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1010.1044
On the Capacity of the $K$-User Cyclic Gaussian Interference Channel
cs.IT math.IT
This paper studies the capacity region of a $K$-user cyclic Gaussian interference channel, where the $k$th user interferes with only the $(k-1)$th user (mod $K$) in the network. Inspired by the work of Etkin, Tse and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han-Kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region of the $K$-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the $K$-user cyclic Gaussian interference channel, a compact representation of the Han-Kobayashi achievable rate region using Fourier-Motzkin elimination is first derived, a capacity region outer bound is then established. It is shown that the Etkin-Tse-Wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special 3-user case, this gap can be sharpened to 1 1/2 bits by time-sharing of several different strategies. The capacity result of the $K$-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference channel. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.
1010.1052
Mixed integer programming for the resolution of GPS carrier phase ambiguities
cs.IT cs.DM math.IT
This arXiv upload is to clarify that the now well-known sorted QR MIMO decoder was first presented in the 1995 IUGG General Assembly. We clearly go much further in the sense that we directly incorporated reduction into this one step, non-exact suboptimal integer solution. Except for these first few lines up to this point, this paper is an unaltered version of the paper presented at the IUGG1995 Assembly in Boulder. Ambiguity resolution of GPS carrier phase observables is crucial in high precision geodetic positioning and navigation applications. It consists of two aspects: estimating the integer ambiguities in the mixed integer observation model and examining whether they are sufficiently accurate to be fixed as known nonrandom integers. We shall discuss the first point in this paper from the point of view of integer programming. A one-step nonexact approach is proposed by employing minimum diagonal pivoting Gaussian decompositions, which may be thought of as an improvement of the simple rounding-off method, since the weights and correlations of the floating-estimated ambiguities are fully taken into account. The second approach is to reformulate the mixed integer least squares problem into the standard 0-1 linear integer programming model, which can then be solved by using, for instance, the practically robust and efficient simplex algorithm for linear integer programming. It is exact, if proper bounds for the ambiguities are given. Theoretical results on decorrelation by unimodular transformation are given in the form of a theorem.
1010.1060
On the Capacity of Multi-Hop Wireless Networks with Partial Network Knowledge
cs.IT math.IT
In large wireless networks, acquiring full network state information is typically infeasible. Hence, nodes need to flow the information and manage the interference based on partial information about the network. In this paper, we consider multi-hop wireless networks and assume that each source only knows the channel gains that are on the routes from itself to other destinations in the network. We develop several distributed strategies to manage the interference among the users and prove their optimality in maximizing the achievable normalized sum-rate for some classes of networks.
1010.1069
Cooperative Distributed Sequential Spectrum Sensing
cs.IT math.IT stat.AP
We consider cooperative spectrum sensing for cognitive radios. We develop an energy efficient detector with low detection delay using sequential hypothesis testing. Sequential Probability Ratio Test (SPRT) is used at both the local nodes and the fusion center. We also analyse the performance of this algorithm and compare with the simulations. Modelling uncertainties in the distribution parameters are considered. Slow fading with and without perfect channel state information at the cognitive radios is taken into account.
1010.1071
A Novel Algorithm for Cooperative Distributed Sequential Spectrum Sensing in Cognitive Radio
cs.IT math.IT stat.AP
This paper considers cooperative spectrum sensing in Cognitive Radios. In our previous work we have developed DualSPRT, a distributed algorithm for cooperative spectrum sensing using Sequential Probability Ratio Test (SPRT) at the Cognitive Radios as well as at the fusion center. This algorithm works well, but is not optimal. In this paper we propose an improved algorithm- SPRT-CSPRT, which is motivated from Cumulative Sum Procedures (CUSUM). We analyse it theoretically. We also modify this algorithm to handle uncertainties in SNR's and fading.
1010.1147
XML Query Processing and Query Languges: A Survey
cs.DB cs.DS
Today's database is associated with interoperability between different domains and applications. This consequently results in the importance of data portability in database. XML format fits the requirements and it has been increasingly used for serving applications across different domains and purposes. However, querying XML document effectively and efficiently is still a challenging issue. This paper discusses query processing issues on XML and reviews proposed solutions for querying XML databases by various authors.
1010.1149
Bang--bang trajectories with a double switching time: sufficient strong local optimality conditions
math.OC cs.SY
This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in previous papers for more specific cases. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times of the reference trajectory.
1010.1163
Secrecy Capacity of the Gaussian Wire-Tap Channel with Finite Complex Constellation Input
cs.IT math.IT
The secrecy capacity of a discrete memoryless Gaussian Wire-Tap Channel when the input is from a finite complex constellation is studied. It is shown that the secrecy capacity curves of a finite constellation plotted against the SNR, for a fixed noise variance of the eavesdropper's channel has a global maximum at an internal point. This is in contrast to what is known in the case of Gaussian codebook input where the secrecy capacity curve is a bounded, monotonically increasing function of SNR. Secrecy capacity curves for some well known constellations like BPSK, 4-QAM, 16-QAM and 8-PSK are plotted and the SNR at which the maximum occurs is found through simulation. It is conjectured that the secrecy capacity curves for finite constellations have a single maximum.
1010.1256
Entanglement-assisted quantum turbo codes
quant-ph cs.IT math.IT
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin et al., in order to have the constituent decoders pass along only "extrinsic information" to each other rather than a posteriori probabilities as in the decoder of Poulin et al., and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.
1010.1286
Exact Hamming Distortion Analysis of Viterbi Encoded Trellis Coded Quantizers
cs.IT math.IT
Let G be a finite strongly connected aperiodic directed graph in which each edge carries a label from a finite alphabet A. Then G induces a trellis coded quantizer for encoding an alphabet A memoryless source. A source sequence of long finite length is encoded by finding a path in G of that length whose sequence of labels is closest in Hamming distance to the source sequence; finding the minimum distance path is a dynamic programming problem that is solved using the Viterbi algorithm. We show how a Markov chain can be used to obtain a closed form expression for the asymptotic expected Hamming distortion per sample that results as the number of encoded source samples increases without bound.
1010.1295
Optimal Packet Scheduling in an Energy Harvesting Communication System
cs.IT cs.NI math.IT
We consider the optimal packet scheduling problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modeled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the time by which all packets are delivered is minimized. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the data traffic arrivals, we consider two different scenarios. In the first scenario, we assume that all bits have arrived and are ready at the transmitter before the transmission starts. In the second scenario, we consider the case where packets arrive during the transmissions, with known arrival times and sizes. We develop optimal off-line scheduling policies which minimize the time by which all packets are delivered to the destination, under causality constraints on both data and energy arrivals.
1010.1303
Error Exponent for Multiple-Access Channels:Lower Bounds
cs.IT math.IT
A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a two-user discrete memoryless (DM) multiple-access channel (MAC), three lower bounds on the reliability function are derived. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MAC. It is shown that the random coding bound is the performance of the average code in the constant composition code ensemble. The second bound (Typical random coding) is the typical performance of the constant composition code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from the codebook with larger rate. This is the first bound of this type that explicitly uses the method of expurgation for MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger. All these bounds can be universally obtained for all discrete memoryless MACs with given input and output alphabets.
1010.1309
Probing Capacity
cs.IT math.IT
We consider the problem of optimal probing of states of a channel by transmitter and receiver for maximizing rate of reliable communication. The channel is discrete memoryless (DMC) with i.i.d. states. The encoder takes probing actions dependent on the message. It then uses the state information obtained from probing causally or non-causally to generate channel input symbols. The decoder may also take channel probing actions as a function of the observed channel output and use the channel state information thus acquired, along with the channel output, to estimate the message. We refer to the maximum achievable rate for reliable communication for such systems as the 'Probing Capacity'. We characterize this capacity when the encoder and decoder actions are cost constrained. To motivate the problem, we begin by characterizing the trade-off between the capacity and fraction of channel states the encoder is allowed to observe, while the decoder is aware of channel states. In this setting of 'to observe or not to observe' state at the encoder, we compute certain numerical examples and note a pleasing phenomenon, where encoder can observe a relatively small fraction of states and yet communicate at maximum rate, i.e. rate when observing states at encoder is not cost constrained.
1010.1317
Typicality Graphs:Large Deviation Analysis
cs.IT math.IT
Let $\mathcal{X}$ and $\mathcal{Y}$ be finite alphabets and $P_{XY}$ a joint distribution over them, with $P_X$ and $P_Y$ representing the marginals. For any $\epsilon > 0$, the set of $n$-length sequences $x^n$ and $y^n$ that are jointly typical \cite{ckbook} according to $P_{XY}$ can be represented on a bipartite graph. We present a formal definition of such a graph, known as a \emph{typicality} graph, and study some of its properties.
