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0901.0734
|
SPARLS: A Low Complexity Recursive $\mathcal{L}_1$-Regularized Least
Squares Algorithm
|
cs.IT math.IT
|
We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS)
algorithm for the estimation of a sparse tap-weight vector in the adaptive
filtering setting. The SPARLS algorithm exploits noisy observations of the
tap-weight vector output stream and produces its estimate using an
Expectation-Maximization type algorithm. Simulation studies in the context of
channel estimation, employing multi-path wireless channels, show that the
SPARLS algorithm has significant improvement over the conventional widely-used
Recursive Least Squares (RLS) algorithm, in terms of both mean squared error
(MSE) and computational complexity.
|
0901.0749
|
Quantized Compressive Sensing
|
cs.IT math.IT
|
We study the average distortion introduced by scalar, vector, and entropy
coded quantization of compressive sensing (CS) measurements. The asymptotic
behavior of the underlying quantization schemes is either quantified exactly or
characterized via bounds. We adapt two benchmark CS reconstruction algorithms
to accommodate quantization errors, and empirically demonstrate that these
methods significantly reduce the reconstruction distortion when compared to
standard CS techniques.
|
0901.0753
|
Distributed Preemption Decisions: Probabilistic Graphical Model,
Algorithm and Near-Optimality
|
cs.LG
|
Cooperative decision making is a vision of future network management and
control. Distributed connection preemption is an important example where nodes
can make intelligent decisions on allocating resources and controlling traffic
flows for multi-class service networks. A challenge is that nodal decisions are
spatially dependent as traffic flows trespass multiple nodes in a network.
Hence the performance-complexity trade-off becomes important, i.e., how
accurate decisions are versus how much information is exchanged among nodes.
Connection preemption is known to be NP-complete. Centralized preemption is
optimal but computationally intractable. Decentralized preemption is
computationally efficient but may result in a poor performance. This work
investigates distributed preemption where nodes decide whether and which flows
to preempt using only local information exchange with neighbors. We develop,
based on the probabilistic graphical models, a near-optimal distributed
algorithm. The algorithm is used by each node to make collectively near-optimal
preemption decisions. We study trade-offs between near-optimal performance and
complexity that corresponds to the amount of information-exchange of the
distributed algorithm. The algorithm is validated by both analysis and
simulation.
|
0901.0760
|
A Theoretical Analysis of Joint Manifolds
|
cs.LG cs.CV
|
The emergence of low-cost sensor architectures for diverse modalities has
made it possible to deploy sensor arrays that capture a single event from a
large number of vantage points and using multiple modalities. In many
scenarios, these sensors acquire very high-dimensional data such as audio
signals, images, and video. To cope with such high-dimensional data, we
typically rely on low-dimensional models. Manifold models provide a
particularly powerful model that captures the structure of high-dimensional
data when it is governed by a low-dimensional set of parameters. However, these
models do not typically take into account dependencies among multiple sensors.
We thus propose a new joint manifold framework for data ensembles that exploits
such dependencies. We show that simple algorithms can exploit the joint
manifold structure to improve their performance on standard signal processing
applications. Additionally, recent results concerning dimensionality reduction
for manifolds enable us to formulate a network-scalable data compression scheme
that uses random projections of the sensed data. This scheme efficiently fuses
the data from all sensors through the addition of such projections, regardless
of the data modalities and dimensions.
|
0901.0763
|
Distributed Power Allocation in Multi-User Multi-Channel Relay Networks
|
cs.IT math.IT
|
This paper has been withdrawn by the authors as they feel it inappropriate to
publish this paper for the time being.
|
0901.0786
|
Approximate inference on planar graphs using Loop Calculus and Belief
Propagation
|
cs.AI
|
We introduce novel results for approximate inference on planar graphical
models using the loop calculus framework. The loop calculus (Chertkov and
Chernyak, 2006) allows to express the exact partition function of a graphical
model as a finite sum of terms that can be evaluated once the belief
propagation (BP) solution is known. In general, full summation over all
correction terms is intractable. We develop an algorithm for the approach
presented in (Certkov et al., 2008) which represents an efficient truncation
scheme on planar graphs and a new representation of the series in terms of
Pfaffians of matrices. We analyze the performance of the algorithm for the
partition function approximation for models with binary variables and pairwise
interactions on grids and other planar graphs. We study in detail both the loop
series and the equivalent Pfaffian series and show that the first term of the
Pfaffian series for the general, intractable planar model, can provide very
accurate approximations. The algorithm outperforms previous truncation schemes
of the loop series and is competitive with other state-of-the-art methods for
approximate inference.
|
0901.0824
|
A Characterization of Max-Min SIR-Balanced Power Allocation with
Applications
|
cs.IT math.IT
|
We consider a power-controlled wireless network with an established network
topology in which the communication links (transmitter-receiver pairs) are
corrupted by the co-channel interference and background noise. We have fairly
general power constraints since the vector of transmit powers is confined to
belong to an arbitrary convex polytope. The interference is completely
determined by a so-called gain matrix. Assuming irreducibility of this gain
matrix, we provide an elegant characterization of the max-min SIR-balanced
power allocation under such general power constraints. This characterization
gives rise to two types of algorithms for computing the max-min SIR-balanced
power allocation. One of the algorithms is a utility-based power control
algorithm to maximize a weighted sum of the utilities of the link SIRs. Our
results show how to choose the weight vector and utility function so that the
utility-based solution is equal to the solution of the max-min SIR-balancing
problem. The algorithm is not amenable to distributed implementation as the
weights are global variables. In order to mitigate the problem of computing the
weight vector in distributed wireless networks, we point out a saddle point
characterization of the Perron root of some extended gain matrices and discuss
how this characterization can be used in the design of algorithms in which each
link iteratively updates its weight vector in parallel to the power control
recursion. Finally, the paper provides a basis for the development of
distributed power control and beamforming algorithms to find a global solution
of the max-min SIR-balancing problem.
|
0901.0825
|
A new muscle fatigue and recovery model and its ergonomics application
in human simulation
|
cs.RO
|
Although automatic techniques have been employed in manufacturing industries
to increase productivity and efficiency, there are still lots of manual
handling jobs, especially for assembly and maintenance jobs. In these jobs,
musculoskeletal disorders (MSDs) are one of the major health problems due to
overload and cumulative physical fatigue. With combination of conventional
posture analysis techniques, digital human modelling and simulation (DHM)
techniques have been developed and commercialized to evaluate the potential
physical exposures. However, those ergonomics analysis tools are mainly based
on posture analysis techniques, and until now there is still no fatigue index
available in the commercial software to evaluate the physical fatigue easily
and quickly. In this paper, a new muscle fatigue and recovery model is proposed
and extended to evaluate joint fatigue level in manual handling jobs. A special
application case is described and analyzed by digital human simulation
technique.
|
0901.0834
|
Simple Channel Coding Bounds
|
cs.IT math.IT
|
New channel coding converse and achievability bounds are derived for a single
use of an arbitrary channel. Both bounds are expressed using a quantity called
the "smooth 0-divergence", which is a generalization of Renyi's divergence of
order 0. The bounds are also studied in the limit of large block-lengths. In
particular, they combine to give a general capacity formula which is equivalent
to the one derived by Verdu and Han.
|
0901.0948
|
A New Universal Random-Coding Bound for Average Probability Error
Exponent for Multiple-Access Channels
|
cs.IT math.IT
|
In this work, a new upper bound for average error probability of a two-user
discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound
can be universally obtained for all discrete memoryless MACs with given input
and output alphabets. This is the first bound of this type that explicitly uses
the method of expurgation. It is shown that the exponent of this bound is
greater than or equal to those of previously known bounds.
|
0901.1043
|
The Symmetries of the $\pi$-metric
|
cs.IT cs.DM math.CO math.IT math.MG
|
Let V be an n-dimensional vector space over a finite field F_q. We consider
on V the $\pi$-metric recently introduced by K. Feng, L. Xu and F. J.
Hickernell. In this short note we give a complete description of the group of
symmetries of V under the $\pi$-metric.
|
0901.1084
|
When do nonlinear filters achieve maximal accuracy?
|
math.PR cs.IT math.IT
|
The nonlinear filter for an ergodic signal observed in white noise is said to
achieve maximal accuracy if the stationary filtering error vanishes as the
signal to noise ratio diverges. We give a general characterization of the
maximal accuracy property in terms of various systems theoretic notions. When
the signal state space is a finite set explicit necessary and sufficient
conditions are obtained, while the linear Gaussian case reduces to a classic
result of Kwakernaak and Sivan (1972).
|
0901.1144
|
Bayesian Inference Based on Stationary Fokker-Planck Sampling
|
cond-mat.dis-nn cs.NE physics.data-an
|
A novel formalism for Bayesian learning in the context of complex inference
models is proposed. The method is based on the use of the Stationary
Fokker--Planck (SFP) approach to sample from the posterior density. Stationary
Fokker--Planck sampling generalizes the Gibbs sampler algorithm for arbitrary
and unknown conditional densities. By the SFP procedure approximate analytical
expressions for the conditionals and marginals of the posterior can be
constructed. At each stage of SFP, the approximate conditionals are used to
define a Gibbs sampling process, which is convergent to the full joint
posterior. By the analytical marginals efficient learning methods in the
context of Artificial Neural Networks are outlined. Off--line and incremental
Bayesian inference and Maximum Likelihood Estimation from the posterior is
performed in classification and regression examples. A comparison of SFP with
other Monte Carlo strategies in the general problem of sampling from arbitrary
densities is also presented. It is shown that SFP is able to jump large
low--probabilty regions without the need of a careful tuning of any step size
parameter. In fact, the SFP method requires only a small set of meaningful
parameters which can be selected following clear, problem--independent
guidelines. The computation cost of SFP, measured in terms of loss function
evaluations, grows linearly with the given model's dimension.
|
0901.1152
|
A nonclassical symbolic theory of working memory, mental computations,
and mental set
|
cs.AI cs.NE
|
The paper tackles four basic questions associated with human brain as a
learning system. How can the brain learn to (1) mentally simulate different
external memory aids, (2) perform, in principle, any mental computations using
imaginary memory aids, (3) recall the real sensory and motor events and
synthesize a combinatorial number of imaginary events, (4) dynamically change
its mental set to match a combinatorial number of contexts? We propose a
uniform answer to (1)-(4) based on the general postulate that the human
neocortex processes symbolic information in a "nonclassical" way. Instead of
manipulating symbols in a read/write memory, as the classical symbolic systems
do, it manipulates the states of dynamical memory representing different
temporary attributes of immovable symbolic structures stored in a long-term
memory. The approach is formalized as the concept of E-machine. Intuitively, an
E-machine is a system that deals mainly with characteristic functions
representing subsets of memory pointers rather than the pointers themselves.
