1,096 research outputs found
On asymptotically good ramp secret sharing schemes
Asymptotically good sequences of linear ramp secret sharing schemes have been
intensively studied by Cramer et al. in terms of sequences of pairs of nested
algebraic geometric codes. In those works the focus is on full privacy and full
reconstruction. In this paper we analyze additional parameters describing the
asymptotic behavior of partial information leakage and possibly also partial
reconstruction giving a more complete picture of the access structure for
sequences of linear ramp secret sharing schemes. Our study involves a detailed
treatment of the (relative) generalized Hamming weights of the considered
codes
Constructions of Rank Modulation Codes
Rank modulation is a way of encoding information to correct errors in flash
memory devices as well as impulse noise in transmission lines. Modeling rank
modulation involves construction of packings of the space of permutations
equipped with the Kendall tau distance.
We present several general constructions of codes in permutations that cover
a broad range of code parameters. In particular, we show a number of ways in
which conventional error-correcting codes can be modified to correct errors in
the Kendall space. Codes that we construct afford simple encoding and decoding
algorithms of essentially the same complexity as required to correct errors in
the Hamming metric. For instance, from binary BCH codes we obtain codes
correcting Kendall errors in memory cells that support the order of
messages, for any constant We also construct
families of codes that correct a number of errors that grows with at
varying rates, from to . One of our constructions
gives rise to a family of rank modulation codes for which the trade-off between
the number of messages and the number of correctable Kendall errors approaches
the optimal scaling rate. Finally, we list a number of possibilities for
constructing codes of finite length, and give examples of rank modulation codes
with specific parameters.Comment: Submitted to IEEE Transactions on Information Theor
Asymptotic information leakage under one-try attacks
We study the asymptotic behaviour of (a) information leakage and (b) adversary’s error probability in information hiding systems modelled as noisy channels. Specifically, we assume the attacker can make a single guess after observing n independent executions of the system, throughout which the secret information is kept fixed. We show that the asymptotic behaviour of quantities (a) and (b) can be determined in a simple way from the channel matrix. Moreover, simple and tight bounds on them as functions of n show that the convergence is exponential. We also discuss feasible methods to evaluate the rate of convergence. Our results cover both the Bayesian case, where a prior probability distribution on the secrets is assumed known to the attacker, and the maximum-likelihood case, where the attacker does not know such distribution. In the Bayesian case, we identify the distributions that maximize the leakage. We consider both the min-entropy setting studied by Smith and the additive form recently proposed by Braun et al., and show the two forms do agree asymptotically. Next, we extend these results to a more sophisticated eavesdropping scenario, where the attacker can perform a (noisy) observation at each state of the computation and the systems are modelled as hidden Markov models
Group Analysis of Self-organizing Maps based on Functional MRI using Restricted Frechet Means
Studies of functional MRI data are increasingly concerned with the estimation
of differences in spatio-temporal networks across groups of subjects or
experimental conditions. Unsupervised clustering and independent component
analysis (ICA) have been used to identify such spatio-temporal networks. While
these approaches have been useful for estimating these networks at the
subject-level, comparisons over groups or experimental conditions require
further methodological development. In this paper, we tackle this problem by
showing how self-organizing maps (SOMs) can be compared within a Frechean
inferential framework. Here, we summarize the mean SOM in each group as a
Frechet mean with respect to a metric on the space of SOMs. We consider the use
of different metrics, and introduce two extensions of the classical sum of
minimum distance (SMD) between two SOMs, which take into account the
spatio-temporal pattern of the fMRI data. The validity of these methods is
illustrated on synthetic data. Through these simulations, we show that the
three metrics of interest behave as expected, in the sense that the ones
capturing temporal, spatial and spatio-temporal aspects of the SOMs are more
likely to reach significance under simulated scenarios characterized by
temporal, spatial and spatio-temporal differences, respectively. In addition, a
re-analysis of a classical experiment on visually-triggered emotions
demonstrates the usefulness of this methodology. In this study, the
multivariate functional patterns typical of the subjects exposed to pleasant
and unpleasant stimuli are found to be more similar than the ones of the
subjects exposed to emotionally neutral stimuli. Taken together, these results
indicate that our proposed methods can cast new light on existing data by
adopting a global analytical perspective on functional MRI paradigms.Comment: 23 pages, 5 figures, 4 tables. Submitted to Neuroimag
Application of Permutation Group Theory in Reversible Logic Synthesis
The paper discusses various applications of permutation group theory in the
synthesis of reversible logic circuits consisting of Toffoli gates with
negative control lines. An asymptotically optimal synthesis algorithm for
circuits consisting of gates from the NCT library is described. An algorithm
for gate complexity reduction, based on equivalent replacements of gates
compositions, is introduced. A new approach for combining a group-theory-based
synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is
described. Experimental results are presented to show that the proposed
synthesis techniques allow a reduction in input lines count, gate complexity or
quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016
conferenc
Bounds on the size of codes
In this dissertation we determine new bounds and properties of codes in
three different finite metric spaces, namely the ordered Hamming space, the
binary Hamming space, and the Johnson space.
The ordered Hamming space is a generalization of the Hamming space that
arises in several different problems of coding theory and numerical
integration. Structural properties of this space are well described in the
framework of Delsarte's theory of association schemes. Relying on this
theory, we perform a detailed study of polynomials related to the ordered
Hamming space and derive new asymptotic bounds on the size of codes in this
space which improve upon the estimates known earlier.
A related project concerns linear codes in the ordered Hamming space. We
define and analyze a class of near-optimal codes, called near-Maximum
Distance Separable codes. We determine the weight distribution and provide
constructions of such codes. Codes in the ordered Hamming space are dual to
a certain type of point distributions in the unit cube used in numerical
integration. We show that near-Maximum Distance Separable codes are
equivalently represented as certain near-optimal point distributions.
In the third part of our study we derive a new upper bound on the size of
a family of subsets of a finite set with restricted pairwise intersections,
which improves upon the well-known Frankl-Wilson upper bound. The new bound
is obtained by analyzing a refinement of the association scheme of the
Hamming space (the Terwilliger algebra) and intertwining functions of the
symmetric group.
Finally, in the fourth set of problems we determine new estimates on the
size of codes in the Johnson space. We also suggest a new approach to the
derivation of the well-known Johnson bound for codes in this space. Our
estimates are often valid in the region where the Johnson bound is vacuous.
We show that these methods are also applicable to the case of multiple
packings in the Hamming space (list-decodable codes). In this context we
recover the best known estimate on the size of list-decodable codes in
a new way
- …