1010.1322
A New Upper Bound on the Average Error Exponent for Multiple-Access Channels
cs.IT math.IT
A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by Haroutunian. However, since explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) results in a tighter sphere-packing exponent in comparison to Haroutunian's. Also, the relationship between average and maximal error probabilities is studied. Finally, by using a known sphere packing bound on the maximal probability of error, a lower bound on the average error probability is derived.
1010.1328
Complejidad descriptiva y computacional en maquinas de Turing pequenas
cs.CC cs.IT math.IT
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of complexity, particularly algorithmic (program-size) and computational (time) complexity as a mean to explain these measure in a novel manner. The investigation proceeds by an exhaustive exploration and systematic study of the functions computed by a large set of small Turing machines with 2 and 3 states with particular attention to runtimes, space-usages and patterns corresponding to the computed functions when the machines have access to larger resources (more states). We report that the average runtime of Turing machines computing a function increases as a function of the number of states, indicating that non-trivial machines tend to occupy all the resources at hand. General slow-down was witnessed and some incidental cases of (linear) speed-up were found. Throughout our study various interesting structures were encountered. We unveil a study of structures in the micro-cosmos of small Turing machines.
1010.1331
Improved Combinatorial Algorithms for Wireless Information Flow
cs.IT math.IT
The work of Avestimehr et al. '07 has recently proposed a deterministic model for wireless networks and characterized the unicast capacity C of such networks as the minimum rank of the adjacency matrices describing all possible source-destination cuts. Amaudruz & Fragouli first proposed a polynomial-time algorithm for finding the unicast capacity of a linear deterministic wireless network in their 2009 paper. In this work, we improve upon Amaudruz & Fragouli's work and further reduce the computational complexity of the algorithm by fully exploring the useful combinatorial features intrinsic in the problem. Our improvement applies generally with any size of finite fields associated with the channel model. Comparing with other algorithms on solving the same problem, our improved algorithm is very competitive in terms of complexity.
1010.1358
Tight exponential analysis of universally composable privacy amplification and its applications
cs.IT cs.CR math.IT
Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.
1010.1391
On the Full Column-Rank Condition of the Channel Estimation Matrix in Doubly-Selective MIMO-OFDM Systems
cs.IT math.IT
Recently, this journal has published a paper which dealt with basis expansion model (BEM) based least-squares (LS) channel estimation in doubly-selective orthogonal frequency-division multiplexing (DS-OFDM) systems. The least-squares channel estimator computes the pseudo-inverse of a channel estimation matrix. For the existence of the pseudo-inverse, it is necessary that the channel estimation matrix be of full column rank. In this paper, we investigate the conditions that need to be satisfied that ensures the full column-rank condition of the channel estimation matrix. In particular, we derive conditions that the BEM and pilot pattern designs should satisfy to ensure that the channel estimation matrix is of full column rank. We explore the polynomial BEM (P-BEM), complex exponential BEM (CE-BEM), Slepian BEM (S-BEM) and generalized complex exponential BEM (GCE-BEM). We present one possible way to design the pilot patterns which satisfy the full column-rank conditions. Furthermore, the proposed method is extended to the case of multiple-input multiple-output (MIMO) DS-OFDM systems as well. Examples of pilot pattern designs are presented, that ensure the channel estimation matrix is of full column rank for a large DS-MIMO-OFDM system with as many as six transmitters, six receivers and 1024 subcarriers.
1010.1429
Optimizing Monotone Functions Can Be Difficult
cs.NE
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these functions are easy to optimize. The choice of the constant $c$ in the mutation probability $p(n) = c/n$ can make a decisive difference. We show that if $c < 1$, then the (1+1) evolutionary algorithm finds the optimum of every such function in $\Theta(n \log n)$ iterations. For $c=1$, we can still prove an upper bound of $O(n^{3/2})$. However, for $c > 33$, we present a strictly monotone function such that the (1+1) evolutionary algorithm with overwhelming probability does not find the optimum within $2^{\Omega(n)}$ iterations. This is the first time that we observe that a constant factor change of the mutation probability changes the run-time by more than constant factors.
1010.1437
Mixed-Membership Stochastic Block-Models for Transactional Networks
stat.ML cs.AI cs.SI stat.AP stat.ME
Transactional network data can be thought of as a list of one-to-many communications(e.g., email) between nodes in a social network. Most social network models convert this type of data into binary relations between pairs of nodes. We develop a latent mixed membership model capable of modeling richer forms of transactional network data, including relations between more than two nodes. The model can cluster nodes and predict transactions. The block-model nature of the model implies that groups can be characterized in very general ways. This flexible notion of group structure enables discovery of rich structure in transactional networks. Estimation and inference are accomplished via a variational EM algorithm. Simulations indicate that the learning algorithm can recover the correct generative model. Interesting structure is discovered in the Enron email dataset and another dataset extracted from the Reddit website. Analysis of the Reddit data is facilitated by a novel performance measure for comparing two soft clusterings. The new model is superior at discovering mixed membership in groups and in predicting transactions.
1010.1438
Coalition Formation Games for Distributed Cooperation Among Roadside Units in Vehicular Networks
cs.IT cs.GT cs.SY math.IT
Vehicle-to-roadside (V2R) communications enable vehicular networks to support a wide range of applications for enhancing the efficiency of road transportation. While existing work focused on non-cooperative techniques for V2R communications between vehicles and roadside units (RSUs), this paper investigates novel cooperative strategies among the RSUs in a vehicular network. We propose a scheme whereby, through cooperation, the RSUs in a vehicular network can coordinate the classes of data being transmitted through V2R communications links to the vehicles. This scheme improves the diversity of the information circulating in the network while exploiting the underlying content-sharing vehicle-to-vehicle communication network. We model the problem as a coalition formation game with transferable utility and we propose an algorithm for forming coalitions among the RSUs. For coalition formation, each RSU can take an individual decision to join or leave a coalition, depending on its utility which accounts for the generated revenues and the costs for coalition coordination. We show that the RSUs can self-organize into a Nash-stable partition and adapt this partition to environmental changes. Simulation results show that, depending on different scenarios, coalition formation presents a performance improvement, in terms of the average payoff per RSU, ranging between 20.5% and 33.2%, relative to the non-cooperative case.
1010.1456
A Hybrid Parallelization of AIM for Multi-Core Clusters: Implementation Details and Benchmark Results on Ranger
cs.CE cs.MS
This paper presents implementation details and empirical results for a hybrid message passing and shared memory paralleliziation of the adaptive integral method (AIM). AIM is implemented on a (near) petaflop supercomputing cluster of quad-core processors and its accuracy, complexity, and scalability are investigated by solving benchmark scattering problems. The timing and speedup results on up to 1024 processors show that the hybrid MPI/OpenMP parallelization of AIM exhibits better strong scalability (fixed problem size speedup) than pure MPI parallelization of it when multiple cores are used on each processor.
1010.1496
Profile Based Sub-Image Search in Image Databases
cs.CV cs.IR cs.MM
Sub-image search with high accuracy in natural images still remains a challenging problem. This paper proposes a new feature vector called profile for a keypoint in a bag of visual words model of an image. The profile of a keypoint captures the spatial geometry of all the other keypoints in an image with respect to itself, and is very effective in discriminating true matches from false matches. Sub-image search using profiles is a single-phase process requiring no geometric validation, yields high precision on natural images, and works well on small visual codebook. The proposed search technique differs from traditional methods that first generate a set of candidates disregarding spatial information and then verify them geometrically. Conventional methods also use large codebooks. We achieve a precision of 81% on a combined data set of synthetic and real natural images using a codebook size of 500 for top-10 queries; that is 31% higher than the conventional candidate generation approach.
1010.1499
Completely Stale Transmitter Channel State Information is Still Very Useful
cs.IT math.IT
Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser MIMO and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in a MIMO broadcast channel with $K$ transmit antennas and $K$ receivers each with 1 receive antenna, $\frac{K}{1+1/2+ ...+ \frac{1}{K}} (> 1) $ degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.
1010.1508
Certain Relations between Mutual Information and Fidelity of Statistical Estimation
stat.AP cs.IT math.IT
I present several new relations between mutual information (MI) and statistical estimation error for a system that can be regarded simultaneously as a communication channel and as an estimator of an input parameter. I first derive a second-order result between MI and Fisher information (FI) that is valid for sufficiently narrow priors, but arbitrary channels. A second relation furnishes a lower bound on the MI in terms of the minimum mean-squared error (MMSE) on the Bayesian estimation of the input parameter from the channel output, one that is valid for arbitrary channels and priors. The existence of such a lower bound, while extending previous work relating the MI to the FI that is valid only in the asymptotic and high-SNR limits, elucidates further the fundamental connection between information and estimation theoretic measures of fidelity. The remaining relations I present are inequalities and correspondences among MI, FI, and MMSE in the presence of nuisance parameters.
1010.1514
Quarantine generated phase transition in epidemic spreading
physics.soc-ph cond-mat.stat-mech cs.SI physics.bio-ph
We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w_c separating a phase (w<w_c) where the disease reaches a large fraction of the population, from a phase (w >= w_c) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that w_c increases with the mean degree and heterogeneity of the network. We also find that w_c is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.