This nonclassical symbolic paradigm is Turing universal, and, unlike the
classical one, is efficiently implementable in homogeneous neural networks with
temporal modulation topologically resembling that of the neocortex.
|
0901.1162
|
Folded Algebraic Geometric Codes From Galois Extensions
|
cs.IT math.IT
|
We describe a new class of list decodable codes based on Galois extensions of
function fields and present a list decoding algorithm. These codes are obtained
as a result of folding the set of rational places of a function field using
certain elements (automorphisms) from the Galois group of the extension. This
work is an extension of Folded Reed Solomon codes to the setting of Algebraic
Geometric codes. We describe two constructions based on this framework
depending on if the order of the automorphism used to fold the code is large or
small compared to the block length. When the automorphism is of large order,
the codes have polynomially bounded list size in the worst case. This
construction gives codes of rate $R$ over an alphabet of size independent of
block length that can correct a fraction of $1-R-\epsilon$ errors subject to
the existence of asymptotically good towers of function fields with large
automorphisms. The second construction addresses the case when the order of the
element used to fold is small compared to the block length. In this case a
heuristic analysis shows that for a random received word, the expected list
size and the running time of the decoding algorithm are bounded by a polynomial
in the block length. When applied to the Garcia-Stichtenoth tower, this yields
codes of rate $R$ over an alphabet of size
$(\frac{1}{\epsilon^2})^{O(\frac{1}{\epsilon})}$, that can correct a fraction
of $1-R-\epsilon$ errors.
|
0901.1230
|
Logical Algorithms meets CHR: A meta-complexity result for Constraint
Handling Rules with rule priorities
|
cs.PL cs.AI cs.CC
|
This paper investigates the relationship between the Logical Algorithms
language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR).
We present a translation schema from LA to CHR-rp: CHR with rule priorities,
and show that the meta-complexity theorem for LA can be applied to a subset of
CHR-rp via inverse translation. Inspired by the high-level implementation
proposal for Logical Algorithm by Ganzinger and McAllester and based on a new
scheduling algorithm, we propose an alternative implementation for CHR-rp that
gives strong complexity guarantees and results in a new and accurate
meta-complexity theorem for CHR-rp. It is furthermore shown that the
translation from Logical Algorithms to CHR-rp combined with the new CHR-rp
implementation, satisfies the required complexity for the Logical Algorithms
meta-complexity result to hold.
|
0901.1244
|
Constructions of Quasi-Twisted Two-Weight Codes
|
cs.IT math.IT
|
A code is said to be two-weight if the non-zero codewords have only two
different a weight w1 and w2. Two-weight codes are closely related to strongly
regular graphs. In this paper. It is shown that a consta-cyclic code of
composite length can be put in the quasi-twisted form. Based on this
transformation, a new construction method of quasi-twisted (QT) two-weight
codes is presented. A large amount of QT two-weight codes are found, and some
new codes are also constructed.
|
0901.1287
|
Infinite families of recursive formulas generating power moments of
Kloosterman sums: O^- (2n, 2^r) case
|
math.NT cs.IT math.IT
|
In this paper, we construct eight infinite families of binary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the special orthogonal group $SO^-(2n,2^r)$. Then we obtain four
infinite families of recursive formulas for the power moments of Kloosterman
sums and four those of 2-dimensional Kloosterman sums in terms of the
frequencies of weights in the codes. This is done via Pless power moment
identity and by utilizing the explicit expressions of exponential sums over
those double cosets related to the evaluations of "Gauss sums" for the
orthogonal groups $O^-(2n,2^r)$
|
0901.1288
|
Power-Controlled Feedback and Training for Two-way MIMO Channels
|
cs.IT math.IT
|
Most communication systems use some form of feedback, often related to
channel state information. The common models used in analyses either assume
perfect channel state information at the receiver and/or noiseless state
feedback links. However, in practical systems, neither is the channel estimate
known perfectly at the receiver and nor is the feedback link perfect. In this
paper, we study the achievable diversity multiplexing tradeoff using i.i.d.
Gaussian codebooks, considering the errors in training the receiver and the
errors in the feedback link for FDD systems, where the forward and the feedback
are independent MIMO channels.
Our key result is that the maximum diversity order with one-bit of feedback
information is identical to systems with more feedback bits. Thus,
asymptotically in $\mathsf{SNR}$, more than one bit of feedback does not
improve the system performance at constant rates. Furthermore, the one-bit
diversity-multiplexing performance is identical to the system which has perfect
channel state information at the receiver along with noiseless feedback link.
This achievability uses novel concepts of power controlled feedback and
training, which naturally surface when we consider imperfect channel estimation
and noisy feedback links. In the process of evaluating the proposed training
and feedback protocols, we find an asymptotic expression for the joint
probability of the $\mathsf{SNR}$ exponents of eigenvalues of the actual
channel and the estimated channel which may be of independent interest.
|
0901.1289
|
N-norm and N-conorm in Neutrosophic Logic and Set, and the Neutrosophic
Topologies
|
cs.AI
|
In this paper we present the N-norms/N-conorms in neutrosophic logic and set
as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an
extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic
Topologies.
|
0901.1315
|
Stochastic Volatility Models Including Open, Close, High and Low Prices
|
q-fin.ST cs.CE cs.NA
|
Mounting empirical evidence suggests that the observed extreme prices within
a trading period can provide valuable information about the volatility of the
process within that period. In this paper we define a class of stochastic
volatility models that uses opening and closing prices along with the minimum
and maximum prices within a trading period to infer the dynamics underlying the
volatility process of asset prices and compares it with similar models that
have been previously presented in the literature. The paper also discusses
sequential Monte Carlo algorithms to fit this class of models and illustrates
its features using both a simulation study and data form the SP500 index.
|
0901.1408
|
A Message-Passing Approach for Joint Channel Estimation, Interference
Mitigation and Decoding
|
cs.IT math.IT
|
Channel uncertainty and co-channel interference are two major challenges in
the design of wireless systems such as future generation cellular networks.
This paper studies receiver design for a wireless channel model with both
time-varying Rayleigh fading and strong co-channel interference of similar form
as the desired signal. It is assumed that the channel coefficients of the
desired signal can be estimated through the use of pilots, whereas no pilot for
the interference signal is available, as is the case in many practical wireless
systems. Because the interference process is non-Gaussian, treating it as
Gaussian noise generally often leads to unacceptable performance. In order to
exploit the statistics of the interference and correlated fading in time, an
iterative message-passing architecture is proposed for joint channel
estimation, interference mitigation and decoding. Each message takes the form
of a mixture of Gaussian densities where the number of components is limited so
that the overall complexity of the receiver is constant per symbol regardless
of the frame and code lengths. Simulation of both coded and uncoded systems
shows that the receiver performs significantly better than conventional
receivers with linear channel estimation, and is robust with respect to
mismatch in the assumed fading model.
|
0901.1444
|
Algebraic gossip on Arbitrary Networks
|
cs.IT math.IT
|
Consider a network of nodes where each node has a message to communicate to
all other nodes. For this communication problem, we analyze a gossip based
protocol where coded messages are exchanged. This problem was studied by Aoyama
and Shah where a bound to the dissemination time based on the spectral
properties of the underlying communication graph is provided. Our contribution
is a uniform bound that holds for arbitrary networks.
|
0901.1473
|
Communication over Individual Channels
|
cs.IT math.IT
|
We consider the problem of communicating over a channel for which no
mathematical model is specified. We present achievable rates as a function of
the channel input and output known a-posteriori for discrete and continuous
channels, as well as a rate-adaptive scheme employing feedback which achieves
these rates asymptotically without prior knowledge of the channel behavior.
|
0901.1492
|
An information inequality for the BSSC channel
|
cs.IT math.IT
|
We establish an information theoretic inequality concerning the binary
skew-symmetric broadcast channel that was conjectured by one of the authors.
This inequality helps to quantify the gap between the sum rate obtained by the
inner bound and outer bound for the binary skew-symmetric broadcast channel.
|
0901.1503
|
A Greedy Omnidirectional Relay Scheme
|
cs.IT math.IT
|
A greedy omnidirectional relay scheme is developed, and the corresponding
achievable rate region is obtained for the all-source all-cast problem. The
discussions are first based on the general discrete memoryless channel model,
and then applied to the additive white Gaussian noise (AWGN) models, with both
full-duplex and half-duplex modes.
|
0901.1610
|
Towards a Framework for Observing Artificial Evolutionary Systems
|
cs.NE cs.MA
|
Establishing the emergence of evolutionary behavior as a defining
characteristic of 'life' is a major step in the Artificial life (ALife)
studies. We present here an abstract formal framework for this aim based upon
the notion of high-level observations made on the ALife model at hand during
its simulations. An observation process is defined as a computable
transformation from the underlying dynamic structure of the model universe to a
tuple consisting of abstract components needed to establish the evolutionary
processes in the model. Starting with defining entities and their evolutionary
relationships observed during the simulations of the model, the framework
prescribes a series of definitions, followed by the axioms (conditions) that
must be met in order to establish the level of evolutionary behavior in the
model. The examples of Cellular Automata based Langton Loops and Lambda
calculus based Algorithmic Chemistry are used to illustrate the framework.
