focussing on the case t=2. We investigate constructions of
binary matrices for which the desired properties hold with the maximum
probability. Upper bounds on these probabilities are obtained via a quadratic
programming approach, while lower bounds can be obtained from combinatorial
constructions based on symmetric BIBDs and cyclotomy. We also report some
results on exhaustive searches and random constructions for small values of s.Comment: 23 page
Long MDS Codes for Optimal Repair Bandwidth
MDS codes are erasure-correcting codes that can
correct the maximum number of erasures given the number of
redundancy or parity symbols. If an MDS code has r parities
and no more than r erasures occur, then by transmitting all
the remaining data in the code one can recover the original
information. However, it was shown that in order to recover a
single symbol erasure, only a fraction of 1/r of the information
needs to be transmitted. This fraction is called the repair
bandwidth (fraction). Explicit code constructions were given in
previous works. If we view each symbol in the code as a vector
or a column, then the code forms a 2D array and such codes
are especially widely used in storage systems. In this paper, we
ask the following question: given the length of the column l, can
we construct high-rate MDS array codes with optimal repair
bandwidth of 1/r, whose code length is as long as possible? In
this paper, we give code constructions such that the code length
is (r + 1)log_r l
CSI Feedback Reduction for MIMO Interference Alignment
Interference alignment (IA) is a linear precoding strategy that can achieve
optimal capacity scaling at high SNR in interference networks. Most of the
existing IA designs require full channel state information (CSI) at the
transmitters, which induces a huge CSI signaling cost. Hence it is desirable to
improve the feedback efficiency for IA and in this paper, we propose a novel IA
scheme with a significantly reduced CSI feedback. To quantify the CSI feedback
cost, we introduce a novel metric, namely the feedback dimension. This metric
serves as a first-order measurement of CSI feedback overhead. Due to the
partial CSI feedback constraint, conventional IA schemes can not be applied and
hence, we develop a novel IA precoder / decorrelator design and establish new
IA feasibility conditions. Via dynamic feedback profile design, the proposed IA
scheme can also achieve a flexible tradeoff between the degree of freedom (DoF)
requirements for data streams, the antenna resources and the CSI feedback cost.
We show by analysis and simulations that the proposed scheme achieves
substantial reductions of CSI feedback overhead under the same DoF requirement
in MIMO interference networks.Comment: 30 pages, 7 figures, accepted for publication by IEEE transactions on
signal processing in June, 201
Invertible completions of partial operator matrices: The nonsymmetric case
AbstractWe consider nonsymmetric partial operator matrices R whose directed graphs belong to a certain class and for which certain key, fully specified principal submatrices are invertible. Under these circumstances, we prove the existence of a unique invertible completion F of R such that (F-1)ij is block zero whenever Rij is unspecified. In this way, the existing results of Johnson and Lundquist are generalized to the nonsymmetric case
Graphical Markov models, unifying results and their interpretation
Graphical Markov models combine conditional independence constraints with
graphical representations of stepwise data generating processes.The models
started to be formulated about 40 years ago and vigorous development is
ongoing. Longitudinal observational studies as well as intervention studies are
best modeled via a subclass called regression graph models and, especially
traceable regressions. Regression graphs include two types of undirected graph
and directed acyclic graphs in ordered sequences of joint responses. Response
components may correspond to discrete or continuous random variables and may
depend exclusively on variables which have been generated earlier. These
aspects are essential when causal hypothesis are the motivation for the
planning of empirical studies.
To turn the graphs into useful tools for tracing developmental pathways and
for predicting structure in alternative models, the generated distributions
have to mimic some properties of joint Gaussian distributions. Here, relevant
results concerning these aspects are spelled out and illustrated by examples.
With regression graph models, it becomes feasible, for the first time, to
derive structural effects of (1) ignoring some of the variables, of (2)
selecting subpopulations via fixed levels of some other variables or of (3)
changing the order in which the variables might get generated. Thus, the most
important future applications of these models will aim at the best possible
integration of knowledge from related studies.Comment: 34 Pages, 11 figures, 1 tabl
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