1010.1523
Fuzzy overlapping communities in networks
physics.soc-ph cs.SI
Networks commonly exhibit a community structure, whereby groups of vertices are more densely connected to each other than to other vertices. Often these communities overlap, such that each vertex may occur in more than one community. However, two distinct types of overlapping are possible: crisp (where each vertex belongs fully to each community of which it is a member) and fuzzy (where each vertex belongs to each community to a different extent). We investigate the effects of the fuzziness of community overlap. We find that it has a strong effect on the performance of community detection methods: some algorithms perform better with fuzzy overlapping while others favour crisp overlapping. We also evaluate the performance of some algorithms that recover the belonging coefficients when the overlap is fuzzy. Finally, we investigate whether real networks contain fuzzy or crisp overlapping.
1010.1526
Time Series Classification by Class-Specific Mahalanobis Distance Measures
cs.LG
To classify time series by nearest neighbors, we need to specify or learn one or several distance measures. We consider variations of the Mahalanobis distance measures which rely on the inverse covariance matrix of the data. Unfortunately --- for time series data --- the covariance matrix has often low rank. To alleviate this problem we can either use a pseudoinverse, covariance shrinking or limit the matrix to its diagonal. We review these alternatives and benchmark them against competitive methods such as the related Large Margin Nearest Neighbor Classification (LMNN) and the Dynamic Time Warping (DTW) distance. As we expected, we find that the DTW is superior, but the Mahalanobis distance measures are one to two orders of magnitude faster. To get best results with Mahalanobis distance measures, we recommend learning one distance measure per class using either covariance shrinking or the diagonal approach.
1010.1561
A Clustering Coefficient Network Formation Game
cs.SI cs.DS cs.GT physics.soc-ph
For the most up-to-date version please visit http://www.cis.upenn.edu/~brautbar/ccgame.pdf
1010.1584
High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution
cs.IT math.IT
In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers $\eta$ goes to 0. We prove for general node distributions and fading statistics that the success probability $\p \sim 1-\gamma \eta^{\kappa}$ for $\eta \rightarrow 0$, and provide values of $\gamma$ and $\kappa$ for a number of important special cases. We show that $\kappa$ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.
1010.1605
Communicating Under Channel Uncertainty
cs.IT math.IT
For a single transmit and receive antenna system, a new constellation design is proposed to combat errors in the phase estimate of the channel coefficient. The proposed constellation is a combination of PSK and PAM constellations, where PSK is used to provide protection against phase errors, while PAM is used to increase the transmission rate using the knowledge of the magnitude of the channel coefficient. The performance of the proposed constellation is shown to be significantly better than the widely used QAM in terms of probability of error. The proposed strategy can also be extended to systems using multiple transmit and receive antennas.
1010.1622
Manipulating quantum information on the controllable systems or subspaces
quant-ph cs.SY math.OC
In this paper, we explore how to constructively manipulate qubits by rotating Bloch spheres. It is revealed that three-rotation and one-rotation Hamiltonian controls can be constructed to steer qubits when two tunable Hamiltonian controls are available. It is demonstrated in this research that local-wave function controls such as Bang-Bang, triangle-function and quadratic function controls can be utilized to manipulate quantum states on the Bloch sphere. A new kind of time-energy performance index is proposed to trade-off time and energy resource cost, in which control magnitudes are optimized in terms of this kind of performance. It is further exemplified that this idea can be generalized to manipulate encoded qubits on the controllable subspace.
1010.1646
Thresholds for epidemic spreading in networks
cond-mat.stat-mech cs.SI physics.soc-ph
We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible (SIS) model the activity threshold lambda_c vanishes in the large size limit on any network whose maximum degree k_max diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has not to do with the scale-free nature of the connectivity pattern and is instead originated by the largest hub in the system being active for any spreading rate lambda>1/sqrt{k_max} and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed (SIR) model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.
1010.1648
Large-System Analysis of Multiuser Detection with an Unknown Number of Users: A High-SNR Approach
cs.IT math.IT
We analyze multiuser detection under the assumption that the number of users accessing the channel is unknown by the receiver. In this environment, users' activity must be estimated along with any other parameters such as data, power, and location. Our main goal is to determine the performance loss caused by the need for estimating the identities of active users, which are not known a priori. To prevent a loss of optimality, we assume that identities and data are estimated jointly, rather than in two separate steps. We examine the performance of multiuser detectors when the number of potential users is large. Statistical-physics methodologies are used to determine the macroscopic performance of the detector in terms of its multiuser efficiency. Special attention is paid to the fixed-point equation whose solution yields the multiuser efficiency of the optimal (maximum a posteriori) detector in the large signal-to-noise ratio regime. Our analysis yields closed-form approximate bounds to the minimum mean-squared error in this regime. These illustrate the set of solutions of the fixed-point equation, and their relationship with the maximum system load. Next, we study the maximum load that the detector can support for a given quality of service (specified by error probability).
1010.1669
Rate-Equivocation Optimal Spatially Coupled LDPC Codes for the BEC Wiretap Channel
cs.IT math.IT
We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use convolutional LDPC ensembles based on the coset encoding scheme. More precisely, we consider regular two edge type convolutional LDPC ensembles. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. Convolutional LDPC ensemble were introduced by Felstr\"om and Zigangirov and are known to have excellent thresholds. Recently, Kudekar, Richardson, and Urbanke proved that the phenomenon of "Spatial Coupling" converts MAP threshold into BP threshold for transmission over the BEC. The phenomenon of spatial coupling has been observed to hold for general binary memoryless symmetric channels. Hence, we conjecture that our construction is a universal rate-equivocation achieving construction when the main channel and wiretapper's channel are binary memoryless symmetric channels, and the wiretapper's channel is degraded with respect to the main channel.
1010.1705
Rich-club connectivity dominates assortativity and transitivity of complex networks
physics.soc-ph cs.SI
Rich-club, assortativity and clustering coefficients are frequently-used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be payed to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individuals. Moreover, by manipulating the connectivity pattern in a very small rich-club, it is sufficient to produce a network with desired assortativity or transitivity. Conversely, our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks --- such biases can be explained by the connectivities among the richest nodes.
1010.1746
Mapping XML Data to Relational Data: A DOM-Based Approach
cs.DB cs.DS
XML has emerged as the standard for representing and exchanging data on the World Wide Web. It is critical to have efficient mechanisms to store and query XML data to exploit the full power of this new technology. Several researchers have proposed to use relational databases to store and query XML data. While several algorithms of schema mapping and query mapping have been proposed, the problem of mapping XML data to relational data, i.e., mapping an XML INSERT statement to a sequence of SQL INSERT statements, has not been addressed thoroughly in the literature. In this paper, we propose an efficient linear algorithm for mapping XML data to relational data. This algorithm is based on our previous proposed inlining algorithm for mapping DTDs to relational schemas and can be easily adapted to other inlining algorithms.
1010.1763
Algorithms for nonnegative matrix factorization with the beta-divergence
cs.LG
This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean distance, the Kullback-Leibler divergence and the Itakura-Saito divergence as special cases (beta = 2,1,0, respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization (MM) algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a beta-dependent power exponent. The monotonicity of the heuristic algorithm can however be proven for beta in (0,1) using the proposed auxiliary function. Then we introduce the concept of majorization-equalization (ME) algorithm which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than MM. Simulations on synthetic and real data illustrate the faster convergence of the ME approach. The paper also describes how the proposed algorithms can be adapted to two common variants of NMF : penalized NMF (i.e., when a penalty function of the factors is added to the criterion function) and convex-NMF (when the dictionary is assumed to belong to a known subspace).
1010.1800
Proactive Resource Allocation: Turning Predictable Behavior into Spectral Gain
cs.IT cs.NI cs.SI math.IT
This paper introduces the novel concept of proactive resource allocation in which the predictability of user behavior is exploited to balance the wireless traffic over time, and hence, significantly reduce the bandwidth required to achieve a given blocking/outage probability. We start with a simple model in which the smart wireless devices are assumed to predict the arrival of new requests and submit them to the network T time slots in advance. Using tools from large deviation theory, we quantify the resulting prediction diversity gain to establish that the decay rate of the outage event probabilities increases linearly with the prediction duration T. This model is then generalized to incorporate the effect of prediction errors and the randomness in the prediction lookahead time T. Remarkably, we also show that, in the cognitive networking scenario, the appropriate use of proactive resource allocation by the primary users results in more spectral opportunities for the secondary users at a marginal, or no, cost in the primary network outage. Finally, we conclude by a discussion of the new research questions posed under the umbrella of the proposed proactive (non-causal) wireless networking framework.