Generic design suggestions for the ALife research are also drawn based upon the
framework design and case study analysis.
|
0901.1655
|
Multishot Codes for Network Coding: Bounds and a Multilevel Construction
|
cs.IT math.IT
|
The subspace channel was introduced by Koetter and Kschischang as an adequate
model for the communication channel from the source node to a sink node of a
multicast network that performs random linear network coding. So far, attention
has been given to one-shot subspace codes, that is, codes that use the subspace
channel only once. In contrast, this paper explores the idea of using the
subspace channel more than once and investigates the so called multishot
subspace codes. We present definitions for the problem, a motivating example,
lower and upper bounds for the size of codes, and a multilevel construction of
codes based on block-coded modulation.
|
0901.1683
|
New Bounds for Binary and Ternary Overloaded CDMA
|
cs.IT cs.DM math.CO math.IT
|
In this paper, we study binary and ternary matrices that are used for CDMA
applications that are injective on binary or ternary user vectors. In other
words, in the absence of additive noise, the interference of overloaded CDMA
can be removed completely. Some new algorithms are proposed for constructing
such matrices. Also, using an information theoretic approach, we conjecture the
extent to which such CDMA matrix codes exist. For overloaded case, we also show
that some of the codes derived from our algorithms perform better than the
binary Welch Bound Equality codes; the decoding is ML but of low complexity.
|
0901.1694
|
Degrees of Freedom of a Communication Channel: Using Generalised
Singular Values
|
cs.IT math.IT
|
A fundamental problem in any communication system is: given a communication
channel between a transmitter and a receiver, how many "independent" signals
can be exchanged between them? Arbitrary communication channels that can be
described by linear compact channel operators mapping between normed spaces are
examined in this paper. The (well-known) notions of degrees of freedom at level
$\epsilon$ and essential dimension of such channels are developed in this
general setting. We argue that the degrees of freedom at level $\epsilon$ and
the essential dimension fundamentally limit the number of independent signals
that can be exchanged between the transmitter and the receiver. We also
generalise the concept of singular values of compact operators to be applicable
to compact operators defined on arbitrary normed spaces which do not
necessarily carry a Hilbert space structure. We show how these generalised
singular values can be used to calculate the degrees of freedom at level
$\epsilon$ and the essential dimension of compact operators that describe
communication channels. We describe physically realistic channels that require
such general channel models.
|
0901.1695
|
On the Degrees-of-Freedom of the K-User Gaussian Interference Channel
|
cs.IT math.IT
|
The degrees-of-freedom of a K-user Gaussian interference channel (GIFC) has
been defined to be the multiple of (1/2)log_2(P) at which the maximum sum of
achievable rates grows with increasing P. In this paper, we establish that the
degrees-of-freedom of three or more user, real, scalar GIFCs, viewed as a
function of the channel coefficients, is discontinuous at points where all of
the coefficients are non-zero rational numbers. More specifically, for all K>2,
we find a class of K-user GIFCs that is dense in the GIFC parameter space for
which K/2 degrees-of-freedom are exactly achievable, and we show that the
degrees-of-freedom for any GIFC with non-zero rational coefficients is strictly
smaller than K/2. These results are proved using new connections with number
theory and additive combinatorics.
|
0901.1703
|
Pilot Contamination and Precoding in Multi-Cell TDD Systems
|
cs.IT math.IT
|
This paper considers a multi-cell multiple antenna system with precoding used
at the base stations for downlink transmission. For precoding at the base
stations, channel state information (CSI) is essential at the base stations. A
popular technique for obtaining this CSI in time division duplex (TDD) systems
is uplink training by utilizing the reciprocity of the wireless medium. This
paper mathematically characterizes the impact that uplink training has on the
performance of such multi-cell multiple antenna systems. When non-orthogonal
training sequences are used for uplink training, the paper shows that the
precoding matrix used by the base station in one cell becomes corrupted by the
channel between that base station and the users in other cells in an
undesirable manner. This paper analyzes this fundamental problem of pilot
contamination in multi-cell systems. Furthermore, it develops a new multi-cell
MMSE-based precoding method that mitigate this problem. In addition to being a
linear precoding method, this precoding method has a simple closed-form
expression that results from an intuitive optimization problem formulation.
Numerical results show significant performance gains compared to certain
popular single-cell precoding methods.
|
0901.1705
|
Rate-Distortion with Side-Information at Many Decoders
|
cs.IT math.IT
|
We present a new inner bound for the rate region of the $t$-stage
successive-refinement problem with side-information. We also present a new
upper bound for the rate-distortion function for lossy-source coding with
multiple decoders and side-information. Characterising this rate-distortion
function is a long-standing open problem, and it is widely believed that the
tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper
"Rate Distortion when Side Information may be Absent", \emph{IEEE Trans.
Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.
|
0901.1708
|
A statistical mechanical interpretation of instantaneous codes
|
cs.IT math.IT
|
In this paper we develop a statistical mechanical interpretation of the
noiseless source coding scheme based on an absolutely optimal instantaneous
code. The notions in statistical mechanics such as statistical mechanical
entropy, temperature, and thermal equilibrium are translated into the context
of noiseless source coding. Especially, it is discovered that the temperature 1
corresponds to the average codeword length of an instantaneous code in this
statistical mechanical interpretation of noiseless source coding scheme. This
correspondence is also verified by the investigation using box-counting
dimension. Using the notion of temperature and statistical mechanical
arguments, some information-theoretic relations can be derived in the manner
which appeals to intuition.
|
0901.1732
|
Feedback Communication over Individual Channels
|
cs.IT math.IT
|
We consider the problem of communicating over a channel for which no
mathematical model is specified. We present achievable rates as a function of
the channel input and output sequences known a-posteriori for discrete and
continuous channels. Furthermore we present a rate-adaptive scheme employing
feedback which achieves these rates asymptotically without prior knowledge of
the channel behavior.
|
0901.1737
|
Power Adaptive Feedback Communication over an Additive Individual Noise
Sequence Channel
|
cs.IT math.IT
|
We consider a real-valued additive channel with an individual unknown noise
sequence. We present a simple sequential communication scheme based on the
celebrated Schalkwijk-Kailath scheme, which varies the transmit power according
to the power of the sequence, so that asymptotically the relation between the
SNR and the rate matches the Gaussian channel capacity 1/2 log(1+SNR)for almost
every noise sequence.
|
0901.1753
|
A Channel Coding Perspective of Recommendation Systems
|
cs.IT math.IT
|
Motivated by recommendation systems, we consider the problem of estimating
block constant binary matrices (of size $m \times n$) from sparse and noisy
observations. The observations are obtained from the underlying block constant
matrix after unknown row and column permutations, erasures, and errors. We
derive upper and lower bounds on the achievable probability of error. For fixed
erasure and error probability, we show that there exists a constant $C_1$ such
that if the cluster sizes are less than $C_1 \ln(mn)$, then for any algorithm
the probability of error approaches one as $m, n \tends \infty$. On the other
hand, we show that a simple polynomial time algorithm gives probability of
error diminishing to zero provided the cluster sizes are greater than $C_2
\ln(mn)$ for a suitable constant $C_2$.
|
0901.1762
|
A Tight Estimate for Decoding Error-Probability of LT Codes Using
Kovalenko's Rank Distribution
|
cs.IT cs.DM math.CO math.IT
|
A new approach for estimating the Decoding Error-Probability (DEP) of LT
codes with dense rows is derived by using the conditional Kovalenko's rank
distribution. The estimate by the proposed approach is very close to the DEP
approximated by Gaussian Elimination, and is significantly less complex. As a
key application, we utilize the estimates for obtaining optimal LT codes with
dense rows, whose DEP is very close to the Kovalenko's Full-Rank Limit within a
desired error-bound. Experimental evidences which show the viability of the
estimates are also provided.
|
0901.1821
|
Semidefinite representation of convex hulls of rational varieties
|
math.OC cs.SY math.AG
|
Using elementary duality properties of positive semidefinite moment matrices
and polynomial sum-of-squares decompositions, we prove that the convex hull of
rationally parameterized algebraic varieties is semidefinite representable
(that is, it can be represented as a projection of an affine section of the
cone of positive semidefinite matrices) in the case of (a) curves; (b)
hypersurfaces parameterized by quadratics; and (c) hypersurfaces parameterized
by bivariate quartics; all in an ambient space of arbitrary dimension.
|
0901.1824
|
A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes
Fields of Even Degree
|
cs.IT math.IT
|
Functions with low differential uniformity can be used as the s-boxes of
symmetric cryptosystems as they have good resistance to differential attacks.
The AES (Advanced Encryption Standard) uses a differentially-4 uniform function
called the inverse function. Any function used in a symmetric cryptosystem
should be a permutation. Also, it is required that the function is highly
nonlinear so that it is resistant to Matsui's linear attack. In this article we
demonstrate that a highly nonlinear permutation discovered by Hans Dobbertin
has differential uniformity of four and hence, with respect to differential and
linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem
as the inverse function.
|
0901.1827
|
Triple-Error-Correcting BCH-Like Codes
|
cs.IT math.IT
|
The binary primitive triple-error-correcting BCH code is a cyclic code of
minimum distance 7 with generator polynomial having zeros $\alpha$, $\alpha^3$
and $\alpha^5$ where $\alpha$ is a primitive root of unity. The zero set of the
code is said to be {1,3,5}. In the 1970's Kasami showed that one can construct
similar triple-error-correcting codes using zero sets consisting of different
triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new
triples leading to triple-error-correcting codes. In this paper a new such
triple is presented. In addition a new method is presented that may be of
interest in finding further such triples.
|
0901.1853
|
Binary Causal-Adversary Channels
|
cs.IT math.IT
|
In this work we consider the communication of information in the presence of
a causal adversarial jammer. In the setting under study, a sender wishes to
communicate a message to a receiver by transmitting a codeword x=(x_1,...,x_n)
bit-by-bit over a communication channel. The adversarial jammer can view the
transmitted bits x_i one at a time, and can change up to a p-fraction of them.
