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0903.1150
|
Stochastic Constraint Programming: A Scenario-Based Approach
|
cs.AI
|
To model combinatorial decision problems involving uncertainty and
probability, we introduce scenario based stochastic constraint programming.
Stochastic constraint programs contain both decision variables, which we can
set, and stochastic variables, which follow a discrete probability
distribution. We provide a semantics for stochastic constraint programs based
on scenario trees. Using this semantics, we can compile stochastic constraint
programs down into conventional (non-stochastic) constraint programs. This
allows us to exploit the full power of existing constraint solvers. We have
implemented this framework for decision making under uncertainty in stochastic
OPL, a language which is based on the OPL constraint modelling language
[Hentenryck et al., 1999]. To illustrate the potential of this framework, we
model a wide range of problems in areas as diverse as portfolio
diversification, agricultural planning and production/inventory management.
|
0903.1152
|
Stochastic Constraint Programming
|
cs.AI
|
To model combinatorial decision problems involving uncertainty and
probability, we introduce stochastic constraint programming. Stochastic
constraint programs contain both decision variables (which we can set) and
stochastic variables (which follow a probability distribution). They combine
together the best features of traditional constraint satisfaction, stochastic
integer programming, and stochastic satisfiability. We give a semantics for
stochastic constraint programs, and propose a number of complete algorithms and
approximation procedures. Finally, we discuss a number of extensions of
stochastic constraint programming to relax various assumptions like the
independence between stochastic variables, and compare with other approaches
for decision making under uncertainty.
|
0903.1157
|
Information Propagation Speed in Mobile and Delay Tolerant Networks
|
cs.IT cs.NI math.IT
|
The goal of this paper is to increase our understanding of the fundamental
performance limits of mobile and Delay Tolerant Networks (DTNs), where
end-to-end multi-hop paths may not exist and communication routes may only be
available through time and mobility. We use analytical tools to derive generic
theoretical upper bounds for the information propagation speed in large scale
mobile and intermittently connected networks. In other words, we upper-bound
the optimal performance, in terms of delay, that can be achieved using any
routing algorithm. We then show how our analysis can be applied to specific
mobility and graph models to obtain specific analytical estimates. In
particular, in two-dimensional networks, when nodes move at a maximum speed $v$
and their density $\nu$ is small (the network is sparse and surely
disconnected), we prove that the information propagation speed is upper bounded
by ($1+O(\nu^2))v$ in the random way-point model, while it is upper bounded by
$O(\sqrt{\nu v} v)$ for other mobility models (random walk, Brownian motion).
We also present simulations that confirm the validity of the bounds in these
scenarios. Finally, we generalize our results to one-dimensional and
three-dimensional networks.
|
0903.1183
|
Fast Cycle Frequency Domain Feature Detection for Cognitive Radio
Systems
|
cs.IT math.IT
|
In cognitive radio systems, one of the main requirements is to detect the
presence of the primary users' transmission, especially in weak signal cases.
Cyclostationary detection is always used to solve weak signal detection,
however, the computational complexity prevents it from wide usage. In this
paper, a fast cycle frequency domain feature detection algorithm has been
proposed, in which only feature frequency with significant cyclic signature is
considered for a certain modulation mode. Simulation results show that the
proposed algorithm has remarkable performance gain than energy detection when
supporting real-time detection with low computational complexity.
|
0903.1337
|
Efficient quantization for average consensus
|
math.OC cs.SY
|
This paper presents an algorithm which solves exponentially fast the average
consensus problem on strongly connected network of digital links. The algorithm
is based on an efficient zooming-in/zooming-out quantization scheme.
|
0903.1379
|
Optimum Pilot Overhead in Wireless Communication: A Unified Treatment of
Continuous and Block-Fading Channels
|
cs.IT math.IT
|
The optimization of the pilot overhead in single-user wireless fading
channels is investigated, and the dependence of this overhead on various system
parameters of interest (e.g., fading rate, signal-to-noise ratio) is
quantified. The achievable pilot-based spectral efficiency is expanded with
respect to the fading rate about the no-fading point, which leads to an
accurate order expansion for the pilot overhead. This expansion identifies that
the pilot overhead, as well as the spectral efficiency penalty with respect to
a reference system with genie-aided CSI (channel state information) at the
receiver, depend on the square root of the normalized Doppler frequency.
Furthermore, it is shown that the widely-used block fading model is only a
special case of more accurate continuous fading models in terms of the
achievable pilot-based spectral efficiency, and that the overhead optimization
for multiantenna systems is effectively the same as for single-antenna systems
with the normalized Doppler frequency multiplied by the number of transmit
antennas.
|
0903.1389
|
A Linear Programming Driven Genetic Algorithm for Meta-Scheduling on
Utility Grids
|
cs.DC cs.NE
|
The user-level brokers in grids consider individual application QoS
requirements and minimize their cost without considering demands from other
users. This results in contention for resources and sub-optimal schedules.
Meta-scheduling in grids aims to address this scheduling problem, which is NP
hard due to its combinatorial nature. Thus, many heuristic-based solutions
using Genetic Algorithm (GA) have been proposed, apart from traditional
algorithms such as Greedy and FCFS.
We propose a Linear Programming/Integer Programming model (LP/IP) for
scheduling these applications to multiple resources. We also propose a novel
algorithm LPGA (Linear programming driven Genetic Algorithm) which combines the
capabilities of LP and GA. The aim of this algorithm is to obtain the best
metaschedule for utility grids which minimize combined cost of all users in a
coordinated manner. Simulation results show that our proposed integrated
algorithm offers the best schedule having the minimum processing cost with
negligible time overhead.
|
0903.1443
|
Dynamic Updating for L1 Minimization
|
cs.IT math.IT
|
The theory of compressive sensing (CS) suggests that under certain
conditions, a sparse signal can be recovered from a small number of linear
incoherent measurements. An effective class of reconstruction algorithms
involve solving a convex optimization program that balances the L1 norm of the
solution against a data fidelity term. Tremendous progress has been made in
recent years on algorithms for solving these L1 minimization programs. These
algorithms, however, are for the most part static: they focus on finding the
solution for a fixed set of measurements.
In this paper, we will discuss "dynamic algorithms" for solving L1
minimization programs for streaming sets of measurements. We consider cases
where the underlying signal changes slightly between measurements, and where
new measurements of a fixed signal are sequentially added to the system. We
develop algorithms to quickly update the solution of several different types of
L1 optimization problems whenever these changes occur, thus avoiding having to
solve a new optimization problem from scratch. Our proposed schemes are based
on homotopy continuation, which breaks down the solution update in a systematic
and efficient way into a small number of linear steps. Each step consists of a
low-rank update and a small number of matrix-vector multiplications -- very
much like recursive least squares. Our investigation also includes dynamic
updating schemes for L1 decoding problems, where an arbitrary signal is to be
recovered from redundant coded measurements which have been corrupted by sparse
errors.
|
0903.1448
|
The Digital Restoration of Da Vinci's Sketches
|
cs.CV cs.GR
|
A sketch, found in one of Leonardo da Vinci's notebooks and covered by the
written notes of this genius, has been recently restored. The restoration
reveals a possible self-portrait of the artist, drawn when he was young. Here,
we discuss the discovery of this self-portrait and the procedure used for
restoration. Actually, this is a restoration performed on the digital image of
the sketch, a procedure that can easily extended and applied to ancient
documents for studies of art and palaeography.
|
0903.1451
|
Definition of evidence fusion rules on the basis of Referee Functions
|
cs.AI math.PR stat.AP
|
This chapter defines a new concept and framework for constructing fusion
rules for evidences. This framework is based on a referee function, which does
a decisional arbitrament conditionally to basic decisions provided by the
several sources of information. A simple sampling method is derived from this
framework. The purpose of this sampling approach is to avoid the combinatorics
which are inherent to the definition of fusion rules of evidences. This
definition of the fusion rule by the means of a sampling process makes possible
the construction of several rules on the basis of an algorithmic implementation
of the referee function, instead of a mathematical formulation. Incidentally,
it is a versatile and intuitive way for defining rules. The framework is
implemented for various well known evidence rules. On the basis of this
framework, new rules for combining evidences are proposed, which takes into
account a consensual evaluation of the sources of information.
|
0903.1476
|
The Power of Convex Relaxation: Near-Optimal Matrix Completion
|
cs.IT math.IT
|
This paper is concerned with the problem of recovering an unknown matrix from
a small fraction of its entries. This is known as the matrix completion
problem, and comes up in a great number of applications, including the famous
Netflix Prize and other similar questions in collaborative filtering. In
general, accurate recovery of a matrix from a small number of entries is
impossible; but the knowledge that the unknown matrix has low rank radically
changes this premise, making the search for solutions meaningful.
This paper presents optimality results quantifying the minimum number of
entries needed to recover a matrix of rank r exactly by any method whatsoever
(the information theoretic limit). More importantly, the paper shows that,
under certain incoherence assumptions on the singular vectors of the matrix,
recovery is possible by solving a convenient convex program as soon as the
number of entries is on the order of the information theoretic limit (up to
logarithmic factors). This convex program simply finds, among all matrices
consistent with the observed entries, that with minimum nuclear norm. As an
example, we show that on the order of nr log(n) samples are needed to recover a
random n x n matrix of rank r by any method, and to be sure, nuclear norm
minimization succeeds as soon as the number of entries is of the form nr
polylog(n).
|
0903.1484
|
Physics of the Shannon Limits
|
cs.IT math.IT
|
We provide a simple physical interpretation, in the context of the second law
of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality,
which is also equivalent to the log-sum inequality), asserting that the
relative entropy between two probability distributions cannot be negative.