1010.1824
Implications of Inter-Rater Agreement on a Student Information Retrieval Evaluation
cs.IR
This paper is about an information retrieval evaluation on three different retrieval-supporting services. All three services were designed to compensate typical problems that arise in metadata-driven Digital Libraries, which are not adequately handled by a simple tf-idf based retrieval. The services are: (1) a co-word analysis based query expansion mechanism and re-ranking via (2) Bradfordizing and (3) author centrality. The services are evaluated with relevance assessments conducted by 73 information science students. Since the students are neither information professionals nor domain experts the question of inter-rater agreement is taken into consideration. Two important implications emerge: (1) the inter-rater agreement rates were mainly fair to moderate and (2) after a data-cleaning step which erased the assessments with poor agreement rates the evaluation data shows that the three retrieval services returned disjoint but still relevant result sets.
1010.1826
A probabilistic top-down parser for minimalist grammars
cs.CL
This paper describes a probabilistic top-down parser for minimalist grammars. Top-down parsers have the great advantage of having a certain predictive power during the parsing, which takes place in a left-to-right reading of the sentence. Such parsers have already been well-implemented and studied in the case of Context-Free Grammars, which are already top-down, but these are difficult to adapt to Minimalist Grammars, which generate sentences bottom-up. I propose here a way of rewriting Minimalist Grammars as Linear Context-Free Rewriting Systems, allowing to easily create a top-down parser. This rewriting allows also to put a probabilistic field on these grammars, which can be used to accelerate the parser. Finally, I propose a method of refining the probabilistic field by using algorithms used in data compression.
1010.1845
Navigation in non-uniform density social networks
physics.soc-ph cs.SI
Recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $d$ scales as $P(d)\propto d^{-1}$. Since population density is non-uniform in real social networks, a scale invariant friendship network(SIFN) based on the above empirical law is introduced to capture this phenomenon. We prove the time complexity of navigation in 2-dimensional SIFN is at most $O(\log^4 n)$. In the real searching experiment, individuals often resort to extra information besides geography location. Thus, real-world searching process may be seen as a projection of navigation in a $k$-dimensional SIFN($k>2$). Therefore, we also discuss the relationship between high and low dimensional SIFN. Particularly, we prove a 2-dimensional SIFN is the projection of a 3-dimensional SIFN. As a matter of fact, this result can also be generated to any $k$-dimensional SIFN.
1010.1847
Restricted Isometries for Partial Random Circulant Matrices
cs.IT math.IT math.PR
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to succeed when the restricted isometry constants of the sampling matrix are small. Many potential applications of compressed sensing involve a data-acquisition process that proceeds by convolution with a random pulse followed by (nonrandom) subsampling. At present, the theoretical analysis of this measurement technique is lacking. This paper demonstrates that the $s$th order restricted isometry constant is small when the number $m$ of samples satisfies $m \gtrsim (s \log n)^{3/2}$, where $n$ is the length of the pulse. This bound improves on previous estimates, which exhibit quadratic scaling.
1010.1862
Utility Optimal Scheduling in Processing Networks
math.OC cs.SY
We consider the problem of utility optimal scheduling in general \emph{processing networks} with random arrivals and network conditions. These are generalizations of traditional data networks where commodities in one or more queues can be combined to produce new commodities that are delivered to other parts of the network. This can be used to model problems such as in-network data fusion, stream processing, and grid computing. Scheduling actions are complicated by the \emph{underflow problem} that arises when some queues with required components go empty. In this paper, we develop the Perturbed Max-Weight algorithm (PMW) to achieve optimal utility. The idea of PMW is to perturb the weights used by the usual Max-Weight algorithm to ``push'' queue levels towards non-zero values (avoiding underflows). We show that when the perturbations are carefully chosen, PMW is able to achieve a utility that is within $O(1/V)$ of the optimal value for any $V\geq1$, while ensuring an average network backlog of $O(V)$.
1010.1864
Transforming complex network to the acyclic one
physics.soc-ph cond-mat.dis-nn cs.SI
Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an acyclic network allows finding structural properties of the network. With our approach one can find the communities and key nodes in complex networks. Also we propose a new parameter of complex networks which can mark most vulnerable nodes of the system. The proposed algorithm can be applied to finding communities and bottlenecks in general complex networks.
1010.1865
Corrections to "Unified Laguerre polynomial-series-based distribution of small-scale fading envelopes''
math.PR cs.IT math.IT
In this correspondence, we point out two typographical errors in Chai and Tjhung's paper and we offer the correct formula of the unified Laguerre polynomial-series-based cumulative distribution function (cdf) for small-scale fading distributions. A Laguerre polynomial-series-based cdf formula for non-central chi-square distribution is also provided as a special case of our unified cdf result.
1010.1866
Fast error-tolerant quartet phylogeny algorithms
q-bio.PE cs.CE cs.DS
We present an algorithm for phylogenetic reconstruction using quartets that returns the correct topology for $n$ taxa in $O(n \log n)$ time with high probability, in a probabilistic model where a quartet is not consistent with the true topology of the tree with constant probability, independent of other quartets. Our incremental algorithm relies upon a search tree structure for the phylogeny that is balanced, with high probability, no matter what the true topology is. Our experimental results show that our method is comparable in runtime to the fastest heuristics, while still offering consistency guarantees.
1010.1886
Inner Product Spaces for MinSum Coordination Mechanisms
cs.GT cs.DS cs.MA
We study policies aiming to minimize the weighted sum of completion times of jobs in the context of coordination mechanisms for selfish scheduling problems. Our goal is to design local policies that achieve a good price of anarchy in the resulting equilibria for unrelated machine scheduling. To obtain the approximation bounds, we introduce a new technique that while conceptually simple, seems to be quite powerful. With this method we are able to prove the following results. First, we consider Smith's Rule, which orders the jobs on a machine in ascending processing time to weight ratio, and show that it achieves an approximation ratio of 4. We also demonstrate that this is the best possible for deterministic non-preemptive strongly local policies. Since Smith's Rule is always optimal for a given assignment, this may seem unsurprising, but we then show that better approximation ratios can be obtained if either preemption or randomization is allowed. We prove that ProportionalSharing, a preemptive strongly local policy, achieves an approximation ratio of 2.618 for the weighted sum of completion times, and an approximation ratio of 2.5 in the unweighted case. Again, we observe that these bounds are tight. Next, we consider Rand, a natural non-preemptive but randomized policy. We show that it achieves an approximation ratio of at most 2.13; moreover, if the sum of the weighted completion times is negligible compared to the cost of the optimal solution, this improves to \pi /2. Finally, we show that both ProportionalSharing and Rand induce potential games, and thus always have a pure Nash equilibrium (unlike Smith's Rule). This also allows us to design the first \emph{combinatorial} constant-factor approximation algorithm minimizing weighted completion time for unrelated machine scheduling that achieves a factor of 2+ \epsilon for any \epsilon > 0.
1010.1888
Multi-Objective Genetic Programming Projection Pursuit for Exploratory Data Modeling
cs.LG cs.NE
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the number of samples needed for a classification task increases exponentially as the number of dimensions (variables, features) increases. On the other hand, it is costly to collect, store and process data. Moreover, irrelevant and redundant features might hinder classifier performance. In exploratory analysis settings, high dimensionality prevents the users from exploring the data visually. Feature extraction is a two-step process: feature construction and feature selection. Feature construction creates new features based on the original features and feature selection is the process of selecting the best features as in filter, wrapper and embedded methods. In this work, we focus on feature construction methods that aim to decrease data dimensionality for visualization tasks. Various linear (such as principal components analysis (PCA), multiple discriminants analysis (MDA), exploratory projection pursuit) and non-linear (such as multidimensional scaling (MDS), manifold learning, kernel PCA/LDA, evolutionary constructive induction) techniques have been proposed for dimensionality reduction. Our algorithm is an adaptive feature extraction method which consists of evolutionary constructive induction for feature construction and a hybrid filter/wrapper method for feature selection.
1010.1899
The Failure Probability at Sink Node of Random Linear Network Coding
cs.IT math.IT
In practice, since many communication networks are huge in scale or complicated in structure even dynamic, the predesigned network codes based on the network topology is impossible even if the topological structure is known. Therefore, random linear network coding was proposed as an acceptable coding technique. In this paper, we further study the performance of random linear network coding by analyzing the failure probabilities at sink node for different knowledge of network topology and get some tight and asymptotically tight upper bounds of the failure probabilities. In particular, the worst cases are indicated for these bounds. Furthermore, if the more information about the network topology is utilized, the better upper bounds are obtained. These bounds improve on the known ones. Finally, we also discuss the lower bound of this failure probability and show that it is also asymptotically tight.