However, the decisions of the jammer must be made in an online or causal
manner. Namely, for each bit x_i the jammer's decision on whether to corrupt it
or not (and on how to change it) must depend only on x_j for j <= i. This is in
contrast to the "classical" adversarial jammer which may base its decisions on
its complete knowledge of x. We present a non-trivial upper bound on the amount
of information that can be communicated. We show that the achievable rate can
be asymptotically no greater than min{1-H(p),(1-4p)^+}. Here H(.) is the binary
entropy function, and (1-4p)^+ equals 1-4p for p < 0.25, and 0 otherwise.
|
0901.1864
|
Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using
Reactive Tabu Search
|
cs.IT math.IT
|
Non-orthogonal space-time block codes (STBC) with {\em large dimensions} are
attractive because they can simultaneously achieve both high spectral
efficiencies (same spectral efficiency as in V-BLAST for a given number of
transmit antennas) {\em as well as} full transmit diversity. Decoding of
non-orthogonal STBCs with large dimensions has been a challenge. In this paper,
we present a reactive tabu search (RTS) based algorithm for decoding
non-orthogonal STBCs from cyclic division algebras (CDA) having large
dimensions. Under i.i.d fading and perfect channel state information at the
receiver (CSIR), our simulation results show that RTS based decoding of
$12\times 12$ STBC from CDA and 4-QAM with 288 real dimensions achieves $i)$
$10^{-3}$ uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance,
and $ii)$ a coded BER performance close to within about 5 dB of the theoretical
MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz.
RTS is shown to achieve near SISO AWGN performance with less number of
dimensions than with LAS algorithm (which we reported recently) at some extra
complexity than LAS. We also report good BER performance of RTS when i.i.d
fading and perfect CSIR assumptions are relaxed by considering a spatially
correlated MIMO channel model, and by using a training based iterative RTS
decoding/channel estimation scheme.
|
0901.1866
|
Capacity Achieving Codes From Randomness Condensers
|
cs.IT math.IT
|
We establish a general framework for construction of small ensembles of
capacity achieving linear codes for a wide range of (not necessarily
memoryless) discrete symmetric channels, and in particular, the binary erasure
and symmetric channels. The main tool used in our constructions is the notion
of randomness extractors and lossless condensers that are regarded as central
tools in theoretical computer science. Same as random codes, the resulting
ensembles preserve their capacity achieving properties under any change of
basis. Using known explicit constructions of condensers, we obtain specific
ensembles whose size is as small as polynomial in the block length. By applying
our construction to Justesen's concatenation scheme (Justesen, 1972) we obtain
explicit capacity achieving codes for BEC (resp., BSC) with almost linear time
encoding and almost linear time (resp., quadratic time) decoding and
exponentially small error probability.
|
0901.1867
|
Belief Propagation Based Decoding of Large Non-Orthogonal STBCs
|
cs.IT math.IT
|
In this paper, we present a belief propagation (BP) based algorithm for
decoding non-orthogonal space-time block codes (STBC) from cyclic division
algebras (CDA) having {\em large dimensions}. The proposed approach involves
message passing on Markov random field (MRF) representation of the STBC MIMO
system. Adoption of BP approach to decode non-orthogonal STBCs of large
dimensions has not been reported so far. Our simulation results show that the
proposed BP-based decoding achieves increasingly closer to SISO AWGN
performance for increased number of dimensions. In addition, it also achieves
near-capacity turbo coded BER performance; for e.g., with BP decoding of
$24\times 24$ STBC from CDA using BPSK (i.e., 576 real dimensions) and rate-1/2
turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close
to within just about 2.5 dB from the theoretical MIMO capacity is achieved.
|
0901.1869
|
Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs Using PDA
|
cs.IT math.IT
|
Non-orthogonal space-time block codes (STBC) from cyclic division algebras
(CDA) having large dimensions are attractive because they can simultaneously
achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST
for a given number of transmit antennas) {\em as well as} full transmit
diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has
been a challenge. In this paper, we present a probabilistic data association
(PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions.
Our simulation results show that the proposed PDA-based algorithm achieves near
SISO AWGN uncoded BER as well as near-capacity coded BER (within about 5 dB of
the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the
effect of spatial correlation on the BER, and show that the performance loss
due to spatial correlation can be alleviated by providing more receive spatial
dimensions. We report good BER performance when a training-based iterative
decoding/channel estimation is used (instead of assuming perfect channel
knowledge) in channels with large coherence times. A comparison of the
performances of the PDA algorithm and the likelihood ascent search (LAS)
algorithm (reported in our recent work) is also presented.
|
0901.1886
|
Efficient erasure decoding of Reed-Solomon codes
|
cs.IT cs.DS math.IT
|
We present a practical algorithm to decode erasures of Reed-Solomon codes
over the q elements binary field in O(q \log_2^2 q) time where the constant
implied by the O-notation is very small. Asymptotically fast algorithms based
on fast polynomial arithmetic were already known, but even if their complexity
is similar, they are mostly impractical. By comparison our algorithm uses only
a few Walsh transforms and has been easily implemented.
|
0901.1892
|
A New Achievable Rate Region for the Discrete Memoryless Multiple-Access
Channel with Noiseless Feedback
|
cs.IT math.IT
|
A new single-letter achievable rate region is proposed for the two-user
discrete memoryless multiple-access channel(MAC) with noiseless feedback. The
proposed region includes the Cover-Leung rate region [1], and it is shown that
the inclusion is strict. The proof uses a block-Markov superposition strategy
based on the observation that the messages of the two users are correlated
given the feedback. The rates of transmission are too high for each encoder to
decode the other's message directly using the feedback, so they transmit
correlated information in the next block to learn the message of one another.
They then cooperate in the following block to resolve the residual uncertainty
of the decoder. The coding scheme may be viewed as a natural generalization of
the Cover-Leung scheme with a delay of one extra block and a pair of additional
auxiliary random variables. We compute the proposed rate region for two
different MACs and compare the results with other known rate regions for the
MAC with feedback. Finally, we show how the coding scheme can be extended to
obtain larger rate regions with more auxiliary random variables.
|
0901.1898
|
Efficient and Guaranteed Rank Minimization by Atomic Decomposition
|
math.NA cs.IT math.IT
|
Recht, Fazel, and Parrilo provided an analogy between rank minimization and
$\ell_0$-norm minimization. Subject to the rank-restricted isometry property,
nuclear norm minimization is a guaranteed algorithm for rank minimization. The
resulting semidefinite formulation is a convex problem but in practice the
algorithms for it do not scale well to large instances. Instead, we explore
missing terms in the analogy and propose a new algorithm which is
computationally efficient and also has a performance guarantee. The algorithm
is based on the atomic decomposition of the matrix variable and extends the
idea in the CoSaMP algorithm for $\ell_0$-norm minimization. Combined with the
recent fast low rank approximation of matrices based on randomization, the
proposed algorithm can efficiently handle large scale rank minimization
problems.
|
0901.1900
|
Performance bounds on compressed sensing with Poisson noise
|
cs.IT math.IT
|
This paper describes performance bounds for compressed sensing in the
presence of Poisson noise when the underlying signal, a vector of Poisson
intensities, is sparse or compressible (admits a sparse approximation). The
signal-independent and bounded noise models used in the literature to analyze
the performance of compressed sensing do not accurately model the effects of
Poisson noise. However, Poisson noise is an appropriate noise model for a
variety of applications, including low-light imaging, where sensing hardware is
large or expensive, and limiting the number of measurements collected is
important. In this paper, we describe how a feasible positivity-preserving
sensing matrix can be constructed, and then analyze the performance of a
compressed sensing reconstruction approach for Poisson data that minimizes an
objective function consisting of a negative Poisson log likelihood term and a
penalty term which could be used as a measure of signal sparsity.
|
0901.1904
|
Joint universal lossy coding and identification of stationary mixing
sources with general alphabets
|
cs.IT cs.LG math.IT
|
We consider the problem of joint universal variable-rate lossy coding and
identification for parametric classes of stationary $\beta$-mixing sources with
general (Polish) alphabets. Compression performance is measured in terms of
Lagrangians, while identification performance is measured by the variational
distance between the true source and the estimated source. Provided that the
sources are mixing at a sufficiently fast rate and satisfy certain smoothness
and Vapnik-Chervonenkis learnability conditions, it is shown that, for bounded
metric distortions, there exist universal schemes for joint lossy compression
and identification whose Lagrangian redundancies converge to zero as $\sqrt{V_n
\log n /n}$ as the block length $n$ tends to infinity, where $V_n$ is the
Vapnik-Chervonenkis dimension of a certain class of decision regions defined by
the $n$-dimensional marginal distributions of the sources; furthermore, for
each $n$, the decoder can identify $n$-dimensional marginal of the active
source up to a ball of radius $O(\sqrt{V_n\log n/n})$ in variational distance,
eventually with probability one. The results are supplemented by several
examples of parametric sources satisfying the regularity conditions.
|
0901.1905
|
Achievability results for statistical learning under communication
constraints
|
cs.IT cs.LG math.IT
|
The problem of statistical learning is to construct an accurate predictor of
a random variable as a function of a correlated random variable on the basis of
an i.i.d. training sample from their joint distribution. Allowable predictors
are constrained to lie in some specified class, and the goal is to approach
asymptotically the performance of the best predictor in the class. We consider
two settings in which the learning agent only has access to rate-limited
descriptions of the training data, and present information-theoretic bounds on
the predictor performance achievable in the presence of these communication
constraints. Our proofs do not assume any separation structure between
compression and learning and rely on a new class of operational criteria
specifically tailored to joint design of encoders and learning algorithms in
rate-constrained settings.
|
0901.1924
|
Interference Avoidance Game in the Gaussian Interference Channel:
Sub-Optimal and Optimal Schemes
|
cs.IT math.IT
|
This paper considers a distributed interference avoidance problem employing
frequency assignment in the Gaussian interference channel (IC). We divide the
common channel into several subchannels and each user chooses the subchannel
with less amount of interference from other users as the transmit channel. This
mechanism named interference avoidance in this paper can be modeled as a
competitive game model. And a completely autonomous distributed iterative
algorithm called Tdistributed interference avoidance algorithm (DIA) is adopted
to achieve the Nash equilibriumT (NE) of the game. Due to the self-optimum, DIA
is a sub-optimal algorithm. Therefore, through introducing an optimal
compensation into the competitive game model, we successfully develop a
compensation-based game model to approximate the optimal interference avoidance
problem. Moreover, an optimal algorithm called iterative optimal interference
avoidance algorithm (IOIA) is proposed to reach the optimality of the
interference avoidance scheme. We analyze the implementation complexities of
the two algorithms. We also give the proof on the convergence of the proposed
algorithms. The performance upper bound and lower bound are also derived for
the proposed algorithms. The simulation results show that IOIA does reach the
optimality under condition of interference avoidance mechanism.