Since this inequality stands at the basis of the data processing theorem (DPT),
and the DPT in turn is at the heart of most, if not all, proofs of converse
theorems in Shannon theory, it is observed that conceptually, the roots of
fundamental limits of Information Theory can actually be attributed to the laws
of physics, in particular, to the second law of thermodynamics, and at least
indirectly, also to the law of energy conservation. By the same token, in the
other direction: one can view the second law as stemming from
information-theoretic principles.
|
0903.1496
|
How Much Information can One Get from a Wireless Ad Hoc Sensor Network
over a Correlated Random Field?
|
cs.IT math.IT
|
New large deviations results that characterize the asymptotic information
rates for general $d$-dimensional ($d$-D) stationary Gaussian fields are
obtained. By applying the general results to sensor nodes on a two-dimensional
(2-D) lattice, the asymptotic behavior of ad hoc sensor networks deployed over
correlated random fields for statistical inference is investigated. Under a 2-D
hidden Gauss-Markov random field model with symmetric first order conditional
autoregression and the assumption of no in-network data fusion, the behavior of
the total obtainable information [nats] and energy efficiency [nats/J] defined
as the ratio of total gathered information to the required energy is obtained
as the coverage area, node density and energy vary. When the sensor node
density is fixed, the energy efficiency decreases to zero with rate
$\Theta({area}^{-1/2})$ and the per-node information under fixed per-node
energy also diminishes to zero with rate $O(N_t^{-1/3})$ as the number $N_t$ of
network nodes increases by increasing the coverage area. As the sensor spacing
$d_n$ increases, the per-node information converges to its limit $D$ with rate
$D-\sqrt{d_n}e^{-\alpha d_n}$ for a given diffusion rate $\alpha$. When the
coverage area is fixed and the node density increases, the per-node information
is inversely proportional to the node density. As the total energy $E_t$
consumed in the network increases, the total information obtainable from the
network is given by $O(\log E_t)$ for the fixed node density and fixed coverage
case and by $\Theta (E_t^{2/3})$ for the fixed per-node sensing energy and
fixed density and increasing coverage case.
|
0903.1502
|
Low-Density Graph Codes for slow fading Relay Channels
|
cs.IT math.IT
|
We study Low-Density Parity-Check (LDPC) codes with iterative decoding on
block-fading (BF) Relay Channels. We consider two users that employ coded
cooperation, a variant of decode-and-forward with a smaller outage probability
than the latter. An outage probability analysis for discrete constellations
shows that full diversity can be achieved only when the coding rate does not
exceed a maximum value that depends on the level of cooperation. We derive a
new code structure by extending the previously published full-diversity
root-LDPC code, designed for the BF point-to-point channel, to exhibit a
rate-compatibility property which is necessary for coded cooperation. We
estimate the asymptotic performance through a new density evolution analysis
and the word error rate performance is determined for finite length codes. We
show that our code construction exhibits near-outage limit performance for all
block lengths and for a range of coding rates up to 0.5, which is the highest
possible coding rate for two cooperating users.
|
0903.1556
|
Enumerative Encoding in the Grassmannian Space
|
cs.IT math.IT
|
Codes in the Grassmannian space have found recently application in network
coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally
an essential role in solving coding problems in the Grassmannian, and in
particular in encoding subspaces of the Grassmannian. Different representations
of subspaces in the Grassmannian are presented. We use two of these
representations for enumerative encoding of the Grassmannian. One enumerative
encoding is based on Ferrers diagrams representation of subspaces; and another
is based on identifying vector and reduced row echelon form representation of
subspaces. A third method which combine the previous two is more efficient than
the other two enumerative encodings.
|
0903.1588
|
On the Growth Rate of the Weight Distribution of Irregular
Doubly-Generalized LDPC Codes
|
cs.IT math.IT
|
In this paper, an expression for the asymptotic growth rate of the number of
small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC)
codes is derived. The expression is compact and generalizes existing results
for LDPC and generalized LDPC (GLDPC) codes. Ensembles with check or variable
node minimum distance greater than 2 are shown to be have good growth rate
behavior, while for other ensembles a fundamental parameter is identified which
discriminates between an asymptotically small and an asymptotically large
expected number of small linear-weight codewords. Also, in the latter case it
is shown that the growth rate depends only on the check and variable nodes with
minimum distance 2. An important connection between this new result and the
stability condition of D-GLDPC codes over the BEC is highlighted. Such a
connection, previously observed for LDPC and GLDPC codes, is now extended to
the case of D-GLDPC codes. Finally, it is shown that the analysis may be
extended to include the growth rate of the stopping set size distribution of
irregular D-GLDPC codes.
|
0903.1621
|
Susceptibility Propagation for Constraint Satisfaction Problems
|
cond-mat.dis-nn cond-mat.stat-mech cs.IT math.IT
|
We study the susceptibility propagation, a message-passing algorithm to
compute correlation functions. It is applied to constraint satisfaction
problems and its accuracy is examined. As a heuristic method to find a
satisfying assignment, we propose susceptibility-guided decimation where
correlations among the variables play an important role. We apply this novel
decimation to locked occupation problems, a class of hard constraint
satisfaction problems exhibited recently. It is shown that the present method
performs better than the standard belief-guided decimation.
|
0903.1624
|
Instanton-based Techniques for Analysis and Reduction of Error Floors of
LDPC Codes
|
cs.IT math.IT
|
We describe a family of instanton-based optimization methods developed
recently for the analysis of the error floors of low-density parity-check
(LDPC) codes. Instantons are the most probable configurations of the channel
noise which result in decoding failures. We show that the general idea and the
respective optimization technique are applicable broadly to a variety of
channels, discrete or continuous, and variety of sub-optimal decoders.
Specifically, we consider: iterative belief propagation (BP) decoders, Gallager
type decoders, and linear programming (LP) decoders performing over the
additive white Gaussian noise channel (AWGNC) and the binary symmetric channel
(BSC).
The instanton analysis suggests that the underlying topological structures of
the most probable instanton of the same code but different channels and
decoders are related to each other. Armed with this understanding of the
graphical structure of the instanton and its relation to the decoding failures,
we suggest a method to construct codes whose Tanner graphs are free of these
structures, and thus have less significant error floors.
|
0903.1659
|
Heuristic Reasoning on Graph and Game Complexity of Sudoku
|
cs.AI cs.GT cs.SC
|
The Sudoku puzzle has achieved worldwide popularity recently, and attracted
great attention of the computational intelligence community. Sudoku is always
considered as Satisfiability Problem or Constraint Satisfaction Problem. In
this paper, we propose to focus on the essential graph structure underlying the
Sudoku puzzle. First, we formalize Sudoku as a graph. Then a solving algorithm
based on heuristic reasoning on the graph is proposed. The related r-Reduction
theorem, inference theorem and their properties are proved, providing the
formal basis for developments of Sudoku solving systems. In order to evaluate
the difficulty levels of puzzles, a quantitative measurement of the complexity
level of Sudoku puzzles based on the graph structure and information theory is
proposed. Experimental results show that all the puzzles can be solved fast
using the proposed heuristic reasoning, and that the proposed game complexity
metrics can discriminate difficulty levels of puzzles perfectly.
|
0903.1675
|
A Simple Cooperative Transmission Protocol for Energy-Efficient
Broadcasting Over Multi-Hop Wireless Networks
|
cs.NI cs.IT math.IT
|
This paper analyzes a broadcasting technique for wireless multi-hop sensor
networks that uses a form of cooperative diversity called opportunistic large
arrays (OLAs). We propose a method for autonomous scheduling of the nodes,
which limits the nodes that relay and saves as much as 32% of the transmit
energy compared to other broadcast approaches, without requiring Global
Positioning System (GPS), individual node addressing, or inter-node
interaction. This energy-saving is a result of cross-layer interaction, in the
sense that the Medium Access Control (MAC) and routing functions are partially
executed in the Physical (PHY) layer. Our proposed method is called OLA with a
transmission threshold (OLA-T), where a node compares its received power to a
threshold to decide if it should forward. We also investigate OLA with variable
threshold (OLA-VT), which optimizes the thresholds as a function of level.
OLA-T and OLA-VT are compared with OLA broadcasting without a transmission
threshold, each in their minimum energy configuration, using an analytical
method under the orthogonal and continuum assumptions. The trade-off between
the number of OLA levels (or hops) required to achieve successful network
broadcast and transmission energy saved is investigated. The results based on
the analytical assumptions are confirmed with Monte Carlo simulations.
|
0903.1680
|
Faceted Exploration of Emerging Resource Spaces
|
cs.DB cs.DL cs.HC
|
Humans have the ability to regcognize the real world from different facets.
Faceted exploration is a mechanism for browsing and understanding large-scale
resources in information network by multiple facets. This paper proposes an
Emerging Resource Space Model, whose schema is a partially ordered set of
concepts with subclassOf relation and each resource is categorized by multiple
concepts. Emering Resource Space (ERS) is a class of resources characterized by
a concept set. ERSes compose a lattice (ERSL) via concept association. A series
of exploration operations is proposed to guide users to explore through ERSL
with more demanding and richer semantics than current faceted navigation. To
fulfill instant response during faceted exploration, we devise an efficient
algorithm for mining and indexing ERSL. The proposed model can effectively
support faceted exploration in various applications from personal information
management to large-scale information sharing.
|
0903.1716
|
Improved Lower Bounds on Capacities of Symmetric 2-Dimensional
Constraints using Rayleigh Quotients
|
cs.IT cs.DM math.CO math.IT
|
A method for computing lower bounds on capacities of 2-dimensional
constraints having a symmetric presentation in either the horizontal or the
vertical direction is presented. The method is a generalization of the method
of Calkin and Wilf (SIAM J. Discrete Math., 1998). Previous best lower bounds
on capacities of certain constraints are improved using the method. It is also
shown how this method, as well as their method for computing upper bounds on
the capacity, can be applied to constraints which are not of finite-type.
Additionally, capacities of 2 families of multi-dimensional constraints are
given exactly.
|
0903.1724
|
Folding, Tiling, and Multidimensional Coding
|
cs.IT math.IT
|
Folding a sequence $S$ into a multidimensional box is a method that is used
to construct multidimensional codes. The well known operation of folding is
generalized in a way that the sequence $S$ can be folded into various shapes.
The new definition of folding is based on lattice tiling and a direction in the
$D$-dimensional grid. There are potentially $\frac{3^D-1}{2}$ different folding
operations. Necessary and sufficient conditions that a lattice combined with a
direction define a folding are given. The immediate and most impressive
application is some new lower bounds on the number of dots in two-dimensional
synchronization patterns. This can be also generalized for multidimensional
synchronization patterns. We show how folding can be used to construct
multidimensional error-correcting codes and to generate multidimensional
pseudo-random arrays.
|
0903.1765
|
A Lower Bound on Arbitrary $f$--Divergences in Terms of the Total
Variation
|
math.PR cs.IT math.IT math.ST stat.TH
|
An important tool to quantify the likeness of two probability measures are
f-divergences, which have seen widespread application in statistics and
information theory. An example is the total variation, which plays an
exceptional role among the f-divergences. It is shown that every f-divergence
is bounded from below by a monotonous function of the total variation. Under
appropriate regularity conditions, this function is shown to be monotonous.
Remark: The proof of the main proposition is relatively easy, whence it is
highly likely that the result is known. The author would be very grateful for
any information regarding references or related work.
|
0903.1788
|
The Role of Tag Suggestions in Folksonomies
|
cs.HC cs.IR
|
Most tagging systems support the user in the tag selection process by
providing tag suggestions, or recommendations, based on a popularity
measurement of tags other users provided when tagging the same resource. In
this paper we investigate the influence of tag suggestions on the emergence of
power law distributions as a result of collaborative tag behavior. Although
previous research has already shown that power laws emerge in tagging systems,
the cause of why power law distributions emerge is not understood empirically.