1010.1904
Weighted Indices for Evaluating the Quality of Research with Multiple Authorship
cs.IR cs.CY cs.DL
Devising an index to measure the quality of research is a challenging task. In this paper, we propose a set of indices to evaluate the quality of research produced by an author. Our indices utilize a policy that assigns the weights to multiple authors of a paper. We have considered two weight assignment policies: positionally weighted and equally weighted. We propose two classes of weighted indices: weighted h-indices and weighted citation h-cuts. Further, we compare our weighted h-indices with the original h-index for a selected set of authors. As opposed to h-index, our weighted h-indices take into account the weighted contributions of individual authors in multi-authored papers, and may serve as an improvement over h-index. The other class of weighted indices that we call weighted citation h-cuts take into account the number of citations that are in excess of those required to compute the index, and may serve as a supplement to h-index or its variants.
1010.1911
On a Low-Rate TLDPC Code Ensemble and the Necessary Condition on the Linear Minimum Distance for Sparse-Graph Codes
cs.IT math.IT
This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured. The condition is formulated in terms of degree-1 and degree-2 variable nodes and of low-weight codewords of the underlying code, and it generalizies results known for turbo codes [8] and LDPC codes. Then, we present a new ensemble of low-rate codes, which itself is a subclass of TLDPC codes [4], [5], and which is designed under this necessary condition. The asymptotic analysis of the ensemble shows that its iterative threshold is situated close to the Shannon limit. In addition to the linear minimum distance property, it has a simple structure and enjoys a low decoding complexity and a fast convergence.
1010.1953
Passive Supporters of Terrorism and Phase Transitions
physics.soc-ph cs.SI
We discuss some social contagion processes to describe the formation and spread of radical opinions. The dynamics of opinion spread involves local threshold processes as well as mean field effects. We calculate and observe phase transitions in the dynamical variables resulting in a rapidly increasing number of passive supporters. This strongly indicates that military solutions are inappropriate.
1010.1973
For the Grid and Through the Grid: The Role of Power Line Communications in the Smart Grid
cs.NI cs.IT cs.SY math.IT
Is Power Line Communications (PLC) a good candidate for Smart Grid applications? The objective of this paper is to address this important question. To do so we provide an overview of what PLC can deliver today by surveying its history and describing the most recent technological advances in the area. We then address Smart Grid applications as instances of sensor networking and network control problems and discuss the main conclusion one can draw from the literature on these subjects. The application scenario of PLC within the Smart Grid is then analyzed in detail. Since a necessary ingredient of network planning is modeling, we also discuss two aspects of engineering modeling that relate to our question. The first aspect is modeling the PLC channel through fading models. The second aspect we review is the Smart Grid control and traffic modeling problem which allows us to achieve a better understanding of the communications requirements. Finally, this paper reports recent studies on the electrical and topological properties of a sample power distribution network. Power grid topological studies are very important for PLC networking as the power grid is not only the information source \textit{but also} the information delivery system - a unique feature when PLC is used for the Smart Grid.
1010.1985
Relay Strategies Based on Cross-Determinism for the Broadcast Relay Channel
cs.IT math.IT
We consider a two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with a common multiple-antenna relay, and a shared digital (noiseless) link between the relay and the two destinations. For this channel, this paper introduces an asymptotically sum-capacity-achieving quantize-and-forward (QF) relay strategy. Our technique to design an asymptotically optimal relay quantizer is based on identifying a cross-deterministic relation between the relay observation, the source signal, and the destination observation. In a relay channel, an approximate cross deterministic relation corresponds to an approximately deterministic relation, where the relay observation is to some extent a deterministic function of the source and destination signals. We show that cross determinism can serve as a measure for quantization penalty. By identifying an analogy between a deterministic broadcast relay channel and a Gaussian MIMO relay channel, we propose a three-stage dirty paper coding strategy, along with receiver beamforming and quantization at the relay, to asymptotically achieve an extended achievable rate region for the MIMO broadcast channel with a common multiple-antenna relay.
1010.2030
Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields
cs.IT math.IT
The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average weight distribution are proved. Based on this analysis, a general result, including all previous results as special cases, is established for the minimum distance of individual codes in a regular LDPC code ensemble.
1010.2067
Algorithmic Thermodynamics
math-ph cs.IT math.IT math.MP quant-ph
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In particular, suppose we fix a universal prefix-free Turing machine and let X be the set of programs that halt for this machine. Then we can regard X as a set of 'microstates', and treat any function on X as an 'observable'. For any collection of observables, we can study the Gibbs ensemble that maximizes entropy subject to constraints on expected values of these observables. We illustrate this by taking the log runtime, length, and output of a program as observables analogous to the energy E, volume V and number of molecules N in a container of gas. The conjugate variables of these observables allow us to define quantities which we call the 'algorithmic temperature' T, 'algorithmic pressure' P and algorithmic potential' mu, since they are analogous to the temperature, pressure and chemical potential. We derive an analogue of the fundamental thermodynamic relation dE = T dS - P d V + mu dN, and use it to study thermodynamic cycles analogous to those for heat engines. We also investigate the values of T, P and mu for which the partition function converges. At some points on the boundary of this domain of convergence, the partition function becomes uncomputable. Indeed, at these points the partition function itself has nontrivial algorithmic entropy.
1010.2102
Hierarchical Multiclass Decompositions with Application to Authorship Determination
cs.AI
This paper is mainly concerned with the question of how to decompose multiclass classification problems into binary subproblems. We extend known Jensen-Shannon bounds on the Bayes risk of binary problems to hierarchical multiclass problems and use these bounds to develop a heuristic procedure for constructing hierarchical multiclass decomposition for multinomials. We test our method and compare it to the well known "all-pairs" decomposition. Our tests are performed using a new authorship determination benchmark test of machine learning authors. The new method consistently outperforms the all-pairs decomposition when the number of classes is small and breaks even on larger multiclass problems. Using both methods, the classification accuracy we achieve, using an SVM over a feature set consisting of both high frequency single tokens and high frequency token-pairs, appears to be exceptionally high compared to known results in authorship determination.
1010.2128
Parameter Selection in Periodic Nonuniform Sampling of Multiband Signals
cs.SY
Periodic nonuniform sampling has been considered in literature as an effective approach to reduce the sampling rate far below the Nyquist rate for sparse spectrum multiband signals. In the presence of non-ideality the sampling parameters play an important role on the quality of reconstructed signal. Also the average sampling ratio is directly dependent on the sampling parameters that they should be chosen for a minimum rate and complexity. In this paper we consider the effect of sampling parameters on the reconstruction error and the sampling ratio and suggest feasible approaches for achieving an optimal sampling and reconstruction.
1010.2141
Modeling the evolution of continuously-observed networks: Communication in a Facebook-like community
physics.soc-ph cs.SI
Building on existing stochastic actor-oriented models for panel data, we employ a conditional logistic framework to explore growth mechanisms for tie creation in continuously-observed networks. This framework models the likelihood of tie formation distinguishing it from hazard models that consider time to tie formation. It enables multiple growth mechanisms for network evolution (homophily, focus constraints, reinforcement, reciprocity, triadic closure, and popularity) to be modeled simultaneously. We apply this framework to communication within a Facebook-like community. The findings exemplify the inadequacy of descriptive measures that test single mechanisms independently. They also indicate how system design shapes behavior and network evolution.
1010.2148
Ontological Matchmaking in Recommender Systems
cs.DB
The electronic marketplace offers great potential for the recommendation of supplies. In the so called recommender systems, it is crucial to apply matchmaking strategies that faithfully satisfy the predicates specified in the demand, and take into account as much as possible the user preferences. We focus on real-life ontology-driven matchmaking scenarios and identify a number of challenges, being inspired by such scenarios. A key challenge is that of presenting the results to the users in an understandable and clear-cut fashion in order to facilitate the analysis of the results. Indeed, such scenarios evoke the opportunity to rank and group the results according to specific criteria. A further challenge consists of presenting the results to the user in an asynchronous fashion, i.e. the 'push' mode, along with the 'pull' mode, in which the user explicitly issues a query, and displays the results. Moreover, an important issue to consider in real-life cases is the possibility of submitting a query to multiple providers, and collecting the various results. We have designed and implemented an ontology-based matchmaking system that suitably addresses the above challenges. We have conducted a comprehensive experimental study, in order to investigate the usability of the system, the performance and the effectiveness of the matchmaking strategies with real ontological datasets.
1010.2157
A Wideband Spectrum Sensing Method for Cognitive Radio using Sub-Nyquist Sampling
cs.IT math.IT
Spectrum sensing is a fundamental component in cognitive radio. A major challenge in this area is the requirement of a high sampling rate in the sensing of a wideband signal. In this paper a wideband spectrum sensing model is presented that utilizes a sub-Nyquist sampling scheme to bring substantial savings in terms of the sampling rate. The correlation matrix of a finite number of noisy samples is computed and used by a subspace estimator to detect the occupied and vacant channels of the spectrum. In contrast with common methods, the proposedmethod does not need the knowledge of signal properties that mitigates the uncertainty problem. We evaluate the performance of this method by computing the probability of detecting signal occupancy in terms of the number of samples and the SNR of randomly generated signals. The results show a reliable detection even in low SNR and small number of samples.