|
0901.1936
|
A Lower Bound on the Capacity of Wireless Erasure Networks with Random
Node Locations
|
cs.IT cs.NI math.IT math.PR
|
In this paper, a lower bound on the capacity of wireless ad hoc erasure
networks is derived in closed form in the canonical case where $n$ nodes are
uniformly and independently distributed in the unit area square. The bound
holds almost surely and is asymptotically tight. We assume all nodes have fixed
transmit power and hence two nodes should be within a specified distance $r_n$
of each other to overcome noise. In this context, interference determines
outages, so we model each transmitter-receiver pair as an erasure channel with
a broadcast constraint, i.e. each node can transmit only one signal across all
its outgoing links. A lower bound of $\Theta(n r_n)$ for the capacity of this
class of networks is derived. If the broadcast constraint is relaxed and each
node can send distinct signals on distinct outgoing links, we show that the
gain is a function of $r_n$ and the link erasure probabilities, and is at most
a constant if the link erasure probabilities grow sufficiently large with $n$.
Finally, the case where the erasure probabilities are themselves random
variables, for example due to randomness in geometry or channels, is analyzed.
We prove somewhat surprisingly that in this setting, variability in erasure
probabilities increases network capacity.
|
0901.1945
|
A mathematical proof of the existence of trends in financial time series
|
q-fin.ST cs.CE math.CA math.PR q-fin.CP stat.AP
|
We are settling a longstanding quarrel in quantitative finance by proving the
existence of trends in financial time series thanks to a theorem due to P.
Cartier and Y. Perrin, which is expressed in the language of nonstandard
analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard
Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might
coexist with some altered random walk paradigm and efficient market hypothesis,
seem nevertheless difficult to reconcile with the celebrated Black-Scholes
model. They are estimated via recent techniques stemming from control and
signal theory. Several quite convincing computer simulations on the forecast of
various financial quantities are depicted. We conclude by discussing the r\^ole
of probability theory.
|
0901.1954
|
Two-Way Relay Channels: Error Exponents and Resource Allocation
|
cs.IT math.IT
|
In a two-way relay network, two terminals exchange information over a shared
wireless half-duplex channel with the help of a relay. Due to its fundamental
and practical importance, there has been an increasing interest in this
channel. However, surprisingly, there has been little work that characterizes
the fundamental tradeoff between the communication reliability and transmission
rate across all signal-to-noise ratios. In this paper, we consider
amplify-and-forward (AF) two-way relaying due to its simplicity. We first
derive the random coding error exponent for the link in each direction. From
the exponent expression, the capacity and cutoff rate for each link are also
deduced. We then put forth the notion of the bottleneck error exponent, which
is the worst exponent decay between the two links, to give us insight into the
fundamental tradeoff between the rate pair and information-exchange reliability
of the two terminals. As applications of the error exponent analysis, we
present two optimal resource allocations to maximize the bottleneck error
exponent: i) the optimal rate allocation under a sum-rate constraint and its
closed-form quasi-optimal solution that requires only knowledge of the capacity
and cutoff rate of each link; and ii) the optimal power allocation under a
total power constraint, which is formulated as a quasi-convex optimization
problem. Numerical results verify our analysis and the effectiveness of the
optimal rate and power allocations in maximizing the bottleneck error exponent.
|
0901.1964
|
Optimal Detector for Channels with Non-Gaussian Interference
|
cs.IT math.IT
|
The detection problem in the Gaussian interference channel is addressed, when
transmitters employ non-Gaussian schemes designed for the single-user Gaussian
channel. A structure consisting of a separate symbol-by-symbol detector and a
hard decoder is considered. Given this structure, an optimal detector is
presented that is compared to an interferenceunaware conventional detector, an
interference-aware successive interference cancellation (SIC) detector, and a
minimum-distance detector. It is demonstrated analytically and by simulation
that the optimal detector outperforms both the conventional and the SIC
detector, and that it attains decreasing symbol error rates even in the
presence of strong interference. Moreover, the minimum-distance detector
performs almost as well as the optimal detector in most scenarios and is
significantly less complex.
|
0901.1971
|
Decoding Frequency Permutation Arrays under Infinite norm
|
cs.IT math.IT
|
A frequency permutation array (FPA) of length $n=m\lambda$ and distance $d$
is a set of permutations on a multiset over $m$ symbols, where each symbol
appears exactly $\lambda$ times and the distance between any two elements in
the array is at least $d$. FPA generalizes the notion of permutation array. In
this paper, under the distance metric $\ell_\infty$-norm, we first prove lower
and upper bounds on the size of FPA. Then we give a construction of FPA with
efficient encoding and decoding capabilities. Moreover, we show our design is
locally decodable, i.e., we can decode a message bit by reading at most
$\lambda+1$ symbols, which has an interesting application for private
information retrieval.
|
0901.1988
|
Many-Help-One Problem for Gaussian Sources with a Tree Structure on
their Correlation
|
cs.IT math.IT
|
In this paper we consider the separate coding problem for $L+1$ correlated
Gaussian memoryless sources. We deal with the case where $L$ separately encoded
data of sources work as side information at the decoder for the reconstruction
of the remaining source. The determination problem of the rate distortion
region for this system is the so called many-help-one problem and has been
known as a highly challenging problem. The author determined the rate
distortion region in the case where the $L$ sources working as partial side
information are conditionally independent if the remaining source we wish to
reconstruct is given. This condition on the correlation is called the CI
condition. In this paper we extend the author's previous result to the case
where $L+1$ sources satisfy a kind of tree structure on their correlation. We
call this tree structure of information sources the TS condition, which
contains the CI condition as a special case. In this paper we derive an
explicit outer bound of the rate distortion region when information sources
satisfy the TS condition. We further derive an explicit sufficient condtion for
this outer bound to be tight. In particular, we determine the sum rate part of
the rate distortion region for the case where information sources satisfy the
TS condition. For some class of Gaussian sources with the TS condition we
derive an explicit recursive formula of this sum rate part.
|
0901.2042
|
Average Capacity Analysis of Continuous-Time Frequency-Selective
Rayleigh Fading Channels with Correlated Scattering Using Majorization
|
cs.IT math.IT
|
Correlated scattering occurs naturally in frequency-selective fading channels
and its impact on the performance needs to be understood. In particular, we
answer the question whether the uncorrelated scattering model leads to an
optimistic or pessimistic estimation of the actual average capacity. In the
paper, we use majorization for functions to show that the average rate with
perfectly informed receiver is largest for uncorrelated scattering if the
transmitter is uninformed. If the transmitter knows the channel statistics, it
can exploit this knowledge. We show that for small SNR, the behavior is
opposite, uncorrelated scattering leads to a lower bound on the average
capacity. Finally, we provide an example of the theoretical results for an
attenuated Ornstein-Uhlenbeck process including illustrations.
|
0901.2062
|
Notes on Reed-Muller Codes
|
cs.IT math.IT
|
In this paper, we consider the Reed-Muller (RM) codes. For the first order RM
code, we prove that it is unique in the sense that any linear code with the
same length, dimension and minimum distance must be the first order RM code;
For the second order RM code, we give a constructive linear sub-code family for
the case when m is even. This is an extension of Corollary 17 of Ch. 15 in the
coding book by MacWilliams and Sloane. Furthermore, we show that the specified
sub-codes of length <= 256 have minimum distance equal to the upper bound or
the best known lower bound for all linear codes of the same length and
dimension. As another interesting result, we derive an additive commutative
group of the symplectic matrices with full rank.
|
0901.2082
|
On Source-Channel Separation in Networks
|
cs.IT math.IT
|
This paper has been withdrawn.
|
0901.2090
|
Two-Bit Message Passing Decoders for LDPC Codes Over the Binary
Symmetric Channel
|
cs.IT math.IT
|
In this paper, we consider quantized decoding of LDPC codes on the binary
symmetric channel. The binary message passing algorithms, while allowing
extremely fast hardware implementation, are not very attractive from the
perspective of performance. More complex decoders such as the ones based on
belief propagation exhibit superior performance but lead to slower decoders.
The approach in this paper is to consider message passing decoders that have
larger message alphabet (thereby providing performance improvement) as well as
low complexity (thereby ensuring fast decoding). We propose a class of
message-passing decoders whose messages are represented by two bits. The
thresholds for various decoders in this class are derived using density
evolution. The problem of correcting a fixed number of errors assumes
significance in the error floor region. For a specific decoder, the sufficient
conditions for correcting all patterns with up to three errors are derived. By
comparing these conditions and thresholds to the similar ones when Gallager B
decoder is used, we emphasize the advantage of decoding on a higher number of
bits, even if the channel observation is still one bit.
|
0901.2094
|
The Sensing Capacity of Sensor Networks
|
cs.IT math.IT
|
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.
|
0901.2120
|
Invertible Extractors and Wiretap Protocols
|
cs.IT math.IT
|
A wiretap protocol is a pair of randomized encoding and decoding functions
such that knowledge of a bounded fraction of the encoding of a message reveals
essentially no information about the message, while knowledge of the entire
encoding reveals the message using the decoder. In this paper we study the
notion of efficiently invertible extractors and show that a wiretap protocol
can be constructed from such an extractor. We will then construct invertible
extractors for symbol-fixing, affine, and general sources and apply them to
create wiretap protocols with asymptotically optimal trade-offs between their
rate (ratio of the length of the message versus its encoding) and resilience
(ratio of the observed positions of the encoding and the length of the
encoding). We will then apply our results to create wiretap protocols for
challenging communication problems, such as active intruders who change
portions of the encoding, network coding, and intruders observing arbitrary
boolean functions of the encoding.