The majority of theories and mathematical models of tagging found in the
literature assume that the emergence of power laws in tagging systems is mainly
driven by the imitation behavior of users when observing tag suggestions
provided by the user interface of the tagging system. This imitation behavior
leads to a feedback loop in which some tags are reinforced and get more popular
which is also known as the `rich get richer' or a preferential attachment
model. We present experimental results that show that the power law
distribution forms regardless of whether or not tag suggestions are presented
to the users. Furthermore, we show that the real effect of tag suggestions is
rather subtle; the resulting power law distribution is `compressed' if tag
suggestions are given to the user, resulting in a shorter long tail and a
`compressed' top of the power law distribution. The consequences of this
experiment show that tag suggestions by themselves do not account for the
formation of power law distributions in tagging systems.
|
0903.1820
|
On the Capacity of Free-Space Optical Intensity Channels
|
cs.IT math.IT
|
New upper and lower bounds are presented on the capacity of the free-space
optical intensity channel. This channel is characterized by inputs that are
nonnegative (representing the transmitted optical intensity) and by outputs
that are corrupted by additive white Gaussian noise (because in free space the
disturbances arise from many independent sources). Due to battery and safety
reasons the inputs are simultaneously constrained in both their average and
peak power. For a fixed ratio of the average power to the peak power the
difference between the upper and the lower bounds tends to zero as the average
power tends to infinity, and the ratio of the upper and lower bounds tends to
one as the average power tends to zero. The case where only an average-power
constraint is imposed on the input is treated separately. In this case, the
difference of the upper and lower bound tends to 0 as the average power tends
to infinity, and their ratio tends to a constant as the power tends to zero.
|
0903.1842
|
Decay of Correlations for Sparse Graph Error Correcting Codes
|
cs.IT math.IT
|
The subject of this paper is transmission over a general class of
binary-input memoryless symmetric channels using error correcting codes based
on sparse graphs, namely low-density generator-matrix and low-density
parity-check codes. The optimal (or ideal) decoder based on the posterior
measure over the code bits, and its relationship to the sub-optimal belief
propagation decoder, are investigated. We consider the correlation (or
covariance) between two codebits, averaged over the noise realizations, as a
function of the graph distance, for the optimal decoder. Our main result is
that this correlation decays exponentially fast for fixed general low-density
generator-matrix codes and high enough noise parameter, and also for fixed
general low-density parity-check codes and low enough noise parameter. This has
many consequences. Appropriate performance curves - called GEXIT functions - of
the belief propagation and optimal decoders match in high/low noise regimes.
This means that in high/low noise regimes the performance curves of the optimal
decoder can be computed by density evolution. Another interpretation is that
the replica predictions of spin-glass theory are exact. Our methods are rather
general and use cluster expansions first developed in the context of
mathematical statistical mechanics.
|
0903.1850
|
Free actions and Grassmanian variety
|
math.AG cs.CV q-bio.NC
|
An algebraic notion of representational consistency is defined. A theorem
relating it to free actions is proved. A metrizability problem of the quotient
(a shape space) is discussed. This leads to a new algebraic variety with a
metrizability result. A concrete example is given from stereo vision.
|
0903.1878
|
Contracting preference relations for database applications
|
cs.AI cs.DB
|
The binary relation framework has been shown to be applicable to many
real-life preference handling scenarios. Here we study preference contraction:
the problem of discarding selected preferences. We argue that the property of
minimality and the preservation of strict partial orders are crucial for
contractions. Contractions can be further constrained by specifying which
preferences should be protected. We consider two classes of preference
relations: finite and finitely representable. We present algorithms for
computing minimal and preference-protecting minimal contractions for finite as
well as finitely representable preference relations. We study relationships
between preference change in the binary relation framework and belief change in
the belief revision theory. We also introduce some preference query
optimization techniques which can be used in the presence of contraction. We
evaluate the proposed algorithms experimentally and present the results.
|
0903.1945
|
Hessian and concavity of mutual information, differential entropy, and
entropy power in linear vector Gaussian channels
|
cs.IT math.IT
|
Within the framework of linear vector Gaussian channels with arbitrary
signaling, closed-form expressions for the Jacobian of the minimum mean square
error and Fisher information matrices with respect to arbitrary parameters of
the system are calculated in this paper. Capitalizing on prior research where
the minimum mean square error and Fisher information matrices were linked to
information-theoretic quantities through differentiation, closed-form
expressions for the Hessian of the mutual information and the differential
entropy are derived. These expressions are then used to assess the concavity
properties of mutual information and differential entropy under different
channel conditions and also to derive a multivariate version of the entropy
power inequality due to Costa.
|
0903.1952
|
Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels
|
cs.IT math.IT
|
We investigate MIMO eigenmode transmission using statistical channel state
information at the transmitter. We consider a general jointly-correlated MIMO
channel model, which does not require separable spatial correlations at the
transmitter and receiver. For this model, we first derive a closed-form tight
upper bound for the ergodic capacity, which reveals a simple and interesting
relationship in terms of the matrix permanent of the eigenmode channel coupling
matrix and embraces many existing results in the literature as special cases.
Based on this closed-form and tractable upper bound expression, we then employ
convex optimization techniques to develop low-complexity power allocation
solutions involving only the channel statistics. Necessary and sufficient
optimality conditions are derived, from which we develop an iterative
water-filling algorithm with guaranteed convergence. Simulations demonstrate
the tightness of the capacity upper bound and the near-optimal performance of
the proposed low-complexity transmitter optimization approach.
|
0903.1953
|
Laconic schema mappings: computing core universal solutions by means of
SQL queries
|
cs.DB
|
We present a new method for computing core universal solutions in data
exchange settings specified by source-to-target dependencies, by means of SQL
queries. Unlike previously known algorithms, which are recursive in nature, our
method can be implemented directly on top of any DBMS. Our method is based on
the new notion of a laconic schema mapping. A laconic schema mapping is a
schema mapping for which the canonical universal solution is the core universal
solution. We give a procedure by which every schema mapping specified by FO s-t
tgds can be turned into a laconic schema mapping specified by FO s-t tgds that
may refer to a linear order on the domain of the source instance. We show that
our results are optimal, in the sense that the linear order is necessary and
the method cannot be extended to schema mapping involving target constraints.
|
0903.1967
|
Network error correction for unit-delay, memory-free networks using
convolutional codes
|
cs.IT math.IT
|
A single source network is said to be memory-free if all of the internal
nodes (those except the source and the sinks) do not employ memory but merely
send linear combinations of the symbols received at their incoming edges on
their outgoing edges. In this work, we introduce network-error correction for
single source, acyclic, unit-delay, memory-free networks with coherent network
coding for multicast. A convolutional code is designed at the source based on
the network code in order to correct network-errors that correspond to any of a
given set of error patterns, as long as consecutive errors are separated by a
certain interval which depends on the convolutional code selected. Bounds on
this interval and the field size required for constructing the convolutional
code with the required free distance are also obtained. We illustrate the
performance of convolutional network error correcting codes (CNECCs) designed
for the unit-delay networks using simulations of CNECCs on an example network
under a probabilistic error model.
|
0903.1972
|
On Competing Wireless Service Providers
|
cs.IT cs.GT math.IT
|
We consider a situation where wireless service providers compete for
heterogenous wireless users. The users differ in their willingness to pay as
well as in their individual channel gains. We prove existence and uniqueness of
the Nash equilibrium for the competition of two service providers, for a
generic channel model. Interestingly, the competition of two providers leads to
a globally optimal outcome. We extend some of the results to the case where
more than two providers are competing. Finally, we provide numerical examples
that illustrate the effects of various parameters on the Nash equilibrium.
|
0903.2016
|
Proof of a Conjecture on the Sequence of Exceptional Numbers,
Classifying Cyclic Codes and APN Functions
|
cs.IT math.AG math.IT
|
We prove a conjecture that classifies exceptional numbers. This conjecture
arises in two different ways, from cryptography and from coding theory. An odd
integer $t\geq 3$ is said to be exceptional if $f(x)=x^t$ is APN (Almost
Perfect Nonlinear) over $\mathbb{F}_{2^n}$ for infinitely many values of $n$.
Equivalently, $t$ is exceptional if the binary cyclic code of length $2^n-1$
with two zeros $\omega, \omega^t$ has minimum distance 5 for infinitely many
values of $n$. The conjecture we prove states that every exceptional number has
the form $2^i+1$ or $4^i-2^i+1$.
|
0903.2158
|
Supernodal Analysis Revisited
|
cs.SC cs.CE cs.DM
|
In this paper we show how to extend the known algorithm of nodal analysis in
such a way that, in the case of circuits without nullors and controlled sources
(but allowing for both, independent current and voltage sources), the system of
nodal equations describing the circuit is partitioned into one part, where the
nodal variables are explicitly given as linear combinations of the voltage
sources and the voltages of certain reference nodes, and another, which
contains the node variables of these reference nodes only and which moreover
can be read off directly from the given circuit. Neither do we need
preparational graph transformations, nor do we need to introduce additional
current variables (as in MNA). Thus this algorithm is more accessible to
students, and consequently more suitable for classroom presentations.
|
0903.2174
|
Game theory and the frequency selective interference channel - A
tutorial
|
cs.IT cs.GT math.IT
|
This paper provides a tutorial overview of game theoretic techniques used for
communication over frequency selective interference channels. We discuss both
competitive and cooperative techniques.
Keywords: Game theory, competitive games, cooperative games, Nash
Equilibrium, Nash bargaining solution, Generalized Nash games, Spectrum
optimization, distributed coordination, interference channel, multiple access
channel, iterative water-filling.
|
0903.2203
|
Achievable Error Exponents for Channel with Side Information - Erasure
and List Decoding
|
cs.IT math.IT
|
We consider a decoder with an erasure option and a variable size list decoder
for channels with non-casual side information at the transmitter. First,
universally achievable error exponents are offered for decoding with an erasure
option using a parameterized decoder in the spirit of Csisz\'{a}r and
K\"{o}rner's decoder. Then, the proposed decoding rule is generalized by
extending the range of its parameters to allow variable size list decoding.