1010.2158
Non-uniform sampling and reconstruction of multi-band signals and its application in wideband spectrum sensing of cognitive radio
cs.IT math.IT
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of limitations encountered in current converters are due to a traditional assumption that the sampling state needs to acquire the data at the Nyquist rate, corresponding to twice the signal bandwidth. In this thesis a method of sampling far below the Nyquist rate for sparse spectrum multiband signals is investigated. The method is called periodic non-uniform sampling, and it is useful in a variety of applications such as data converters, sensor array imaging and image compression. Firstly, a model for the sampling system in the frequency domain is prepared. It relates the Fourier transform of observed compressed samples with the unknown spectrum of the signal. Next, the reconstruction process based on the topic of compressed sensing is provided. We show that the sampling parameters play an important role on the average sample ratio and the quality of the reconstructed signal. The concept of condition number and its effect on the reconstructed signal in the presence of noise is introduced, and a feasible approach for choosing a sample pattern with a low condition number is given. We distinguish between the cases of known spectrum and unknown spectrum signals respectively. One of the model parameters is determined by the signal band locations that in case of unknown spectrum signals should be estimated from sampled data. Therefore, we applied both subspace methods and non-linear least square methods for estimation of this parameter. We also used the information theoretic criteria (Akaike and MDL) and the exponential fitting test techniques for model order selection in this case.
1010.2160
Robustness of interdependent networks under targeted attack
physics.soc-ph cs.SI physics.data-an
When an initial failure of nodes occurs in interdependent networks, a cascade of failure between the networks occurs. Earlier studies focused on random initial failures. Here we study the robustness of interdependent networks under targeted attack on high or low degree nodes. We introduce a general technique and show that the {\it targeted-attack} problem in interdependent networks can be mapped to the {\it random-attack} problem in a transformed pair of interdependent networks. We find that when the highly connected nodes are protected and have lower probability to fail, in contrast to single scale free (SF) networks where the percolation threshold $p_c=0$, coupled SF networks are significantly more vulnerable with $p_c$ significantly larger than zero. The result implies that interdependent networks are difficult to defend by strategies such as protecting the high degree nodes that have been found useful to significantly improve robustness of single networks.
1010.2173
Complex network model of the phase transition on the wealth distributions - from Pareto to the society without middle class
physics.soc-ph cond-mat.dis-nn cs.SI
A model of distribution of the wealth in a society based on the properties of complex networks has been proposed. The wealth is interpreted as a consequence of communication possibilities and proportional to the number of connections possessed by a person (as a vertex of the social network). Numerical simulation of wealth distribution shows a transition from the Pareto law to distribution with a gap demonstrating the absence of the middle class. Such a transition has been described as a second-order phase transition, the order parameter has been introduced and the value of the critical exponent has been found.
1010.2186
On Opinion Dynamics in Heterogeneous Networks
math-ph cs.SI math.MP physics.soc-ph
This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: each agent in a group maintains a real number describing its opinion; and each agent updates its opinion by averaging all other opinions that are within some given confidence range. The confidence ranges are distinct for each agent. This heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. We conjecture that any trajectory of this model eventually converges to a steady state under fixed topology. To establish this conjecture, we derive two novel sufficient conditions: both conditions guarantee convergence and constant topology for infinite time, while one condition also guarantees monotonicity of the convergence. In the evolution under fixed topology for infinite time, we define leader groups that determine the followers' rate and direction of convergence.
1010.2198
Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation
cs.IT math.IT
There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces are especially important with many practical applications in computer vision, image and signal processing, communications, and information theory. This paper presents a clustering algorithm for high dimensional data that comes from a union of lower dimensional subspaces of equal and known dimensions. Such cases occur in many data clustering problems, such as motion segmentation and face recognition. The algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset, it generates the best results to date for motion segmentation. The two motion, three motion, and overall segmentation rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively.
1010.2236
On the Scaling Law for Compressive Sensing and its Applications
cs.IT math.IT
$\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity (the size of the support set), under which with high probability a sparse signal can be recovered from i.i.d. Gaussian measurements, have been computed and are referred to as "weak thresholds" \cite{D}. It was also known that there is a tradeoff between the sparsity and the $\ell_1$ minimization recovery stability. In this paper, we give a \emph{closed-form} characterization for this tradeoff which we call the scaling law for compressive sensing recovery stability. In a nutshell, we are able to show that as the sparsity backs off $\varpi$ ($0<\varpi<1$) from the weak threshold of $\ell_1$ recovery, the parameter for the recovery stability will scale as $\frac{1}{\sqrt{1-\varpi}}$. Our result is based on a careful analysis through the Grassmann angle framework for the Gaussian measurement matrix. We will further discuss how this scaling law helps in analyzing the iterative reweighted $\ell_1$ minimization algorithms. If the nonzero elements over the signal support follow an amplitude probability density function (pdf) $f(\cdot)$ whose $t$-th derivative $f^{t}(0) \neq 0$ for some integer $t \geq 0$, then a certain iterative reweighted $\ell_1$ minimization algorithm can be analytically shown to lift the phase transition thresholds (weak thresholds) of the plain $\ell_1$ minimization algorithm.
1010.2247
Regions of Attraction for Hybrid Limit Cycles of Walking Robots
math.OC cs.RO cs.SY
This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the "rimless wheel", and the "compass gait", the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.
1010.2285
Information-based complexity, feedback and dynamics in convex programming
cs.IT cs.SY math.IT math.OC
We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown objective function, and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures; the notable difference is that, unlike in the case of i.i.d. data, a sequential optimization algorithm can gather observations in a {\em controlled} manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimization algorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of information in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information.
1010.2286
Divergence-based characterization of fundamental limitations of adaptive dynamical systems
cs.IT math.IT math.OC
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount importance. In this paper, we consider the general problem of adaptively controlling and/or identifying a stochastic dynamical system, where our {\em a priori} knowledge allows us to place the system in a subset of a metric space (the uncertainty set). We present an information-theoretic meta-theorem that captures the trade-off between the metric complexity (or richness) of the uncertainty set, the amount of information acquired online in the process of controlling and observing the system, and the residual uncertainty remaining after the observations have been collected. Following the approach of Zames, we quantify {\em a priori} information by the Kolmogorov (metric) entropy of the uncertainty set, while the information acquired online is expressed as a sum of information divergences. The general theory is used to derive new minimax lower bounds on the metric identification error, as well as to give a simple derivation of the minimum time needed to stabilize an uncertain stochastic linear system.
1010.2345
Using Context Dependent Semantic Similarity to Browse Information Resources: an Application for the Industrial Design
cs.DL cs.IR
This paper deals with the semantic interpretation of information resources (e.g., images, videos, 3D models). We present a case study of an approach based on semantic and context dependent similarity applied to the industrial design. Different application contexts are considered and modelled to browse a repository of 3D digital objects according to different perspectives. The paper briefly summarises the basic concepts behind the semantic similarity approach and illustrates its application and results.
1010.2358
On Finding Frequent Patterns in Event Sequences
cs.DS cs.DB
Given a directed acyclic graph with labeled vertices, we consider the problem of finding the most common label sequences ("traces") among all paths in the graph (of some maximum length m). Since the number of paths can be huge, we propose novel algorithms whose time complexity depends only on the size of the graph, and on the frequency epsilon of the most frequent traces. In addition, we apply techniques from streaming algorithms to achieve space usage that depends only on epsilon, and not on the number of distinct traces. The abstract problem considered models a variety of tasks concerning finding frequent patterns in event sequences. Our motivation comes from working with a data set of 2 million RFID readings from baggage trolleys at Copenhagen Airport. The question of finding frequent passenger movement patterns is mapped to the above problem. We report on experimental findings for this data set.
1010.2371
On Finding Similar Items in a Stream of Transactions
cs.DS cs.DB
While there has been a lot of work on finding frequent itemsets in transaction data streams, none of these solve the problem of finding similar pairs according to standard similarity measures. This paper is a first attempt at dealing with this, arguably more important, problem. We start out with a negative result that also explains the lack of theoretical upper bounds on the space usage of data mining algorithms for finding frequent itemsets: Any algorithm that (even only approximately and with a chance of error) finds the most frequent k-itemset must use space Omega(min{mb,n^k,(mb/phi)^k}) bits, where mb is the number of items in the stream so far, n is the number of distinct items and phi is a support threshold. To achieve any non-trivial space upper bound we must thus abandon a worst-case assumption on the data stream. We work under the model that the transactions come in random order, and show that surprisingly, not only is small-space similarity mining possible for the most common similarity measures, but the mining accuracy improves with the length of the stream for any fixed support threshold.