As a by-product of our constructions we obtain new explicit extractors for a
restricted family of affine sources over large fields (that in particular
generalizes the notion of symbol-fixing sources) which is of independent
interest. These extractors are able to extract the entire source entropy with
zero error.
Keywords: Wiretap Channel, Extractors, Network Coding, Active Intrusion,
Exposure Resilient Cryptography.
|
0901.2130
|
Hiding Quiet Solutions in Random Constraint Satisfaction Problems
|
cond-mat.stat-mech cond-mat.dis-nn cs.AI cs.CC
|
We study constraint satisfaction problems on the so-called 'planted' random
ensemble. We show that for a certain class of problems, e.g. graph coloring,
many of the properties of the usual random ensemble are quantitatively
identical in the planted random ensemble. We study the structural phase
transitions, and the easy/hard/easy pattern in the average computational
complexity. We also discuss the finite temperature phase diagram, finding a
close connection with the liquid/glass/solid phenomenology.
|
0901.2140
|
Efficient reconciliation protocol for discrete-variable quantum key
distribution
|
cs.IT math.IT quant-ph
|
Reconciliation is an essential part of any secret-key agreement protocol and
hence of a Quantum Key Distribution (QKD) protocol, where two legitimate
parties are given correlated data and want to agree on a common string in the
presence of an adversary, while revealing a minimum amount of information.
In this paper, we show that for discrete-variable QKD protocols, this problem
can be advantageously solved with Low Density Parity Check (LDPC) codes
optimized for the BSC. In particular, we demonstrate that our method leads to a
significant improvement of the achievable secret key rate, with respect to
earlier interactive reconciliation methods used in QKD.
|
0901.2143
|
Coding for Parallel Links to Maximize Expected Decodable-Message Value
|
cs.IT math.IT
|
Future communication scenarios for NASA spacecraft may involve multiple
communication links and relay nodes, so that there is essentially a network in
which there may be multiple paths from a sender to a destination. The
availability of individual links may be uncertain. In this paper, scenarios are
considered in which the goal is to maximize a payoff that assigns weight based
on the worth of data and the probability of successful transmission. Ideally,
the choice of what information to send over the various links will provide
protection of high value data when many links are unavailable, yet result in
communication of significant additional data when most links are available.
Here the focus is on the simple network of multiple parallel links, where the
links have known capacities and outage probabilities. Given a set of simple
inter-link codes, linear programming can be used to find the optimal
timesharing strategy among these codes. Some observations are made about the
problem of determining all potentially useful codes, and techniques to assist
in such determination are presented.
|
0901.2147
|
Bit Precision Analysis for Compressed Sensing
|
cs.IT math.IT
|
This paper studies the stability of some reconstruction algorithms for
compressed sensing in terms of the bit precision. Considering the fact that
practical digital systems deal with discretized signals, we motivate the
importance of the total number of accurate bits needed from the measurement
outcomes in addition to the number of measurements. It is shown that if one
uses a $2k \times n$ Vandermonde matrix with roots on the unit circle as the
measurement matrix, $O(\ell + k \log(n/k))$ bits of precision per measurement
are sufficient to reconstruct a $k$-sparse signal $x \in \R^n$ with dynamic
range (i.e., the absolute ratio between the largest and the smallest nonzero
coefficients) at most $2^\ell$ within $\ell$ bits of precision, hence
identifying its correct support. Finally, we obtain an upper bound on the total
number of required bits when the measurement matrix satisfies a restricted
isometry property, which is in particular the case for random Fourier and
Gaussian matrices. For very sparse signals, the upper bound on the number of
required bits for Vandermonde matrices is shown to be better than this general
upper bound.
|
0901.2160
|
Analysis of Uncoordinated Opportunistic Two-Hop Wireless Ad Hoc Systems
|
cs.IT math.IT
|
We consider a time-slotted two-hop wireless system in which the sources
transmit to the relays in the even time slots (first hop) and the relays
forward the packets to the destinations in the odd time slots (second hop).
Each source may connect to multiple relays in the first hop. In the presence of
interference and without tight coordination of the relays, it is not clear
which relays should transmit the packet. We propose four decentralized methods
of relay selection, some based on location information and others based on the
received signal strength (RSS). We provide a complete analytical
characterization of these methods using tools from stochastic geometry. We use
simulation results to compare these methods in terms of end-to-end success
probability.
|
0901.2164
|
Cooperative Multiplexing in the Multiple Antenna Half Duplex Relay
Channel
|
cs.IT math.IT
|
Cooperation between terminals has been proposed to improve the reliability
and throughput of wireless communication. While recent work has shown that
relay cooperation provides increased diversity, increased multiplexing gain
over that offered by direct link has largely been unexplored. In this work we
show that cooperative multiplexing gain can be achieved by using a half duplex
relay. We capture relative distances between terminals in the high SNR
diversity multiplexing tradeoff (DMT) framework. The DMT performance is then
characterized for a network having a single antenna half-duplex relay between a
single-antenna source and two-antenna destination. Our results show that the
achievable multiplexing gain using cooperation can be greater than that of the
direct link and is a function of the relative distance between source and relay
compared to the destination. Moreover, for multiplexing gains less than 1, a
simple scheme of the relay listening 1/3 of the time and transmitting 2/3 of
the time can achieve the 2 by 2 MIMO DMT.
|
0901.2192
|
On Optimal Secure Message Transmission by Public Discussion
|
cs.CR cs.IT math.IT
|
In a secure message transmission (SMT) scenario a sender wants to send a
message in a private and reliable way to a receiver. Sender and receiver are
connected by $n$ vertex disjoint paths, referred to as wires, $t$ of which can
be controlled by an adaptive adversary with unlimited computational resources.
In Eurocrypt 2008, Garay and Ostrovsky considered an SMT scenario where sender
and receiver have access to a public discussion channel and showed that secure
and reliable communication is possible when $n \geq t+1$. In this paper we will
show that a secure protocol requires at least 3 rounds of communication and 2
rounds invocation of the public channel and hence give a complete answer to the
open question raised by Garay and Ostrovsky. We also describe a round optimal
protocol that has \emph{constant} transmission rate over the public channel.
|
0901.2194
|
Iterative Spectrum Shaping with Opportunistic Multiuser Detection
|
cs.IT math.IT
|
This paper studies a new decentralized resource allocation strategy, named
iterative spectrum shaping (ISS), for the multi-carrier-based multiuser
communication system, where two coexisting users independently and sequentially
update transmit power allocations over parallel subcarriers to maximize their
individual transmit rates. Unlike the conventional iterative water-filling
(IWF) algorithm that applies the single-user detection (SD) at each user's
receiver by treating the interference from the other user as additional noise,
the proposed ISS algorithm applies multiuser detection techniques to decode
both the desired user's and interference user's messages if it is feasible,
thus termed as opportunistic multiuser detection (OMD). Two encoding methods
are considered for ISS: One is carrier independent encoding where independent
codewords are modulated by different subcarriers for which different decoding
methods can be applied; the other is carrier joint encoding where a single
codeword is modulated by all the subcarriers for which a single decoder is
applied. For each encoding method, this paper presents the associated optimal
user power and rate allocation strategy at each iteration of transmit
adaptation. It is shown that under many circumstances the proposed ISS
algorithm employing OMD is able to achieve substantial throughput gains over
the conventional IWF algorithm employing SD for decentralized spectrum sharing.
Applications of ISS in cognitive radio communication systems are also
discussed.
|
0901.2198
|
Feasible alphabets for communicating the sum of sources over a network
|
cs.IT math.IT
|
We consider directed acyclic {\em sum-networks} with $m$ sources and $n$
terminals where the sources generate symbols from an arbitrary alphabet field
$F$, and the terminals need to recover the sum of the sources over $F$. We show
that for any co-finite set of primes, there is a sum-network which is solvable
only over fields of characteristics belonging to that set. We further construct
a sum-network where a scalar solution exists over all fields other than the
binary field $F_2$. We also show that a sum-network is solvable over a field if
and only if its reverse network is solvable over the same field.
|
0901.2204
|
Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite
Number of Iterations
|
cs.IT math.IT
|
Communication over the binary erasure channel (BEC) using low-density
parity-check (LDPC) codes and belief propagation (BP) decoding is considered.
The average bit error probability of an irregular LDPC code ensemble after a
fixed number of iterations converges to a limit, which is calculated via
density evolution, as the blocklength $n$ tends to infinity. The difference
between the bit error probability with blocklength $n$ and the
large-blocklength limit behaves asymptotically like $\alpha/n$, where the
coefficient $\alpha$ depends on the ensemble, the number of iterations and the
erasure probability of the BEC\null. In [1], $\alpha$ is calculated for regular
ensembles. In this paper, $\alpha$ for irregular expurgated ensembles is
derived. It is demonstrated that convergence of numerical estimates of $\alpha$
to the analytic result is significantly fast for irregular unexpurgated
ensembles.
|
0901.2207
|
Performance and Construction of Polar Codes on Symmetric Binary-Input
Memoryless Channels
|
cs.IT math.IT
|
Channel polarization is a method of constructing capacity achieving codes for
symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the
original paper, the construction complexity is exponential in the blocklength.