This extension gives a unified treatment for erasure/list decoding. Exponential
bounds on the probability of list error and the average number of incorrect
messages on the list are given. Relations to Forney's and Csisz\'{a}r and
K\"{o}rner's decoders for discrete memoryless channel are discussed. These
results are obtained by exploring a random binning code with conditionally
constant composition codewords proposed by Moulin and Wang, but with a
different decoding rule.
|
0903.2226
|
On the achievable diversity-multiplexing tradeoff in interference
channels
|
cs.IT math.IT
|
We analyze two-user single-antenna fading interference channels with perfect
receive channel state information (CSI) and no transmit CSI. For the case of
very strong interference, we prove that decoding interference while treating
the intended signal as noise, subtracting the result out, and then decoding the
desired signal, a process known as "stripping", achieves the
diversity-multiplexing tradeoff (DMT) outer bound derived in Akuiyibo and
Leveque, Int. Zurich Seminar on Commun., 2008. The proof is constructive in the
sense that it provides corresponding code design criteria for DMT optimality.
For general interference levels, we compute the DMT of a fixed-power-split Han
and Kobayashi type superposition coding scheme, provide design criteria for the
corresponding superposition codes, and find that this scheme is DMT-optimal for
certain multiplexing rates.
|
0903.2232
|
On the Iterative Decoding of High-Rate LDPC Codes With Applications in
Compressed Sensing
|
cs.IT math.IT
|
This paper considers the performance of $(j,k)$-regular low-density
parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the
high-rate regime. In particular, we derive the high-rate scaling law for MP
decoding of LDPC codes on the binary erasure channel (BEC) and the $q$-ary
symmetric channel ($q$-SC). For the BEC, the density evolution (DE) threshold
of iterative decoding scales like $\Theta(k^{-1})$ and the critical stopping
ratio scales like $\Theta(k^{-j/(j-2)})$. For the $q$-SC, the DE threshold of
verification decoding depends on the details of the decoder and scales like
$\Theta(k^{-1})$ for one decoder.
Using the fact that coding over large finite alphabets is very similar to
coding over the real numbers, the analysis of verification decoding is also
extended to the the compressed sensing (CS) of strictly-sparse signals. A DE
based approach is used to analyze the CS systems with randomized-reconstruction
guarantees. This leads to the result that strictly-sparse signals can be
reconstructed efficiently with high-probability using a constant oversampling
ratio (i.e., when the number of measurements scales linearly with the sparsity
of the signal). A stopping-set based approach is also used to get stronger
(e.g., uniform-in-probability) reconstruction guarantees.
|
0903.2243
|
Pragmatic Information Rates, Generalizations of the Kelly Criterion, and
Financial Market Efficiency
|
cs.IT math.IT q-fin.PM q-fin.TR
|
This paper is part of an ongoing investigation of "pragmatic information",
defined in Weinberger (2002) as "the amount of information actually used in
making a decision". Because a study of information rates led to the Noiseless
and Noisy Coding Theorems, two of the most important results of Shannon's
theory, we begin the paper by defining a pragmatic information rate, showing
that all of the relevant limits make sense, and interpreting them as the
improvement in compression obtained from using the correct distribution of
transmitted symbols.
The first of two applications of the theory extends the information theoretic
analysis of the Kelly Criterion, and its generalization, the horse race, to a
series of races where the stochastic process of winning horses, payoffs, and
strategies depend on some stationary process, including, but not limited to the
history of previous races. If the bettor is receiving messages (side
information) about the probability distribution of winners, the doubling rate
of the bettor's winnings is bounded by the pragmatic information of the
messages.
A second application is to the question of market efficiency. An efficient
market is, by definition, a market in which the pragmatic information of the
"tradable past" with respect to current prices is zero. Under this definition,
markets whose returns are characterized by a GARCH(1,1) process cannot be
efficient.
Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem
suggests that a cause of market inefficiency is that the underlying
fundamentals are changing so fast that the price discovery mechanism simply
cannot keep up. This may happen most readily in the run-up to a financial
bubble, where investors' willful ignorance degrade the information processing
capabilities of the market.
|
0903.2282
|
Multiagent Learning in Large Anonymous Games
|
cs.MA cs.GT cs.LG
|
In large systems, it is important for agents to learn to act effectively, but
sophisticated multi-agent learning algorithms generally do not scale. An
alternative approach is to find restricted classes of games where simple,
efficient algorithms converge. It is shown that stage learning efficiently
converges to Nash equilibria in large anonymous games if best-reply dynamics
converge. Two features are identified that improve convergence. First, rather
than making learning more difficult, more agents are actually beneficial in
many settings. Second, providing agents with statistical information about the
behavior of others can significantly reduce the number of observations needed.
|
0903.2299
|
Differential Contrastive Divergence
|
cs.LG
|
This paper has been retracted.
|
0903.2310
|
Analysis of the Relationships among Longest Common Subsequences,
Shortest Common Supersequences and Patterns and its application on Pattern
Discovery in Biological Sequences
|
cs.DS cs.DM cs.IR cs.OH q-bio.QM
|
For a set of mulitple sequences, their patterns,Longest Common Subsequences
(LCS) and Shortest Common Supersequences (SCS) represent different aspects of
these sequences profile, and they can all be used for biological sequence
comparisons and analysis. Revealing the relationship between the patterns and
LCS,SCS might provide us with a deeper view of the patterns of biological
sequences, in turn leading to better understanding of them. However, There is
no careful examinaton about the relationship between patterns, LCS and SCS. In
this paper, we have analyzed their relation, and given some lemmas. Based on
their relations, a set of algorithms called the PALS (PAtterns by Lcs and Scs)
algorithms are propsoed to discover patterns in a set of biological sequences.
These algorithms first generate the results for LCS and SCS of sequences by
heuristic, and consequently derive patterns from these results. Experiments
show that the PALS algorithms perform well (both in efficiency and in accuracy)
on a variety of sequences. The PALS approach also provides us with a solution
for transforming between the heuristic results of SCS and LCS.
|
0903.2315
|
Design and Analysis of E2RC Codes
|
cs.IT cs.DM math.IT
|
We consider the design and analysis of the efficiently-encodable
rate-compatible ($E^2RC$) irregular LDPC codes proposed in previous work. In
this work we introduce semi-structured $E^2RC$-like codes and protograph
$E^2RC$ codes. EXIT chart based methods are developed for the design of
semi-structured $E^2RC$-like codes that allow us to determine near-optimal
degree distributions for the systematic part of the code while taking into
account the structure of the deterministic parity part, thus resolving one of
the open issues in the original construction. We develop a fast EXIT function
computation method that does not rely on Monte-Carlo simulations and can be
used in other scenarios as well. Our approach allows us to jointly optimize
code performance across the range of rates under puncturing. We then consider
protograph $E^2RC$ codes (that have a protograph representation) and propose
rules for designing a family of rate-compatible punctured protographs with low
thresholds. For both the semi-structured and protograph $E^2RC$ families we
obtain codes whose gap to capacity is at most 0.3 dB across the range of rates
when the maximum variable node degree is twenty.
|
0903.2361
|
Adaptive Observers and Parameter Estimation for a Class of Systems
Nonlinear in the Parameters
|
math.OC cs.SY math.DS q-bio.QM
|
We consider the problem of asymptotic reconstruction of the state and
parameter values in systems of ordinary differential equations. A solution to
this problem is proposed for a class of systems of which the unknowns are
allowed to be nonlinearly parameterized functions of state and time.
Reconstruction of state and parameter values is based on the concepts of weakly
attracting sets and non-uniform convergence and is subjected to persistency of
excitation conditions. In absence of nonlinear parametrization the resulting
observers reduce to standard estimation schemes. In this respect, the proposed
method constitutes a generalization of the conventional canonical adaptive
observer design.
|
0903.2426
|
Relay Selection and Power Allocation in Cooperative Cellular Networks
|
cs.IT math.IT
|
We consider a system with a single base station communicating with multiple
users over orthogonal channels while being assisted by multiple relays. Several
recent works have suggested that, in such a scenario, selection, i.e., a single
relay helping the source, is the best relaying option in terms of the resulting
complexity and overhead. However, in a multiuser setting, optimal relay
assignment is a combinatorial problem. In this paper, we formulate a related
convex optimization problem that provides an extremely tight upper bound on
performance and show that selection is, almost always, inherent in the
solution. We also provide a heuristic to find a close-to-optimal relay
assignment and power allocation across users supported by a single relay.
Simulation results using realistic channel models demonstrate the efficacy of
the proposed schemes, but also raise the question as to whether the gains from
relaying are worth the additional costs.
|
0903.2448
|
Positive Logic with Adjoint Modalities: Proof Theory, Semantics and
Reasoning about Information
|
cs.LO cs.MA
|
We consider a simple modal logic whose non-modal part has conjunction and
disjunction as connectives and whose modalities come in adjoint pairs, but are
not in general closure operators. Despite absence of negation and implication,
and of axioms corresponding to the characteristic axioms of (e.g.) T, S4 and
S5, such logics are useful, as shown in previous work by Baltag, Coecke and the
first author, for encoding and reasoning about information and misinformation
in multi-agent systems. For such a logic we present an algebraic semantics,
using lattices with agent-indexed families of adjoint pairs of operators, and a
cut-free sequent calculus. The calculus exploits operators on sequents, in the
style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by
constructive syntactic methods. The applicability of the logic is illustrated
by reasoning about the muddy children puzzle, for which the calculus is
augmented with extra rules to express the facts of the muddy children scenario.
|
0903.2471
|
Cooperative Multiplexing: Toward Higher Spectral Efficiency in
Multi-antenna Relay Networks
|
cs.IT math.IT
|
Previous work on cooperative communications has concentrated primarily on the
diversity benefits of such techniques. This paper, instead, considers the
multiplexing benefits of cooperative communications. First, a new
interpretation on the fundamental tradeoff between the transmission rate and
outage probability in multi-antenna relay networks is given. It follows that
multiplexing gains can be obtained at any finite SNR, in full-duplex
multi-antenna relay networks. Thus relaying can offer not only stronger link
reliability, but also higher spectral efficiency.
Specifically, the decode-and-forward protocol is applied and networks that
have one source, one destination, and multiple relays are considered. A receive
power gain at the relays, which captures the network large scale fading
characteristics, is also considered. It is shown that this power gain can
significantly affect the system diversity-multiplexing tradeoff for any finite
SNR value. Several relaying protocols are proposed and are shown to offer
nearly the same outage probability as if the transmit antennas at the source
and the relay(s) were co-located, given certain SNR and receive power gains at
the relays. Thus a higher multiplexing gain than that of the direct link can be
obtained if the destination has more antennas than the source.