1010.2382
Capacity Achieving Modulation for Fixed Constellations with Average Power Constraint
cs.IT math.IT
The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists of first approximating the capacity achieving PMF by a sampled Gaussian density and then to calculate the Huffman code of the sampled Gaussian density. The Huffman code is then used as a prefix-free modulation code. This approach showed good results in practice, can however lead to a significant gap to capacity. In this work, a method is proposed that efficiently constructs optimal prefix-free modulation codes for any finite signal constellation with average power constraint in additive noise. The proposed codes operate as close to capacity as desired. The major part of this work elaborates an analytical proof of this property. The proposed method is applied to 64-QAM in AWGN and numeric results are given, which show that, opposed to Huffman shaping, by using the proposed method, it is possible to operate very close to capacity over the whole range of parameters.
1010.2384
Learning Taxonomy for Text Segmentation by Formal Concept Analysis
cs.CL
In this paper the problems of deriving a taxonomy from a text and concept-oriented text segmentation are approached. Formal Concept Analysis (FCA) method is applied to solve both of these linguistic problems. The proposed segmentation method offers a conceptual view for text segmentation, using a context-driven clustering of sentences. The Concept-oriented Clustering Segmentation algorithm (COCS) is based on k-means linear clustering of the sentences. Experimental results obtained using COCS algorithm are presented.
1010.2433
Capacity of 1-to-K Broadcast Packet Erasure Channels with Channel Output Feedback
cs.IT math.IT
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for general 1-to-3 broadcast PECs, and (ii) The capacity region for two classes of 1-to-K broadcast PECs: the symmetric PECs, and the spatially independent PECs with one-sided fairness constraints. This paper also develops (iii) A pair of outer and inner bounds of the capacity region for arbitrary 1-to-K broadcast PECs, which can be evaluated by any linear programming solver. For most practical scenarios, the outer and inner bounds meet and thus jointly characterize the capacity.
1010.2436
Capacity of 1-to-K Broadcast Packet Erasure Channels with Channel Output Feedback (Full Version)
cs.IT math.IT
This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. The capacity region of the 1-to-K PEC with COF was previously known only for the case K=2. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for general 1-to-3 broadcast PECs, and (ii) The capacity region for two types of 1-to-$K$ broadcast PECs: the symmetric PECs, and the spatially independent PECs with one-sided fairness constraints. This paper also develops (iii) A pair of outer and inner bounds of the capacity region for arbitrary 1-to-K broadcast PECs, which can be easily evaluated by any linear programming solver. The proposed inner bound is proven by a new class of intersession network coding schemes, termed the packet evolution schemes, which is based on the concept of code alignment in GF(q) that is in parallel with the interference alignment techniques for the Euclidean space. Extensive numerical experiments show that the outer and inner bounds meet for almost all broadcast PECs encountered in practical scenarios and thus effectively bracket the capacity of general 1-to-K broadcast PECs with COF.
1010.2437
On Achievable Rates of the Two-user Symmetric Gaussian Interference Channel
cs.IT math.IT
We study the Han-Kobayashi (HK) achievable sum rate for the two-user symmetric Gaussian interference channel. We find the optimal power split ratio between the common and private messages (assuming no time-sharing), and derive a closed form expression for the corresponding sum rate. This provides a finer understanding of the achievable HK sum rate, and allows for precise comparisons between this sum rate and that of orthogonal signaling. One surprising finding is that despite the fact that the channel is symmetric, allowing for asymmetric power split ratio at both users (i.e., asymmetric rates) can improve the sum rate significantly. Considering the high SNR regime, we specify the interference channel value above which the sum rate achieved using asymmetric power splitting outperforms the symmetric case.
1010.2438
On Designing Multicore-aware Simulators for Biological Systems
cs.DC cs.CE q-bio.QM
The stochastic simulation of biological systems is an increasingly popular technique in bioinformatics. It often is an enlightening technique, which may however result in being computational expensive. We discuss the main opportunities to speed it up on multi-core platforms, which pose new challenges for parallelisation techniques. These opportunities are developed in two general families of solutions involving both the single simulation and a bulk of independent simulations (either replicas of derived from parameter sweep). Proposed solutions are tested on the parallelisation of the CWC simulator (Calculus of Wrapped Compartments) that is carried out according to proposed solutions by way of the FastFlow programming framework making possible fast development and efficient execution on multi-cores.
1010.2439
Conservation Law of Utility and Equilibria in Non-Zero Sum Games
cs.GT cs.AI math.OC
This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the law of conservation of utility in a game. In a transformed game, each participant plays against all other players, including the passive player. The advantage of this approach is that the transformed game is zero-sum and has an equilibrium solution. The optimal strategy and the value of the new game, however, can be different from strategies that are rational in the original game. We demonstrate the principle using the Prisoner's Dilemma example.
1010.2440
Enabling Data Discovery through Virtual Internet Repositories
cs.DL cs.IR
Mercury is a federated metadata harvesting, search and retrieval tool based on both open source and software developed at Oak Ridge National Laboratory. It was originally developed for NASA, and the Mercury development consortium now includes funding from NASA, USGS, and DOE. A major new version of Mercury was developed during 2007. This new version provides orders of magnitude improvements in search speed, support for additional metadata formats, integration with Google Maps for spatial queries, support for RSS delivery of search results, among other features. Mercury provides a single portal to information contained in disparate data management systems. It collects metadata and key data from contributing project servers distributed around the world and builds a centralized index. The Mercury search interfaces then allow the users to perform simple, fielded, spatial and temporal searches across these metadata sources. This centralized repository of metadata with distributed data sources provides extremely fast search results to the user, while allowing data providers to advertise the availability of their data and maintain complete control and ownership of that data.
1010.2441
Note on Noisy Group Testing: Asymptotic Bounds and Belief Propagation Reconstruction
cs.IT math.IT
An information theoretic perspective on group testing problems has recently been proposed by Atia and Saligrama, in order to characterise the optimal number of tests. Their results hold in the noiseless case, where only false positives occur, and where only false negatives occur. We extend their results to a model containing both false positives and false negatives, developing simple information theoretic bounds on the number of tests required. Based on these bounds, we obtain an improved order of convergence in the case of false negatives only. Since these results are based on (computationally infeasible) joint typicality decoding, we propose a belief propagation algorithm for the detection of defective items and compare its actual performance to the theoretical bounds.
1010.2457
Optimal designs for Lasso and Dantzig selector using Expander Codes
math.ST cs.IT math.IT math.PR stat.ME stat.ML stat.TH
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are optimal up to an explicit multiplicative constant. Thus we can estimate a high-dimensional target vector with an error term similar to the one obtained in a situation where one knows the support of the largest coordinates in advance. Moreover, we show that these design matrices have an explicit restricted eigenvalue. Precisely, they satisfy the restricted eigenvalue assumption and the compatibility condition with an explicit constant. Eventually, we capitalize on the recent construction of unbalanced expander graphs due to Guruswami, Umans, and Vadhan, to provide a deterministic polynomial time construction of these design matrices.
1010.2460
Line graphs as social networks
physics.soc-ph cs.SI physics.data-an
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.
1010.2521
Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach
physics.soc-ph cs.SI
Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well.
1010.2551
Fractional Repetition Codes for Repair in Distributed Storage Systems
cs.IT math.IT
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity while a precise expression remains an open problem.
1010.2571
Cooperative Precoding with Limited Feedback for MIMO Interference Channels
cs.IT math.IT
Multi-antenna precoding effectively mitigates the interference in wireless networks. However, the resultant performance gains can be significantly compromised in practice if the precoder design fails to account for the inaccuracy in the channel state information (CSI) feedback. This paper addresses this issue by considering finite-rate CSI feedback from receivers to their interfering transmitters in the two-user multiple-input-multiple-output (MIMO) interference channel, called cooperative feedback, and proposing a systematic method for designing transceivers comprising linear precoders and equalizers. Specifically, each precoder/equalizer is decomposed into inner and outer components for nulling the cross-link interference and achieving array gain, respectively. The inner precoders/equalizers are further optimized to suppress the residual interference resulting from finite-rate cooperative feedback. Further- more, the residual interference is regulated by additional scalar cooperative feedback signals that are designed to control transmission power using different criteria including fixed interference margin and maximum sum throughput. Finally, the required number of cooperative precoder feedback bits is derived for limiting the throughput loss due to precoder quantization.
1010.2572
Empirical study on some interconnecting bilayer networks
physics.soc-ph cs.SI
This manuscript serves as an online supplement of a preprint, which presents a study on a kind of bilayer networks where some nodes (called interconnecting nodes) in two layers merge. A model showing an important general property of the bilayer networks is proposed. Then the analytic discussion of the model is compared with empirical conclusions. We present all the empirical observations in this online supplement.