In this paper, a new construction method for arbitrary symmetric binary
memoryless channel (B-MC) with linear complexity in the blocklength is
proposed. Furthermore, new upper and lower bounds of the block error
probability of polar codes are derived for the BEC and the arbitrary symmetric
B-MC, respectively.
|
0901.2216
|
Discovering Global Patterns in Linguistic Networks through Spectral
Analysis: A Case Study of the Consonant Inventories
|
cs.CL physics.data-an
|
Recent research has shown that language and the socio-cognitive phenomena
associated with it can be aptly modeled and visualized through networks of
linguistic entities. However, most of the existing works on linguistic networks
focus only on the local properties of the networks. This study is an attempt to
analyze the structure of languages via a purely structural technique, namely
spectral analysis, which is ideally suited for discovering the global
correlations in a network. Application of this technique to PhoNet, the
co-occurrence network of consonants, not only reveals several natural
linguistic principles governing the structure of the consonant inventories, but
is also able to quantify their relative importance. We believe that this
powerful technique can be successfully applied, in general, to study the
structure of natural languages.
|
0901.2218
|
Slepian-Wolf Coding over Cooperative Networks
|
cs.IT math.IT
|
We present sufficient conditions for multicasting a set of correlated sources
over cooperative networks. We propose joint source-Wyner-Ziv
encoding/sliding-window decoding scheme, in which each receiver considers an
ordered partition of other nodes. Subject to this scheme, we obtain a set of
feasibility constraints for each ordered partition. We consolidate the results
of different ordered partitions by utilizing a result of geometrical approach
to obtain the sufficient conditions. We observe that these sufficient
conditions are indeed necessary conditions for Aref networks. As a consequence
of the main result, we obtain an achievable rate region for networks with
multicast demands. Also, we deduce an achievability result for two-way relay
networks, in which two nodes want to communicate over a relay network.
|
0901.2224
|
Concept-Oriented Model and Query Language
|
cs.DB
|
We describe a new approach to data modeling, called the concept-oriented
model (COM), and a novel concept-oriented query language (COQL). The model is
based on three principles: duality principle postulates that any element is a
couple consisting of one identity and one entity, inclusion principle
postulates that any element has a super-element, and order principle assumes
that any element has a number of greater elements within a partially ordered
set. Concept-oriented query language is based on a new data modeling construct,
called concept, inclusion relation between concepts, and concept partial
ordering in which greater concepts are represented by their field types. It is
demonstrated how COM and COQL can be used to solve three general data modeling
tasks: logical navigation, multidimensional analysis and inference. Logical
navigation is based on two operations of projection and de-projection.
Multidimensional analysis uses product operation for producing a cube from
level concepts chosen along the chosen dimension paths. Inference is defined as
a two-step procedure where input constraints are first propagated downwards
using de-projection and then the constrained result is propagated upwards using
projection.
|
0901.2270
|
A Plotkin-Alamouti Superposition Coding Scheme for Cooperative
Broadcasting in Wireless Networks
|
cs.IT math.IT
|
This paper deals with superposition coding for cooperative broadcasting in
the case of two coordinated source nodes, as introduced in the seminal work of
Bergmans and Cover in 1974. A scheme is introduced for two classes of
destination (or relay) nodes: Close nodes and far nodes, as ranked by their
spatial distances to the pair of transmitting nodes. Two linear codes are
combined using the (u,u+v)-construction devised by Plotkin to construct
two-level linear unequal error protection (LUEP) codes. However, instead of
binary addition of subcode codewords in the source encoder, here modulated
subcode sequences are combined at the destination (or relay) nodes antennae.
Bergmans and Cover referred to this as over-the-air mixing. In the case of
Rayleigh fading, additional diversity order as well as robustness to channel
estimation errors are obtained when source nodes transmit pairs of coded
sequences in accordance to Alamouti's transmit diversity scheme. We refer to
this combination as a Plotkin-Alamouti scheme and study its performance over
AWGN and Rayleigh fading channels with a properly partitioned QPSK
constellation.
|
0901.2321
|
The Redundancy of a Computable Code on a Noncomputable Distribution
|
stat.ML cs.IT math.IT
|
We introduce new definitions of universal and superuniversal computable
codes, which are based on a code's ability to approximate Kolmogorov complexity
within the prescribed margin for all individual sequences from a given set.
Such sets of sequences may be singled out almost surely with respect to certain
probability measures. Consider a measure parameterized with a real parameter
and put an arbitrary prior on the parameter. The Bayesian measure is the
expectation of the parameterized measure with respect to the prior. It appears
that a modified Shannon-Fano code for any computable Bayesian measure, which we
call the Bayesian code, is superuniversal on a set of parameterized
measure-almost all sequences for prior-almost every parameter. According to
this result, in the typical setting of mathematical statistics no computable
code enjoys redundancy which is ultimately much less than that of the Bayesian
code. Thus we introduce another characteristic of computable codes: The
catch-up time is the length of data for which the code length drops below the
Kolmogorov complexity plus the prescribed margin. Some codes may have smaller
catch-up times than Bayesian codes.
|
0901.2333
|
Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum
Throughput and Low Delay in Wireless Networks
|
cs.NI cs.IT math.IT
|
Recently, it has been shown that CSMA-type random access algorithms can
achieve the maximum possible throughput in ad hoc wireless networks. However,
these algorithms assume an idealized continuous-time CSMA protocol where
collisions can never occur. In addition, simulation results indicate that the
delay performance of these algorithms can be quite bad. On the other hand,
although some simple heuristics (such as distributed approximations of greedy
maximal scheduling) can yield much better delay performance for a large set of
arrival rates, they may only achieve a fraction of the capacity region in
general. In this paper, we propose a discrete-time version of the CSMA
algorithm. Central to our results is a discrete-time distributed randomized
algorithm which is based on a generalization of the so-called Glauber dynamics
from statistical physics, where multiple links are allowed to update their
states in a single time slot. The algorithm generates collision-free
transmission schedules while explicitly taking collisions into account during
the control phase of the protocol, thus relaxing the perfect CSMA assumption.
More importantly, the algorithm allows us to incorporate mechanisms which lead
to very good delay performance while retaining the throughput-optimality
property. It also resolves the hidden and exposed terminal problems associated
with wireless networks.
|
0901.2349
|
Beyond word frequency: Bursts, lulls, and scaling in the temporal
distributions of words
|
cs.CL cond-mat.dis-nn physics.data-an physics.soc-ph
|
Background: Zipf's discovery that word frequency distributions obey a power
law established parallels between biological and physical processes, and
language, laying the groundwork for a complex systems perspective on human
communication. More recent research has also identified scaling regularities in
the dynamics underlying the successive occurrences of events, suggesting the
possibility of similar findings for language as well.
Methodology/Principal Findings: By considering frequent words in USENET
discussion groups and in disparate databases where the language has different
levels of formality, here we show that the distributions of distances between
successive occurrences of the same word display bursty deviations from a
Poisson process and are well characterized by a stretched exponential (Weibull)
scaling. The extent of this deviation depends strongly on semantic type -- a
measure of the logicality of each word -- and less strongly on frequency. We
develop a generative model of this behavior that fully determines the dynamics
of word usage.
Conclusions/Significance: Recurrence patterns of words are well described by
a stretched exponential distribution of recurrence times, an empirical scaling
that cannot be anticipated from Zipf's law. Because the use of words provides a
uniquely precise and powerful lens on human thought and activity, our findings
also have implications for other overt manifestations of collective human
dynamics.
|
0901.2356
|
Information-Theoretic Bounds for Multiround Function Computation in
Collocated Networks
|
cs.IT math.IT
|
We study the limits of communication efficiency for function computation in
collocated networks within the framework of multi-terminal block source coding
theory. With the goal of computing a desired function of sources at a sink,
nodes interact with each other through a sequence of error-free, network-wide
broadcasts of finite-rate messages. For any function of independent sources, we
derive a computable characterization of the set of all feasible message coding
rates - the rate region - in terms of single-letter information measures. We
show that when computing symmetric functions of binary sources, the sink will
inevitably learn certain additional information which is not demanded in
computing the function. This conceptual understanding leads to new improved
bounds for the minimum sum-rate. The new bounds are shown to be orderwise
better than those based on cut-sets as the network scales. The scaling law of
the minimum sum-rate is explored for different classes of symmetric functions
and source parameters.
|
0901.2367
|
An Implementable Scheme for Universal Lossy Compression of Discrete
Markov Sources
|
cs.IT math.IT
|
We present a new lossy compressor for discrete sources. For coding a source
sequence $x^n$, the encoder starts by assigning a certain cost to each
reconstruction sequence. It then finds the reconstruction that minimizes this
cost and describes it losslessly to the decoder via a universal lossless
compressor. The cost of a sequence is given by a linear combination of its
empirical probabilities of some order $k+1$ and its distortion relative to the
source sequence. The linear structure of the cost in the empirical count matrix
allows the encoder to employ a Viterbi-like algorithm for obtaining the
minimizing reconstruction sequence simply. We identify a choice of coefficients
for the linear combination in the cost function which ensures that the
algorithm universally achieves the optimum rate-distortion performance of any
Markov source in the limit of large $n$, provided $k$ is increased as $o(\log
n)$.
|
0901.2370
|
Performance of Polar Codes for Channel and Source Coding
|
cs.IT math.IT
|
Polar codes, introduced recently by Ar\i kan, are the first family of codes
known to achieve capacity of symmetric channels using a low complexity
successive cancellation decoder. Although these codes, combined with successive
cancellation, are optimal in this respect, their finite-length performance is
not record breaking. We discuss several techniques through which their
finite-length performance can be improved. We also study the performance of
these codes in the context of source coding, both lossless and lossy, in the
single-user context as well as for distributed applications.
|
0901.2376
|
A Limit Theorem in Singular Regression Problem
|
cs.LG
|
In statistical problems, a set of parameterized probability distributions is
used to estimate the true probability distribution. If Fisher information
matrix at the true distribution is singular, then it has been left unknown what
we can estimate about the true distribution from random samples. In this paper,
we study a singular regression problem and prove a limit theorem which shows
the relation between the singular regression problem and two birational
invariants, a real log canonical threshold and a singular fluctuation. The
obtained theorem has an important application to statistics, because it enables
us to estimate the generalization error from the training error without any
knowledge of the true probability distribution.