Much of the analysis in the paper is valid for arbitrary channel fading
statistics. These results point to a view of relay networks as a means for
providing higher spectral efficiency, rather than only link reliability.
|
0903.2516
|
Effect of Degree Distribution on Evolutionary Search
|
cs.NE
|
This paper introduces a method to generate hierarchically modular networks
with prescribed node degree list and proposes a metric to measure network
modularity based on the notion of edge distance. The generated networks are
used as test problems to explore the effect of modularity and degree
distribution on evolutionary algorithm performance. Results from the
experiments (i) confirm a previous finding that modularity increases the
performance advantage of genetic algorithms over hill climbers, and (ii)
support a new conjecture that test problems with modularized constraint
networks having heavy-tailed right-skewed degree distributions are more easily
solved than test problems with modularized constraint networks having
bell-shaped normal degree distributions.
|
0903.2528
|
Airport Gate Assignment A Hybrid Model and Implementation
|
cs.AI cs.OH
|
With the rapid development of airlines, airports today become much busier and
more complicated than previous days. During airlines daily operations,
assigning the available gates to the arriving aircrafts based on the fixed
schedule is a very important issue, which motivates researchers to study and
solve Airport Gate Assignment Problems (AGAP) with all kinds of
state-of-the-art combinatorial optimization techniques. In this paper, we study
the AGAP and propose a novel hybrid mathematical model based on the method of
constraint programming and 0 - 1 mixed-integer programming. With the objective
to minimize the number of gate conflicts of any two adjacent aircrafts assigned
to the same gate, we build a mathematical model with logical constraints and
the binary constraints. For practical considerations, the potential objective
of the model is also to minimize the number of gates that airlines must lease
or purchase in order to run their business smoothly. We implement the model in
the Optimization Programming Language (OPL) and carry out empirical studies
with the data obtained from online timetable of Continental Airlines, Houston
Gorge Bush Intercontinental Airport IAH, which demonstrate that our model can
provide an efficient evaluation criteria for the airline companies to estimate
the efficiency of their current gate assignments.
|
0903.2543
|
Multi-Agent Crisis Response systems - Design Requirements and Analysis
of Current Systems
|
cs.MA
|
Crisis response is a critical area of research, with encouraging progress in
the past view yeas. The aim of the research is to contribute to building future
crisis environment where software agents, robots, responders, crisis managers,
and crisis organizations interact to provide advice, protection and aid. This
paper discusses the crisis response domain requirements, and provides analysis
of five crisis response systems namely: DrillSim [2], DEFACTO [15], ALADDIN
[1], RoboCup Rescue [18], and FireGrid [3]. Analysis of systems includes
systems architecture and methodology. In addition, we identified features and
limitations of systems based on crisis response domain requirements.
|
0903.2544
|
To Click or not to Click? The Role of Contextualized and User-Centric
Web Snippets
|
cs.IR
|
When searching the web, it is often possible that there are too many results
available for ambiguous queries. Text snippets, extracted from the retrieved
pages, are an indicator of the pages' usefulness to the query intention and can
be used to focus the scope of search results. In this paper, we propose a novel
method for automatically extracting web page snippets that are highly relevant
to the query intention and expressive of the pages' entire content. We show
that the usage of semantics, as a basis for focused retrieval, produces high
quality text snippet suggestions. The snippets delivered by our method are
significantly better in terms of retrieval performance compared to those
derived using the pages' statistical content. Furthermore, our study suggests
that semantically-driven snippet generation can also be used to augment
traditional passage retrieval algorithms based on word overlap or statistical
weights, since they typically differ in coverage and produce different results.
User clicks on the query relevant snippets can be used to refine the query
results and promote the most comprehensive among the relevant documents.
|
0903.2641
|
Multiscale Computations on Neural Networks: From the Individual Neuron
Interactions to the Macroscopic-Level Analysis
|
cs.CE cs.NA q-bio.NC
|
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables.
|
0903.2653
|
Capacity region of the deterministic multi-pair bi-directional relay
network
|
cs.IT math.IT
|
In this paper we study the capacity region of the multi-pair bidirectional
(or two-way) wireless relay network, in which a relay node facilitates the
communication between multiple pairs of users. This network is a generalization
of the well known bidirectional relay channel, where we have only one pair of
users. We examine this problem in the context of the deterministic channel
interaction model, which eliminates the channel noise and allows us to focus on
the interaction between signals. We characterize the capacity region of this
network when the relay is operating at either full-duplex mode or half-duplex
mode (with non adaptive listen-transmit scheduling). In both cases we show that
the cut-set upper bound is tight and, quite interestingly, the capacity region
is achieved by a simple equation-forwarding strategy.
|
0903.2675
|
Construction and Covering Properties of Constant-Dimension Codes
|
cs.IT math.IT
|
Constant-dimension codes (CDCs) have been investigated for noncoherent error
correction in random network coding. The maximum cardinality of CDCs with given
minimum distance and how to construct optimal CDCs are both open problems,
although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are
nearly optimal. In this paper, we first construct a new class of CDCs based on
KK codes, referred to as augmented KK codes, whose cardinalities are greater
than previously proposed CDCs. We then propose a low-complexity decoding
algorithm for our augmented KK codes using that for KK codes. Our decoding
algorithm corrects more errors than a bounded subspace distance decoder by
taking advantage of the structure of our augmented KK codes. In the rest of the
paper we investigate the covering properties of CDCs. We first derive bounds on
the minimum cardinality of a CDC with a given covering radius and then
determine the asymptotic behavior of this quantity. Moreover, we show that
liftings of rank metric codes have the highest possible covering radius, and
hence liftings of rank metric codes are not optimal packing CDCs. Finally, we
construct good covering CDCs by permuting liftings of rank metric codes.
|
0903.2679
|
Valuations and Metrics on Partially Ordered Sets
|
math.CO cs.IT math.IT
|
We extend the definitions of upper and lower valuations on partially ordered
sets, and consider the metrics they induce, in particular the metrics available
(or not) based on the logarithms of such valuations. Motivating applications in
computational linguistics and computational biology are indicated.
|
0903.2695
|
Dynamic Multi-Vehicle Routing with Multiple Classes of Demands
|
cs.RO
|
In this paper we study a dynamic vehicle routing problem in which there are
multiple vehicles and multiple classes of demands. Demands of each class arrive
in the environment randomly over time and require a random amount of on-site
service that is characteristic of the class. To service a demand, one of the
vehicles must travel to the demand location and remain there for the required
on-site service time. The quality of service provided to each class is given by
the expected delay between the arrival of a demand in the class, and that
demand's service completion. The goal is to design a routing policy for the
service vehicles which minimizes a convex combination of the delays for each
class. First, we provide a lower bound on the achievable values of the convex
combination of delays. Then, we propose a novel routing policy and analyze its
performance under heavy load conditions (i.e., when the fraction of time the
service vehicles spend performing on-site service approaches one). The policy
performs within a constant factor of the lower bound (and thus the optimal),
where the constant depends only on the number of classes, and is independent of
the number of vehicles, the arrival rates of demands, the on-site service
times, and the convex combination coefficients.
|
0903.2711
|
Performance Assessment of MIMO-BICM Demodulators based on System
Capacity
|
cs.IT math.IT
|
We provide a comprehensive performance comparison of soft-output and
hard-output demodulators in the context of non-iterative multiple-input
multiple-output bit-interleaved coded modulation (MIMO-BICM). Coded bit error
rate (BER), widely used in literature for demodulator comparison, has the
drawback of depending strongly on the error correcting code being used. This
motivates us to propose a code-independent performance measure in terms of
system capacity, i.e., mutual information of the equivalent modulation channel
that comprises modulator, wireless channel, and demodulator. We present
extensive numerical results for ergodic and quasi-static fading channels under
perfect and imperfect channel state information. These results reveal that the
performance ranking of MIMO demodulators is rate-dependent. Furthermore, they
provide new insights regarding MIMO-BICM system design, i.e., the choice of
antenna configuration, symbol constellation, and demodulator for a given target
rate.
|
0903.2749
|
The Perfect Binary One-Error-Correcting Codes of Length 15: Part
II--Properties
|
cs.IT math.IT
|
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.
|
0903.2774
|
Compressive estimation of doubly selective channels in multicarrier
systems: Leakage effects and sparsity-enhancing processing
|
cs.IT math.IT
|
We consider the application of compressed sensing (CS) to the estimation of
doubly selective channels within pulse-shaping multicarrier systems (which
include OFDM systems as a special case). By exploiting sparsity in the
delay-Doppler domain, CS-based channel estimation allows for an increase in
spectral efficiency through a reduction of the number of pilot symbols. For
combating leakage effects that limit the delay-Doppler sparsity, we propose a
sparsity-enhancing basis expansion and a method for optimizing the basis with
or without prior statistical information about the channel. We also present an
alternative CS-based channel estimator for (potentially) strongly
time-frequency dispersive channels, which is capable of estimating the
"off-diagonal" channel coefficients characterizing intersymbol and intercarrier
interference (ISI/ICI). For this estimator, we propose a basis construction
combining Fourier (exponential) and prolate spheroidal sequences. Simulation
results assess the performance gains achieved by the proposed
sparsity-enhancing processing techniques and by explicit estimation of ISI/ICI
channel coefficients.
|
0903.2791
|
On the Hamming weight of Repeated Root Cyclic and Negacyclic Codes over
Galois Rings
|
cs.IT math.IT
|
Repeated root Cyclic and Negacyclic codes over Galois rings have been studied
much less than their simple root counterparts. This situation is beginning to
change. For example, repeated root codes of length $p^s$, where $p$ is the
characteristic of the alphabet ring, have been studied under some additional
hypotheses. In each one of those cases, the ambient space for the codes has
turned out to be a chain ring. In this paper, all remaining cases of cyclic and
negacyclic codes of length $p^s$ over a Galois ring alphabet are considered. In
these cases the ambient space is a local ring with simple socle but not a chain
ring. Nonetheless, by reducing the problem to one dealing with uniserial
subambients, a method for computing the Hamming distance of these codes is
provided.
|
0903.2792
|
Thermodynamics of Information Retrieval
|
cs.IT cs.CL cs.SI math.IT
|
In this work, we suggest a parameterized statistical model (the gamma
distribution) for the frequency of word occurrences in long strings of English
text and use this model to build a corresponding thermodynamic picture by
constructing the partition function. We then use our partition function to
compute thermodynamic quantities such as the free energy and the specific heat.