1010.2595
Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
cs.LO cs.CC cs.IT math.IT physics.data-an
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using compression and to Kolmogorov complexity from a conceptual point of view. We present and unify these different approaches to classification in terms of Bottom-Up versus Top-Down operational modes, of which we point the fundamental principles and the underlying duality. We look at the way these two dual modes are used in different approaches to information system, particularly the relational model for database introduced by Codd in the 70's. This allows to point out diverse forms of a fundamental duality. These operational modes are also reinterpreted in the context of the comprehension schema of axiomatic set theory ZF. This leads us to develop how Kolmogorov's complexity is linked to intensionality, abstraction, classification and information system.
1010.2619
Graph-theoretical Constructions for Graph Entropy and Network Coding Based Communications
cs.IT cs.NI math.CO math.IT
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number. First, we introduce an undirected graph on all possible configurations of the digraph, referred to as the guessing graph, which encapsulates the essence of dependence amongst configurations. We prove that the guessing number of a digraph is equal to the logarithm of the independence number of its guessing graph. Therefore, network coding solvability is no more a problem on the operations made by each node, but is simplified into a problem on the messages that can transit through the network. By studying the guessing graph of a given digraph, and how to combine digraphs or alphabets, we are thus able to derive bounds on the guessing number of digraphs. Second, we construct specific digraphs with high guessing numbers, yielding network coding instances where a large amount of information can transit. We first propose a construction of digraphs with finite parameters based on cyclic codes, with guessing number equal to the degree of the generator polynomial. We then construct an infinite class of digraphs with arbitrary girth for which the ratio between the linear guessing number and the number of vertices tends to one, despite these digraphs being arbitrarily sparse. These constructions yield solvable network coding instances with a relatively small number of intermediate nodes for which the node operations are known and linear, although these instances are sparse and the sources are arbitrarily far from their corresponding sinks.
1010.2656
Indexing Finite Language Representation of Population Genotypes
cs.DS cs.CE q-bio.QM
With the recent advances in DNA sequencing, it is now possible to have complete genomes of individuals sequenced and assembled. This rich and focused genotype information can be used to do different population-wide studies, now first time directly on whole genome level. We propose a way to index population genotype information together with the complete genome sequence, so that one can use the index to efficiently align a given sequence to the genome with all plausible genotype recombinations taken into account. This is achieved through converting a multiple alignment of individual genomes into a finite automaton recognizing all strings that can be read from the alignment by switching the sequence at any time. The finite automaton is indexed with an extension of Burrows-Wheeler transform to allow pattern search inside the plausible recombinant sequences. The size of the index stays limited, because of the high similarity of individual genomes. The index finds applications in variation calling and in primer design. On a variation calling experiment, we found about 1.0% of matches to novel recombinants just with exact matching, and up to 2.4% with approximate matching.
1010.2667
Virtual Full-Duplex Wireless Communication via Rapid On-Off-Division Duplex
cs.IT cs.NI math.IT
This paper introduces a novel paradigm for design- ing the physical and medium access control (MAC) layers of mobile ad hoc or peer-to-peer networks formed by half-duplex radios. A node equipped with such a radio cannot simultaneously transmit and receive useful signals at the same frequency. Unlike in conventional designs, where a node's transmission frames are scheduled away from its reception, each node transmits its signal through a randomly generated on-off duplex mask (or signature) over every frame interval, and receive a signal through each of its own off-slots. This is called rapid on-off- division duplex (RODD). Over the period of a single frame, every node can transmit a message to some or all of its peers, and may simultaneously receive a message from each peer. Thus RODD achieves virtual full-duplex communication using half-duplex radios and can simplify the design of higher layers of a network protocol stack significantly. The throughput of RODD is evaluated under some general settings, which is significantly larger than that of ALOHA. RODD is especially efficient in case the dominant traffic is simultaneous broadcast from nodes to their one-hop peers, such as in spontaneous wireless social networks, emergency situations or on battlefield. Important design issues of peer discovery, distribution of on-off signatures, synchronization and error-control coding are also addressed.
1010.2686
How to Achieve the Optimal DMT of Selective Fading MIMO Channels?
cs.IT math.IT
In this paper, we consider a particular class of selective fading channel corresponding to a channel that is selective either in time or in frequency. For this class of channel, we propose a systematic way to achieve the optimal DMT derived in Coronel and B\"olcskei, IEEE ISIT, 2007 by extending the non-vanishing determinant (NVD) criterion to the selective channel case. A new code construction based on split NVD parallel codes is then proposed to satisfy the NVD parallel criterion. This result is of significant interest not only in its own right, but also because it settles a long-standing debate in the literature related to the optimal DMT of selective fading channels.
1010.2692
Resource Allocation via Sum-Rate Maximization in the Uplink of Multi-Cell OFDMA Networks
math.OC cs.IT math.IT
In this paper, we consider maximizing the sum-rate in the uplink of a multi-cell OFDMA network. The problem has a non-convex combinatorial structure and is known to be NP hard. Due to the inherent complexity of implementing the optimal solution, firstly, we derive an upper and lower bound to the optimal average network throughput. Moreover, we investigate the performance of a near optimal single cell resource allocation scheme in the presence of ICI which leads to another easily computable lower bound. We then develop a centralized sub-optimal scheme that is composed of a geometric programming based power control phase in conjunction with an iterative subcarrier allocation phase. Although, the scheme is computationally complex, it provides an effective benchmark for low complexity schemes even without the power control phase. Finally, we propose less complex centralized and distributed schemes that are well-suited for practical scenarios. The computational complexity of all schemes is analyzed and performance is compared through simulations. Simulation results demonstrate that the proposed low complexity schemes can achieve comparable performance to the centralized sub-optimal scheme in various scenarios. Moreover, comparisons with the upper and lower bounds provide insight on the performance gap between the proposed schemes and the optimal solution.
1010.2731
A Unified Framework for High-Dimensional Analysis of M-Estimators with Decomposable Regularizers
math.ST cs.IT math.IT stat.ME stat.TH
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a line of recent work has studied models with various types of low-dimensional structure, including sparse vectors, sparse and structured matrices, low-rank matrices and combinations thereof. In such settings, a general approach to estimation is to solve a regularized optimization problem, which combines a loss function measuring how well the model fits the data with some regularization function that encourages the assumed structure. This paper provides a unified framework for establishing consistency and convergence rates for such regularized M-estimators under high-dimensional scaling. We state one main theorem and show how it can be used to re-derive some existing results, and also to obtain a number of new results on consistency and convergence rates, in both $\ell_2$-error and related norms. Our analysis also identifies two key properties of loss and regularization functions, referred to as restricted strong convexity and decomposability, that ensure corresponding regularized M-estimators have fast convergence rates and which are optimal in many well-studied cases.
1010.2733
Combinatorial Continuous Maximal Flows
cs.CV math.OC
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit metrication artefacts in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no metrication errors. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combinatorial continuous max-flow CCMF problem to find a null-divergence solution that exhibits no metrication artefacts and may be solved exactly by a fast, efficient algorithm with provable convergence. Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the fact, already proved by Nozawa in the continuous setting, that the max-flow and the total variation problems are not always equivalent.
1010.2741
MIMO Interference Alignment Over Correlated Channels with Imperfect CSI
cs.IT math.IT
Interference alignment (IA), given uncorrelated channel components and perfect channel state information, obtains the maximum degrees of freedom in an interference channel. Little is known, however, about how the sum rate of IA behaves at finite transmit power, with imperfect channel state information, or antenna correlation. This paper provides an approximate closed-form signal-to-interference-plus-noise-ratio (SINR) expression for IA over multiple-input-multiple-output (MIMO) channels with imperfect channel state information and transmit antenna correlation. Assuming linear processing at the transmitters and zero-forcing receivers, random matrix theory tools are utilized to derive an approximation for the post-processing SINR distribution of each stream for each user. Perfect channel knowledge and i.i.d. channel coefficients constitute special cases. This SINR distribution not only allows easy calculation of useful performance metrics like sum rate and symbol error rate, but also permits a realistic comparison of IA with other transmission techniques. More specifically, IA is compared with spatial multiplexing and beamforming and it is shown that IA may not be optimal for some performance criteria.
1010.2787
Interference Alignment with Analog Channel State Feedback
cs.IT math.IT
Interference alignment (IA) is a multiplexing gain optimal transmission strategy for the interference channel. While the achieved sum rate with IA is much higher than previously thought possible, the improvement often comes at the cost of requiring network channel state information at the transmitters. This can be achieved by explicit feedback, a flexible yet potentially costly approach that incurs large overhead. In this paper we propose analog feedback as an alternative to limited feedback or reciprocity based alignment. We show that the full multiplexing gain observed with perfect channel knowledge is preserved by analog feedback and that the mean loss in sum rate is bounded by a constant when signal-to-noise ratio is comparable in both forward and feedback channels. When signal-to-noise ratios are not quite symmetric, a fraction of the multiplexing gain is achieved. We consider the overhead of training and feedback and use this framework to optimize the system's effective throughput. We present simulation results to demonstrate the performance of IA with analog feedback, verify our theoretical analysis, and extend our conclusions on optimal training and feedback length.