|
0901.2391
|
Weight Distribution of A p-ary Cyclic Code
|
cs.IT cs.DM math.IT
|
For an odd prime $p$ and two positive integers $n\geq 3$ and $k$ with
$\frac{n}{{\rm gcd}(n,k)}$ being odd, the paper determines the weight
distribution of a $p$-ary cyclic code $\mathcal{C}$ over $\mathbb{F}_{p}$ with
nonzeros $\alpha^{-1}$, $\alpha^{-(p^k+1)}$ and $\alpha^{-(p^{3k}+1)}$, where
$\alpha$ is a primitive element of $\mathbb{F}_{p^n}$
|
0901.2396
|
Joint Source-Channel Coding at the Application Layer for Parallel
Gaussian Sources
|
cs.IT math.IT
|
In this paper the multicasting of independent parallel Gaussian sources over
a binary erasure broadcasted channel is considered. Multiresolution embedded
quantizer and layered joint source-channel coding schemes are used in order to
serve simultaneously several users at different channel capacities. The convex
nature of the rate-distortion function, computed by means of reverse
water-filling, allows us to solve relevant convex optimization problems
corresponding to different performance criteria. Then, layered joint
source-channel codes are constructed based on the concatenation of embedded
scalar quantizers with binary rateless encoders.
|
0901.2401
|
MIMO Broadcast Channel Optimization under General Linear Constraints
|
cs.IT math.IT
|
The optimization of the transmit parameters (power allocation and steering
vectors) for the MIMO BC under general linear constraints is treated under the
optimal DPC coding strategy and the simple suboptimal linear zero-forcing
beamforming strategy. In the case of DPC, we show that "SINR duality" and
"min-max duality" yield the same dual MAC problem, and compare two alternatives
for its efficient solution. In the case of zero-forcing beamforming, we provide
a new efficient algorithm based on the direct optimization of a generalized
inverse matrix. In both cases, the algorithms presented here address the
problems in the most general form and can be applied to special cases
previously considered, such as per-antenna and per-group of antennas power
constraints, "forbidden interference direction" constraints, or any combination
thereof.
|
0901.2410
|
On the Energy Benefit of Network Coding for Wireless Multiple Unicast
|
cs.IT math.IT
|
We consider the energy savings that can be obtained by employing network
coding instead of plain routing in wireless multiple unicast problems. We
establish lower bounds on the benefit of network coding, defined as the maximum
of the ratio of the minimum energy required by routing and network coding
solutions, where the maximum is over all configurations. It is shown that if
coding and routing solutions are using the same transmission range, the benefit
in $d$-dimensional networks is at least $2d/\lfloor\sqrt{d}\rfloor$. Moreover,
it is shown that if the transmission range can be optimized for routing and
coding individually, the benefit in 2-dimensional networks is at least 3. Our
results imply that codes following a \emph{decode-and-recombine} strategy are
not always optimal regarding energy efficiency.
|
0901.2483
|
Fast Encoding and Decoding of Gabidulin Codes
|
cs.IT math.IT
|
Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a
major role in practical error control for network coding. This paper presents
new encoding and decoding algorithms for Gabidulin codes based on
low-complexity normal bases. In addition, a new decoding algorithm is proposed
based on a transform-domain approach. Together, these represent the fastest
known algorithms for encoding and decoding Gabidulin codes.
|
0901.2538
|
Capacity Scaling of SDMA in Wireless Ad Hoc Networks
|
cs.IT math.IT
|
We consider an ad hoc network in which each multi-antenna transmitter sends
independent streams to multiple receivers in a Poisson field of interferers. We
provide the outage probability and transmission capacity scaling laws, aiming
at investigating the fundamental limits of Space Division Multiple Access
(SDMA). We first show that super linear capacity scaling with the number of
receive/transmit antennas can be achieved using dirty paper coding.
Nevertheless, the potential benefits of multi-stream, multi-antenna
communications fall off quickly if linear precoding is employed, leading to
sublinear capacity growth in the case of single-antenna receivers. A key
finding is that receive antenna array processing is of vital importance in SDMA
ad hoc networks, as a means to cancel the increased residual interference and
boost the signal power through diversity.
|
0901.2545
|
On the Capacity of the Discrete-Time Channel with Uniform Output
Quantization
|
cs.IT math.IT
|
This paper provides new insight into the classical problem of determining
both the capacity of the discrete-time channel with uniform output quantization
and the capacity achieving input distribution. It builds on earlier work by
Gallager and Witsenhausen to provide a detailed analysis of two particular
quantization schemes. The first is saturation quantization where overflows are
mapped to the nearest quantization bin, and the second is wrapping quantization
where overflows are mapped to the nearest quantization bin after reduction by
some modulus. Both the capacity of wrapping quantization and the capacity
achieving input distribution are determined. When the additive noise is
gaussian and relatively small, the capacity of saturation quantization is shown
to be bounded below by that of wrapping quantization. In the limit of
arbitrarily many uniform quantization levels, it is shown that the difference
between the upper and lower bounds on capacity given by Ihara is only 0.26
bits.
|
0901.2586
|
Information geometries and Microeconomic Theories
|
q-fin.GN cs.IT math.IT
|
More than thirty years ago, Charnes, Cooper and Schinnar (1976) established
an enlightening contact between economic production functions (EPFs) -- a
cornerstone of neoclassical economics -- and information theory, showing how a
generalization of the Cobb-Douglas production function encodes homogeneous
functions.
As expected by Charnes \textit{et al.}, the contact turns out to be much
broader: we show how information geometry as pioneered by Amari and others
underpins static and dynamic descriptions of microeconomic cornerstones.
We show that the most popular EPFs are fundamentally grounded in a very weak
axiomatization of economic transition costs between inputs. The strength of
this characterization is surprising, as it geometrically bonds altogether a
wealth of collateral economic notions
-- advocating for applications in various economic fields --: among all, it
characterizes (i) Marshallian and Hicksian demands and their geometric duality,
(ii) Slutsky-type properties for the transformation paths, (iii) Roy-type
properties for their elementary variations.
|
0901.2588
|
The MIMO Wireless Switch: Relaying Can Increase the Multiplexing Gain
|
cs.IT math.IT
|
This paper considers an interference network composed of K half-duplex
single-antenna pairs of users who wish to establish bi-directional
communication with the aid of a multi-input-multi-output (MIMO) half-duplex
relay node. This channel is referred to as the "MIMO Wireless Switch" since,
for the sake of simplicity, our model assumes no direct link between the two
end nodes of each pair implying that all communication must go through the
relay node (i.e., the MIMO switch). Assuming a delay-limited scenario, the
fundamental limits in the high signal-to-noise ratio (SNR) regime is analyzed
using the diversity multiplexing tradeoff (DMT) framework. Our results sheds
light on the structure of optimal transmission schemes and the gain offered by
the relay node in two distinct cases, namely reciprocal and non-reciprocal
channels (between the relay and end-users). In particular, the existence of a
relay node, equipped with a sufficient number of antennas, is shown to increase
the multiplexing gain; as compared with the traditional fully connected K-pair
interference channel. To the best of our knowledge, this is the first known
example where adding a relay node results in enlarging the pre-log factor of
the sum rate. Moreover, for the case of reciprocal channels, it is shown that,
when the relay has a number of antennas at least equal to the sum of antennas
of all the users, static time allocation of decode and forward (DF) type
schemes is optimal. On the other hand, in the non-reciprocal scenario, we
establish the optimality of dynamic decode and forward in certain relevant
scenarios.
|
0901.2606
|
Capacity Bounds of Half-Duplex Gaussian Cooperative Interference Channel
|
cs.IT math.IT
|
In this paper, we investigate the half-duplex cooperative communication
scheme of a two user Gaussian interference channel. We develop achievable
region and outer bound for the case when the system allow either transmitter or
receiver cooperation. We show that by using our transmitter cooperation scheme,
there is significant capacity improvement compare to the previous results,
especially when the cooperation link is strong. Further, if the cooperation
channel gain is infinity, both our transmitter and receiver cooperation rates
achieve their respective outer bound. It is also shown that transmitter
cooperation provides larger achievable region than receiver cooperation under
the same channel and power conditions.
|
0901.2616
|
On the Delay Limited Secrecy Capacity of Fading Channels
|
cs.IT cs.CR math.IT
|
In this paper, the delay limited secrecy capacity of the flat fading channel
is investigated under two different assumptions on the available transmitter
channel state information (CSI). The first scenario assumes perfect prior
knowledge of both the main and eavesdropper channel gains. Here, upper and
lower bounds on the secure delay limited capacity are derived and shown to be
tight in the high signal-to-noise ratio (SNR) regime (for a wide class of
channel distributions). In the second scenario, only the main channel CSI is
assumed to be available at the transmitter. Remarkably, under this assumption,
we establish the achievability of non-zero secure rate (for a wide class of
channel distributions) under a strict delay constraint. In the two cases, our
achievability arguments are based on a novel two-stage approach that overcomes
the secrecy outage phenomenon observed in earlier works.
|
0901.2665
|
A Density Matrix-based Algorithm for Solving Eigenvalue Problems
|
cs.CE cs.MS
|
A new numerical algorithm for solving the symmetric eigenvalue problem is
presented. The technique deviates fundamentally from the traditional Krylov
subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other
Davidson-Jacobi techniques, and takes its inspiration from the contour
integration and density matrix representation in quantum mechanics. It will be
shown that this new algorithm - named FEAST - exhibits high efficiency,
robustness, accuracy and scalability on parallel architectures. Examples from
electronic structure calculations of Carbon nanotubes (CNT) are presented, and
numerical performances and capabilities are discussed.
|
0901.2684
|
Distributed Large Scale Network Utility Maximization
|
cs.IT cs.DC math.IT math.OC
|
Recent work by Zymnis et al. proposes an efficient primal-dual interior-point
method, using a truncated Newton method, for solving the network utility
maximization (NUM) problem. This method has shown superior performance relative
to the traditional dual-decomposition approach. Other recent work by Bickson et
al. shows how to compute efficiently and distributively the Newton step, which
is the main computational bottleneck of the Newton method, utilizing the
Gaussian belief propagation algorithm.
In the current work, we combine both approaches to create an efficient
distributed algorithm for solving the NUM problem. Unlike the work of Zymnis,
which uses a centralized approach, our new algorithm is easily distributed.
Using an empirical evaluation we show that our new method outperforms previous
approaches, including the truncated Newton method and dual-decomposition
methods. As an additional contribution, this is the first work that evaluates
the performance of the Gaussian belief propagation algorithm vs. the
preconditioned conjugate gradient method, for a large scale problem.
|
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