In this approach, the parameters of the word frequency model vary from word to
word so that each word has a different corresponding thermodynamics and we
suggest that differences in the specific heat reflect differences in how the
words are used in language, differentiating keywords from common and function
words. Finally, we apply our thermodynamic picture to the problem of retrieval
of texts based on keywords and suggest some advantages over traditional
information retrieval methods.
|
0903.2820
|
Cooperative Transmission in a Wireless Relay Network based on Flow
Management
|
cs.IT math.IT
|
In this paper, a cooperative transmission design for a general multi-node
half-duplex wireless relay network is presented. It is assumed that the nodes
operate in half-duplex mode and that channel information is available at the
nodes. The proposed design involves solving a convex flow optimization problem
on a graph that models the relay network. A much simpler generalized-link
selection protocol based on the above design is also presented. Both the
proposed flow-optimized protocol and the generalized-link selection protocol
are shown to achieve the optimal diversity-multiplexing tradeoff (DMT) for the
relay network. Moreover, simulation results are presented to quantify the gap
between the performances of the proposed protocols and that of a
max-flow-min-cut type bound, in terms of outage probability.
|
0903.2851
|
A parameter-free hedging algorithm
|
cs.LG cs.AI
|
We study the problem of decision-theoretic online learning (DTOL). Motivated
by practical applications, we focus on DTOL when the number of actions is very
large. Previous algorithms for learning in this framework have a tunable
learning rate parameter, and a barrier to using online-learning in practical
applications is that it is not understood how to set this parameter optimally,
particularly when the number of actions is large.
In this paper, we offer a clean solution by proposing a novel and completely
parameter-free algorithm for DTOL. We introduce a new notion of regret, which
is more natural for applications with a large number of actions. We show that
our algorithm achieves good performance with respect to this new notion of
regret; in addition, it also achieves performance close to that of the best
bounds achieved by previous algorithms with optimally-tuned parameters,
according to previous notions of regret.
|
0903.2862
|
Tracking using explanation-based modeling
|
cs.LG cs.AI cs.CV
|
We study the tracking problem, namely, estimating the hidden state of an
object over time, from unreliable and noisy measurements. The standard
framework for the tracking problem is the generative framework, which is the
basis of solutions such as the Bayesian algorithm and its approximation, the
particle filters. However, the problem with these solutions is that they are
very sensitive to model mismatches. In this paper, motivated by online
learning, we introduce a new framework -- an {\em explanatory} framework -- for
tracking. We provide an efficient tracking algorithm for this framework. We
provide experimental results comparing our algorithm to the Bayesian algorithm
on simulated data. Our experiments show that when there are slight model
mismatches, our algorithm vastly outperforms the Bayesian algorithm.
|
0903.2870
|
On $p$-adic Classification
|
cs.LG
|
A $p$-adic modification of the split-LBG classification method is presented
in which first clusterings and then cluster centers are computed which locally
minimise an energy function. The outcome for a fixed dataset is independent of
the prime number $p$ with finitely many exceptions. The methods are applied to
the construction of $p$-adic classifiers in the context of learning.
|
0903.2890
|
Kalman Filtering with Intermittent Observations: Weak Convergence to a
Stationary Distribution
|
cs.IT cs.LG math.IT math.ST stat.TH
|
The paper studies the asymptotic behavior of Random Algebraic Riccati
Equations (RARE) arising in Kalman filtering when the arrival of the
observations is described by a Bernoulli i.i.d. process. We model the RARE as
an order-preserving, strongly sublinear random dynamical system (RDS). Under a
sufficient condition, stochastic boundedness, and using a limit-set dichotomy
result for order-preserving, strongly sublinear RDS, we establish the
asymptotic properties of the RARE: the sequence of random prediction error
covariance matrices converges weakly to a unique invariant distribution, whose
support exhibits fractal behavior. In particular, this weak convergence holds
under broad conditions and even when the observations arrival rate is below the
critical probability for mean stability. We apply the weak-Feller property of
the Markov process governing the RARE to characterize the support of the
limiting invariant distribution as the topological closure of a countable set
of points, which, in general, is not dense in the set of positive semi-definite
matrices. We use the explicit characterization of the support of the invariant
distribution and the almost sure ergodicity of the sample paths to easily
compute the moments of the invariant distribution. A one dimensional example
illustrates that the support is a fractured subset of the non-negative reals
with self-similarity properties.
|
0903.2923
|
On uncertainty principles in the finite dimensional setting
|
math.CA cs.IT math.IT
|
The aim of this paper is to prove an uncertainty principle for the
representation of a vector in two bases. Our result extends previously known
qualitative uncertainty principles into quantitative estimates. We then show
how to transfer this result to the discrete version of the Short Time Fourier
Transform. An application to trigonometric polynomials is also given.
|
0903.2972
|
Optimistic Simulated Exploration as an Incentive for Real Exploration
|
cs.LG cs.AI
|
Many reinforcement learning exploration techniques are overly optimistic and
try to explore every state. Such exploration is impossible in environments with
the unlimited number of states. I propose to use simulated exploration with an
optimistic model to discover promising paths for real exploration. This reduces
the needs for the real exploration.
|
0903.3000
|
A Robust Ranging Scheme for OFDMA-Based Networks
|
cs.IT math.IT
|
Uplink synchronization in orthogonal frequency-division multiple-access
(OFDMA) systems is a challenging task. In IEEE 802.16-based networks, users
that intend to establish a communication link with the base station must go
through a synchronization procedure called Initial Ranging (IR). Existing IR
schemes aim at estimating the timing offsets and power levels of ranging
subscriber stations (RSSs) without considering possible frequency misalignments
between the received uplink signals and the base station local reference. In
this work, we present a novel IR scheme for OFDMA systems where carrier
frequency offsets, timing errors and power levels are estimated for all RSSs in
a decoupled fashion. The proposed frequency estimator is based on a subspace
decomposition approach, while timing recovery is accomplished by measuring the
phase shift between the users'channel responses over adjacent subcarriers.
Computer simulations are employed to assess the effectiveness of the proposed
solution and to make comparisons with existing alternatives.
|
0903.3004
|
Decoding of MDP Convolutional Codes over the Erasure Channel
|
cs.IT math.IT
|
This paper studies the decoding capabilities of maximum distance profile
(MDP) convolutional codes over the erasure channel and compares them with the
decoding capabilities of MDS block codes over the same channel. The erasure
channel involving large alphabets is an important practical channel model when
studying packet transmissions over a network, e.g, the Internet.
|
0903.3024
|
A Vector Generalization of Costa's Entropy-Power Inequality with
Applications
|
cs.IT math.IT
|
This paper considers an entropy-power inequality (EPI) of Costa and presents
a natural vector generalization with a real positive semidefinite matrix
parameter. This new inequality is proved using a perturbation approach via a
fundamental relationship between the derivative of mutual information and the
minimum mean-square error (MMSE) estimate in linear vector Gaussian channels.
As an application, a new extremal entropy inequality is derived from the
generalized Costa EPI and then used to establish the secrecy capacity regions
of the degraded vector Gaussian broadcast channel with layered confidential
messages.
|
0903.3072
|
Spatial Skyline Queries: An Efficient Geometric Algorithm
|
cs.DB cs.CG
|
As more data-intensive applications emerge, advanced retrieval semantics,
such as ranking or skylines, have attracted attention. Geographic information
systems are such an application with massive spatial data. Our goal is to
efficiently support skyline queries over massive spatial data. To achieve this
goal, we first observe that the best known algorithm VS2, despite its claim,
may fail to deliver correct results. In contrast, we present a simple and
efficient algorithm that computes the correct results. To validate the
effectiveness and efficiency of our algorithm, we provide an extensive
empirical comparison of our algorithm and VS2 in several aspects.
|
0903.3096
|
The Secrecy Capacity Region of the Gaussian MIMO Multi-receiver Wiretap
Channel
|
cs.IT math.IT
|
In this paper, we consider the Gaussian multiple-input multiple-output (MIMO)
multi-receiver wiretap channel in which a transmitter wants to have
confidential communication with an arbitrary number of users in the presence of
an external eavesdropper. We derive the secrecy capacity region of this channel
for the most general case. We first show that even for the single-input
single-output (SISO) case, existing converse techniques for the Gaussian scalar
broadcast channel cannot be extended to this secrecy context, to emphasize the
need for a new proof technique. Our new proof technique makes use of the
relationships between the minimum-mean-square-error and the mutual information,
and equivalently, the relationships between the Fisher information and the
differential entropy. Using the intuition gained from the converse proof of the
SISO channel, we first prove the secrecy capacity region of the degraded MIMO
channel, in which all receivers have the same number of antennas, and the noise
covariance matrices can be arranged according to a positive semi-definite
order. We then generalize this result to the aligned case, in which all
receivers have the same number of antennas, however there is no order among the
noise covariance matrices. We accomplish this task by using the channel
enhancement technique. Finally, we find the secrecy capacity region of the
general MIMO channel by using some limiting arguments on the secrecy capacity
region of the aligned MIMO channel. We show that the capacity achieving coding
scheme is a variant of dirty-paper coding with Gaussian signals.
|
0903.3103
|
Efficiently Learning a Detection Cascade with Sparse Eigenvectors
|
cs.MM cs.AI cs.LG
|
In this work, we first show that feature selection methods other than
boosting can also be used for training an efficient object detector. In
particular, we introduce Greedy Sparse Linear Discriminant Analysis (GSLDA)
\cite{Moghaddam2007Fast} for its conceptual simplicity and computational
efficiency; and slightly better detection performance is achieved compared with
\cite{Viola2004Robust}. Moreover, we propose a new technique, termed Boosted
Greedy Sparse Linear Discriminant Analysis (BGSLDA), to efficiently train a
detection cascade. BGSLDA exploits the sample re-weighting property of boosting
and the class-separability criterion of GSLDA.
|
0903.3114
|
Markov Random Field Segmentation of Brain MR Images
|
cs.CV cond-mat.stat-mech physics.data-an physics.med-ph
|
We describe a fully-automatic 3D-segmentation technique for brain MR images.
Using Markov random fields the segmentation algorithm captures three important
MR features, i.e. non-parametric distributions of tissue intensities,
neighborhood correlations and signal inhomogeneities. Detailed simulations and
real MR images demonstrate the performance of the segmentation algorithm. The
impact of noise, inhomogeneity, smoothing and structure thickness is analyzed
quantitatively. Even single echo MR images are well classified into gray
matter, white matter, cerebrospinal fluid, scalp-bone and background. A
simulated annealing and an iterated conditional modes implementation are
presented.
Keywords: Magnetic Resonance Imaging, Segmentation, Markov Random Fields
|
0903.3127
|
Norm-Product Belief Propagation: Primal-Dual Message-Passing for
Approximate Inference
|
cs.AI cs.IT math.IT
|
In this paper we treat both forms of probabilistic inference, estimating
marginal probabilities of the joint distribution and finding the most probable
assignment, through a unified message-passing algorithm architecture. We
generalize the Belief Propagation (BP) algorithms of sum-product and
max-product and tree-rewaighted (TRW) sum and max product algorithms (TRBP) and
introduce a new set of convergent algorithms based on "convex-free-energy" and
Linear-Programming (LP) relaxation as a zero-temprature of a
convex-free-energy. The main idea of this work arises from taking a general
perspective on the existing BP and TRBP algorithms while observing that they
all are reductions from the basic optimization formula of $f + \sum_i h_i$
where the function $f$ is an extended-valued, strictly convex but non-smooth
and the functions $h_i$ are extended-valued functions (not necessarily convex).
We use tools from convex duality to present the "primal-dual ascent" algorithm
which is an extension of the Bregman successive projection scheme and is
designed to handle optimization of the general type $f + \sum_i h_i$. Mapping
the fractional-free-energy variational principle to this framework introduces
the "norm-product" message-passing. Special cases include sum-product and
max-product (BP algorithms) and the TRBP algorithms. When the
fractional-free-energy is set to be convex (convex-free-energy) the
norm-product is globally convergent for estimating of marginal probabilities
and for approximating the LP-relaxation. We also introduce another branch of
the norm-product, the "convex-max-product". The convex-max-product is
convergent (unlike max-product) and aims at solving the LP-relaxation.
|
0903.3131
|
Matrix Completion With Noise
|
cs.IT math.IT
|
On the heels of compressed sensing, a remarkable new field has very recently
emerged. This field addresses a broad range of problems of significant
practical interest, namely, the recovery of a data matrix from what appears to
be incomplete, and perhaps even corrupted, information. In its simplest form,
the problem is to recover a matrix from a small sample of its entries, and
comes up in many areas of science and engineering including collaborative
filtering, machine learning, control, remote sensing, and computer vision to
name a few.
This paper surveys the novel literature on matrix completion, which shows
that under some suitable conditions, one can recover an unknown low-rank matrix
from a nearly minimal set of entries by solving a simple convex optimization
problem, namely, nuclear-norm minimization subject to data constraints.
Further, this paper introduces novel results showing that matrix completion is
provably accurate even when the few observed entries are corrupted with a small
amount of noise. A typical result is that one can recover an unknown n x n
matrix of low rank r from just about nr log^2 n noisy samples with an error
which is proportional to the noise level. We present numerical results which
complement our quantitative analysis and show that, in practice, nuclear norm
minimization accurately fills in the many missing entries of large low-rank
matrices from just a few noisy samples. Some analogies between matrix
completion and compressed sensing are discussed throughout.
|
0903.3204
|
On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel
|
cs.IT math.IT
|
We consider the Additive White Gaussian Noise channel with Binary Phase Shift
Keying modulation. Our aim is to enable an algebraic hard decision Bounded
Minimum Distance decoder for a binary block code to exploit soft information
obtained from the demodulator. This idea goes back to Forney and is based on
treating received symbols with low reliability as erasures. This erasing at the
decoder is done using a threshold, each received symbol with reliability
falling below the threshold is erased. Depending on the target overall
complexity of the decoder this pseudo-soft decision decoding can be extended
from one threshold T to z>1 thresholds T_1<...<T_z for erasing received symbols
with lowest reliability. The resulting technique is widely known as Generalized
Minimum Distance decoding. In this paper we provide a means for explicit
determination of the optimal threshold locations in terms of minimal decoding
error probability. We do this for the one and the general z>1 thresholds case,
starting with a geometric interpretation of the optimal threshold location
problem and using an approach from Zyablov.
|
0903.3257
|
A New Local Distance-Based Outlier Detection Approach for Scattered
Real-World Data
|
cs.LG cs.IR
|
Detecting outliers which are grossly different from or inconsistent with the
remaining dataset is a major challenge in real-world KDD applications. Existing
outlier detection methods are ineffective on scattered real-world datasets due
to implicit data patterns and parameter setting issues. We define a novel
"Local Distance-based Outlier Factor" (LDOF) to measure the {outlier-ness} of
objects in scattered datasets which addresses these issues. LDOF uses the
relative location of an object to its neighbours to determine the degree to
which the object deviates from its neighbourhood. Properties of LDOF are
theoretically analysed including LDOF's lower bound and its false-detection
probability, as well as parameter settings. In order to facilitate parameter
settings in real-world applications, we employ a top-n technique in our outlier
detection approach, where only the objects with the highest LDOF values are
regarded as outliers. Compared to conventional approaches (such as top-n KNN
and top-n LOF), our method top-n LDOF is more effective at detecting outliers
in scattered data. It is also easier to set parameters, since its performance
is relatively stable over a large range of parameter values, as illustrated by
experimental results on both real-world and synthetic datasets.
|
0903.3261
|
The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel
|
cs.IT math.IT
|
In this paper, we consider a scenario where a source node wishes to broadcast
two confidential messages for two respective receivers via a Gaussian MIMO
broadcast channel. A wire-tapper also receives the transmitted signal via
another MIMO channel. First we assumed that the channels are degraded and the
wire-tapper has the worst channel. We establish the capacity region of this
scenario. Our achievability scheme is a combination of the superposition of
Gaussian codes and randomization within the layers which we will refer to as
Secret Superposition Coding. For the outerbound, we use the notion of enhanced
channel to show that the secret superposition of Gaussian codes is optimal. We
show that we only need to enhance the channels of the legitimate receivers, and
the channel of the eavesdropper remains unchanged. Then we extend the result of
the degraded case to non-degraded case. We show that the secret superposition
of Gaussian codes along with successive decoding cannot work when the channels
are not degraded. we develop a Secret Dirty Paper Coding (SDPC) scheme and show
that SDPC is optimal for this channel. Finally, we investigate practical
characterizations for the specific scenario in which the transmitter and the
eavesdropper have multiple antennas, while both intended receivers have a
single antenna. We characterize the secrecy capacity region in terms of
generalized eigenvalues of the receivers channel and the eavesdropper channel.
We refer to this configuration as the MISOME case. In high SNR we show that the
capacity region is a convex closure of two rectangular regions.
|
0903.3317
|
Discovering Matching Dependencies
|
cs.DB
|
The concept of matching dependencies (mds) is recently pro- posed for
specifying matching rules for object identification. Similar to the functional
dependencies (with conditions), mds can also be applied to various data quality
applications such as violation detection. In this paper, we study the problem
of discovering matching dependencies from a given database instance. First, we
formally define the measures, support and confidence, for evaluating utility of
mds in the given database instance. Then, we study the discovery of mds with
certain utility requirements of support and confidence. Exact algorithms are
developed, together with pruning strategies to improve the time performance.
Since the exact algorithm has to traverse all the data during the computation,
we propose an approximate solution which only use some of the data. A bound of
relative errors introduced by the approximation is also developed. Finally, our
experimental evaluation demonstrates the efficiency of the proposed methods.
|
0903.3329
|
Optimal Policies Search for Sensor Management
|
cs.LG stat.AP
|
This paper introduces a new approach to solve sensor management problems.
Classically sensor management problems can be well formalized as
Partially-Observed Markov Decision Processes (POMPD). The original approach
developped here consists in deriving the optimal parameterized policy based on
a stochastic gradient estimation. We assume in this work that it is possible to
learn the optimal policy off-line (in simulation) using models of the
environement and of the sensor(s). The learned policy can then be used to
manage the sensor(s). In order to approximate the gradient in a stochastic
context, we introduce a new method to approximate the gradient, based on
Infinitesimal Perturbation Approximation (IPA). The effectiveness of this
general framework is illustrated by the managing of an Electronically Scanned
Array Radar. First simulations results are finally proposed.
|
0903.3433
|
Fixed point theorems on partial randomness
|
cs.IT cs.CC math.IT math.LO math.PR
|
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434,
2008], we developed a statistical mechanical interpretation of algorithmic
information theory by introducing the notion of thermodynamic quantities at
temperature T, such as free energy F(T), energy E(T), and statistical
mechanical entropy S(T), into the theory. These quantities are real functions
of real argument T>0. We then discovered that, in the interpretation, the
temperature T equals to the partial randomness of the values of all these
thermodynamic quantities, where the notion of partial randomness is a stronger
representation of the compression rate by program-size complexity. Furthermore,
we showed that this situation holds for the temperature itself as a
thermodynamic quantity. Namely, the computability of the value of partition
function Z(T) gives a sufficient condition for T in (0,1) to be a fixed point
on partial randomness. In this paper, we show that the computability of each of
all the thermodynamic quantities above gives the sufficient condition also.
Moreover, we show that the computability of F(T) gives completely different
fixed points from the computability of Z(T).
|
0903.3480
|
Worst case attacks against binary probabilistic traitor tracing codes
|
cs.IT cs.CR math.IT
|
An insightful view into the design of traitor tracing codes should
necessarily consider the worst case attacks that the colluders can lead. This
paper takes an information-theoretic point of view where the worst case attack
is defined as the collusion strategy minimizing the achievable rate of the
traitor tracing code. Two different decoders are envisaged, the joint decoder
and the simple decoder, as recently defined by P. Moulin
\cite{Moulin08universal}. Several classes of colluders are defined with
increasing power. The worst case attack is derived for each class and each
decoder when applied to Tardos' codes and a probabilistic version of the
Boneh-Shaw construction. This contextual study gives the real rates achievable
by the binary probabilistic traitor tracing codes. Attacks usually considered
in literature, such as majority or minority votes, are indeed largely
suboptimal. This article also shows the utmost importance of the time-sharing
concept in a probabilistic codes.
|
0903.3487
|
Sending a Bivariate Gaussian Source over a Gaussian MAC with Feedback
|
cs.IT math.IT
|
We study the power-versus-distortion trade-off for the transmission of a
memoryless bivariate Gaussian source over a two-to-one Gaussian multiple-access
channel with perfect causal feedback. In this problem, each of two separate
transmitters observes a different component of a memoryless bivariate Gaussian
source as well as the feedback from the channel output of the previous
time-instants. Based on the observed source sequence and the feedback, each
transmitter then describes its source component to the common receiver via an
average-power constrained Gaussian multiple-access channel. From the resulting
channel output, the receiver wishes to reconstruct both source components with
the least possible expected squared-error distortion. We study the set of
distortion pairs that can be achieved by the receiver on the two source
components.
We present sufficient conditions and necessary conditions for the
achievability of a distortion pair. These conditions are expressed in terms of
the source correlation and of the signal-to-noise ratio (SNR) of the channel.
In several cases the necessary conditions and sufficient conditions coincide.
This allows us to show that if the channel SNR is below a certain threshold,
then an uncoded transmission scheme that ignores the feedback is optimal. Thus,
below this SNR-threshold feedback is useless. We also derive the precise
high-SNR asymptotics of optimal schemes.
|
0903.3537
|
Optimization and Analysis of Distributed Averaging with Short Node
Memory
|
cs.DC cs.IT cs.MA math.IT
|
In this paper, we demonstrate, both theoretically and by numerical examples,
that adding a local prediction component to the update rule can significantly
improve the convergence rate of distributed averaging algorithms. We focus on
the case where the local predictor is a linear combination of the node's two
previous values (i.e., two memory taps), and our update rule computes a
combination of the predictor and the usual weighted linear combination of
values received from neighbouring nodes. We derive the optimal mixing parameter
for combining the predictor with the neighbors' values, and carry out a
theoretical analysis of the improvement in convergence rate that can be
obtained using this acceleration methodology. For a chain topology on n nodes,
this leads to a factor of n improvement over the one-step algorithm, and for a
two-dimensional grid, our approach achieves a factor of n^1/2 improvement, in
terms of the number of iterations required to reach a prescribed level of
accuracy.
|
0903.3623
|
Matrix plots of reordered bistochastized transaction flow tables: A
United States intercounty migration example
|
physics.soc-ph cs.SI physics.data-an stat.AP
|
We present a number of variously rearranged matrix plots of the $3, 107
\times 3, 107$ 1995-2000 (asymmetric) intercounty migration table for the
United States, principally in its bistochasticized form (all 3,107 row and
column sums iteratively proportionally fitted to equal 1). In one set of plots,
the counties are seriated on the bases of the subdominant (left and right)
eigenvectors of the bistochastic matrix. In another set, we use the ordering of
counties in the dendrogram generated by the associated strong component
hierarchical clustering. Interesting, diverse features of U. S. intercounty
migration emerge--such as a contrast in centralized, hub-like
(cosmopolitan/provincial) properties between cosmopolitan "Sunbelt" and
provincial "Black Belt" counties. The methodologies employed should also be
insightful for the many other diverse forms of interesting transaction
flow-type data--interjournal citations being an obvious, much-studied example,
where one might expect that the journals Science, Nature and PNAS would display
"cosmopolitan" characteristics.
|
0903.3624
|
Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic
and Dynamic Environment
|
cs.RO
|
In this paper we present distributed and adaptive algorithms for motion
coordination of a group of m autonomous vehicles. The vehicles operate in a
convex environment with bounded velocity and must service demands whose time of
arrival, location and on-site service are stochastic; the objective is to
minimize the expected system time (wait plus service) of the demands. The
general problem is known as the m-vehicle Dynamic Traveling Repairman Problem
(m-DTRP). The best previously known control algorithms rely on centralized
a-priori task assignment and are not robust against changes in the environment,
e.g. changes in load conditions; therefore, they are of limited applicability
in scenarios involving ad-hoc networks of autonomous vehicles operating in a
time-varying environment. First, we present a new class of policies for the
1-DTRP problem that: (i) are provably optimal both in light- and heavy-load
condition, and (ii) are adaptive, in particular, they are robust against
changes in load conditions. Second, we show that partitioning policies, whereby
the environment is partitioned among the vehicles and each vehicle follows a
certain set of rules in its own region, are optimal in heavy-load conditions.
Finally, by combining the new class of algorithms for the 1-DTRP with suitable
partitioning policies, we design distributed algorithms for the m-DTRP problem
that (i) are spatially distributed, scalable to large networks, and adaptive to
network changes, (ii) are within a constant-factor of optimal in heavy-load
conditions and stabilize the system in any load condition. Simulation results
are presented and discussed.
|
0903.3627
|
Statistical RIP and Semi-Circle Distribution of Incoherent Dictionaries
|
cs.IT cs.DM math.IT math.PR
|
In this paper we formulate and prove a statistical version of the Candes-Tao
restricted isometry property (SRIP for short) which holds in general for any
incoherent dictionary which is a disjoint union of orthonormal bases. In
addition, we prove that, under appropriate normalization, the eigenvalues of
the associated Gram matrix fluctuate around 1 according to the Wigner
semicircle distribution. The result is then applied to various dictionaries
that arise naturally in the setting of finite harmonic analysis, giving, in
particular, a better understanding on a remark of
Applebaum-Howard-Searle-Calderbank concerning RIP for the Heisenberg dictionary
of chirp like functions.
|
0903.3667
|
How random are a learner's mistakes?
|
cs.LG cs.IT math.IT math.PR
|
Given a random binary sequence $X^{(n)}$ of random variables, $X_{t},$
$t=1,2,...,n$, for instance, one that is generated by a Markov source (teacher)
of order $k^{*}$ (each state represented by $k^{*}$ bits). Assume that the
probability of the event $X_{t}=1$ is constant and denote it by $\beta$.
Consider a learner which is based on a parametric model, for instance a Markov
model of order $k$, who trains on a sequence $x^{(m)}$ which is randomly drawn
by the teacher. Test the learner's performance by giving it a sequence
$x^{(n)}$ (generated by the teacher) and check its predictions on every bit of
$x^{(n)}.$ An error occurs at time $t$ if the learner's prediction $Y_{t}$
differs from the true bit value $X_{t}$. Denote by $\xi^{(n)}$ the sequence of
errors where the error bit $\xi_{t}$ at time $t$ equals 1 or 0 according to
whether the event of an error occurs or not, respectively. Consider the
subsequence $\xi^{(\nu)}$ of $\xi^{(n)}$ which corresponds to the errors of
predicting a 0, i.e., $\xi^{(\nu)}$ consists of the bits of $\xi^{(n)}$ only at
times $t$ such that $Y_{t}=0.$ In this paper we compute an estimate on the
deviation of the frequency of 1s of $\xi^{(\nu)}$ from $\beta$. The result
shows that the level of randomness of $\xi^{(\nu)}$ decreases relative to an
increase in the complexity of the learner.
|
0903.3669
|
Comment on "Language Trees and Zipping" arXiv:cond-mat/0108530
|
cs.AI cs.IT math.IT
|
Every encoding has priori information if the encoding represents any semantic
information of the unverse or object. Encoding means mapping from the unverse
to the string or strings of digits. The semantic here is used in the
model-theoretic sense or denotation of the object. If encoding or strings of
symbols is the adequate and true mapping of model or object, and the mapping is
recursive or computable, the distance between two strings (text) is mapping the
distance between models. We then are able to measure the distance by computing
the distance between the two strings. Otherwise, we may take a misleading
course. "Language tree" may not be a family tree in the sense of historical
linguistics. Rather it just means the similarity.
|
0903.3676
|
Combinatorial Ricci Curvature and Laplacians for Image Processing
|
cs.CV cs.CG
|
A new Combinatorial Ricci curvature and Laplacian operators for grayscale
images are introduced and tested on 2D synthetic, natural and medical images.
Analogue formulae for voxels are also obtained. These notions are based upon
more general concepts developed by R. Forman. Further applications, in
particular a fitting Ricci flow, are discussed.
|
0903.3685
|
Quasiperfect domination in triangular lattices
|
math.CO cs.IT math.IT
|
A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect)
dominating set in $G$ if each vertex $v$ of $G\setminus S$ is adjacent to only
one vertex ($d_v\in\{1,2\}$ vertices) of $S$. Perfect and quasiperfect
dominating sets in the regular tessellation graph of Schl\"afli symbol
$\{3,6\}$ and in its toroidal quotients are investigated, yielding the
classification of their perfect dominating sets and most of their quasiperfect
dominating sets $S$ with induced components of the form $K_{\nu}$, where
$\nu\in\{1,2,3\}$ depends only on $S$.
|
0903.3715
|
Optimal sparse CDMA detection at high load
|
cs.IT math.IT
|
Balancing efficiency of bandwidth use and complexity of detection involves
choosing a suitable load for a multi-access channel. In the case of synchronous
CDMA, with random codes, it is possible to demonstrate the existence of a
threshold in the load beyond which there is an apparent jump in computational
complexity. At small load unit clause propagation can determine a jointly
optimal detection of sources on a noiseless channel, but fails at high load.
Analysis provides insight into the difference between the standard dense random
codes and sparse codes, and the limitations of optimal detection in the sparse
case.
|
0903.3759
|
GeoP2P: An adaptive peer-to-peer overlay for efficient search and update
of spatial information
|
cs.NI cs.DB cs.DC
|
This paper proposes a fully decentralized peer-to-peer overlay structure
GeoP2P, to facilitate geographic location based search and retrieval of
information. Certain limitations of centralized geographic indexes favor
peer-to-peer organization of the information, which, in addition to avoiding
performance bottleneck, allows autonomy over local information. Peer-to-peer
systems for geographic or multidimensional range queries built on existing DHTs
suffer from the inaccuracy in linearization of the multidimensional space.
Other overlay structures that are based on hierarchical partitioning of the
search space are not scalable because they use special super-peers to represent
the nodes in the hierarchy. GeoP2P partitions the search space hierarchically,
maintains the overlay structure and performs the routing without the need of
any super-peers. Although similar fully-decentralized overlays have been
previously proposed, they lack the ability to dynamically grow and retract the
partition hierarchy when the number of peers change. GeoP2P provides such
adaptive features with minimum perturbation of the system state. Such
adaptation makes both the routing delay and the state size of each peer
logarithmic to the total number of peers, irrespective of the size of the
multidimensional space. Our analysis also reveals that the overlay structure
and the routing algorithm are generic and independent of several aspects of the
partitioning hierarchy, such as the geometric shape of the zones or the
dimensionality of the search space.
|
0903.3786
|
Multiple-Input Multiple-Output Gaussian Broadcast Channels with
Confidential Messages
|
cs.IT cs.CR math.IT
|
This paper considers the problem of secret communication over a two-receiver
multiple-input multiple-output (MIMO) Gaussian broadcast channel. The
transmitter has two independent messages, each of which is intended for one of
the receivers but needs to be kept asymptotically perfectly secret from the
other. It is shown that, surprisingly, under a matrix power constraint both
messages can be simultaneously transmitted at their respective maximal secrecy
rates. To prove this result, the MIMO Gaussian wiretap channel is revisited and
a new characterization of its secrecy capacity is provided via a new coding
scheme that uses artificial noise and random binning.
|
0903.3889
|
On generating independent random strings
|
cs.IT cs.CC math.IT
|
It is shown that from two strings that are partially random and independent
(in the sense of Kolmogorov complexity) it is possible to effectively construct
polynomially many strings that are random and pairwise independent. If the two
initial strings are random, then the above task can be performed in polynomial
time. It is also possible to construct in polynomial time a random string, from
two strings that have constant randomness rate.
|
0903.3926
|
Designing a GUI for Proofs - Evaluation of an HCI Experiment
|
cs.AI
|
Often user interfaces of theorem proving systems focus on assisting
particularly trained and skilled users, i.e., proof experts. As a result, the
systems are difficult to use for non-expert users. This paper describes a paper
and pencil HCI experiment, in which (non-expert) students were asked to make
suggestions for a GUI for an interactive system for mathematical proofs. They
had to explain the usage of the GUI by applying it to construct a proof sketch
for a given theorem. The evaluation of the experiment provides insights for the
interaction design for non-expert users and the needs and wants of this user
group.
|
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