arXiv subjects

Venugopal V. Veeravalli

Publications and source records attributed to Venugopal V. Veeravalli.

At least 73 records · Page 4Linked to original sources

arXiv2014

Universal Scheme for Optimal Search and Stop

The problem of universal search and stop using an adaptive search policy is considered. When the target location is searched, the observation is distributed according to the target distribution, otherwise it is distributed according to the absence distribution. A universal sequential scheme for search and stop is proposed using only the knowledge of the absence distribution, and its asymptotic performance is analyzed. The universal test is shown to yield a vanishing error probability, and to achieve the optimal reliability when the target is present, universally for every target distribution. Consequently, it is established that the knowledge of the target distribution is only useful for improving the reliability for detecting a missing target. It is also shown that a multiplicative gain for the search reliability equal to the number of searched locations is achieved by allowing adaptivity in the search.

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arXiv2014

Universal Sequential Outlier Hypothesis Testing

Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are generated by an "outlier" distribution, distinct from a common "typical" distribution governing the majority of the sequences. Apart from being distinct, the outlier and typical distributions can be arbitrarily close. The goal is to design a universal test to best discern all the outlier sequences. A universal test with the flavor of the repeated significance test is proposed and its asymptotic performance is characterized under various universal settings. The proposed test is shown to be universally consistent. For the model with identical outliers, the test is shown to be asymptotically optimal universally when the number of outliers is the largest possible and with the typical distribution being known, and its asymptotic performance otherwise is also characterized. An extension of the findings to the model with multiple distinct outliers is also discussed. In all cases, it is shown that the asymptotic performance guarantees for the proposed test when neither the outlier nor typical distribution is known converge to those when the typical distribution is known.

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arXiv2014

Data-Efficient Quickest Outlying Sequence Detection in Sensor Networks

A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the outlying sequences as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and algorithms are proposed that are shown to be asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by using the outcome of a sequence of biased coin tosses, independent of the observation process.

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arXiv2014

Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in some sense. An algorithm is proposed in which on-off observation control is employed using the least favorable distribution, and a generalized likelihood ratio based approach is used for change detection. Under the additional condition that either the post-change family of distributions is finite, or both the pre- and post-change distributions belong to a one parameter exponential family, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.

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arXiv2014

Universal Outlier Hypothesis Testing

Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed according to an ``outlier'' distribution, distinct from the ``typical'' distribution governing the observations in all the other sequences. Nothing is known about the outlier and typical distributions except that they are distinct and have full supports. The goal is to design a universal test to best discern the outlier sequence(s). It is shown that the generalized likelihood test is universally exponentially consistent under various settings. The achievable error exponent is also characterized. In the other settings, it is also shown that there cannot exist any universally exponentially consistent test.

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arXiv2014

Flexible Backhaul Design and Degrees of Freedom for Linear Interference Networks

The considered problem is that of maximizing the degrees of freedom (DoF) in cellular downlink, under a backhaul load constraint that limits the number of messages that can be delivered from a centralized controller to the base station transmitters. A linear interference channel model is considered, where each transmitter is connected to the receiver having the same index as well as one succeeding receiver. The backhaul load is defined as the sum of all the messages available at all the transmitters normalized by the number of users. When the backhaul load is constrained to an integer level B, the asymptotic per user DoF is shown to equal (4B-1)/(4B), and it is shown that the optimal assignment of messages to transmitters is asymmetric and satisfies a local cooperation constraint and that the optimal coding scheme relies only on zero-forcing transmit beamforming. Finally, an extension of the presented coding scheme is shown to apply for more general locally connected and two-dimensional networks.

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arXiv2013

Dynamic Interference Management

A linear interference network is considered. Long-term fluctuations (shadow fading) in the wireless channel can lead to any link being erased with probability p. Each receiver is interested in one unique message that can be available at M transmitters. In a cellular downlink scenario, the case where M=1 reflects the cell association problem, and the case where M>1 reflects the problem of setting up the backhaul links for Coordinated Multi-Point (CoMP) transmission. In both cases, we analyze Degrees of Freedom (DoF) optimal schemes for the case of no erasures, and propose new schemes with better average DoF performance at high probabilities of erasure. For M=1, we characterize the average per user DoF, and identify the optimal assignment of messages to transmitters at each value of p. For general values of M, we show that there is no strategy for assigning messages to transmitters in large networks that is optimal for all values of p.

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arXiv2013

MCUIUC -- A New Framework for Metagenomic Read Compression

Metagenomics is an emerging field of molecular biology concerned with analyzing the genomes of environmental samples comprising many different diverse organisms. Given the nature of metagenomic data, one usually has to sequence the genomic material of all organisms in a batch, leading to a mix of reads coming from different DNA sequences. In deep high-throughput sequencing experiments, the volume of the raw reads is extremely high, frequently exceeding 600 Gb. With an ever increasing demand for storing such reads for future studies, the issue of efficient metagenomic compression becomes of paramount importance. We present the first known approach to metagenome read compression, termed MCUIUC (Metagenomic Compression at UIUC). The gist of the proposed algorithm is to perform classification of reads based on unique organism identifiers, followed by reference-based alignment of reads for individually identified organisms, and metagenomic assembly of unclassified reads. Once assembly and classification are completed, lossless reference based compression is performed via positional encoding. We evaluate the performance of the algorithm on moderate sized synthetic metagenomic samples involving 15 randomly selected organisms and describe future directions for improving the proposed compression method.

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arXiv2013

MetaPar: Metagenomic Sequence Assembly via Iterative Reclassification

We introduce a parallel algorithmic architecture for metagenomic sequence assembly, termed MetaPar, which allows for significant reductions in assembly time and consequently enables the processing of large genomic datasets on computers with low memory usage. The gist of the approach is to iteratively perform read (re)classification based on phylogenetic marker genes and assembler outputs generated from random subsets of metagenomic reads. Once a sufficiently accurate classification within genera is performed, de novo metagenomic assemblers (such as Velvet or IDBA-UD) or reference based assemblers may be used for contig construction. We analyze the performance of MetaPar on synthetic data consisting of 15 randomly chosen species from the NCBI database through the effective gap and effective coverage metrics.

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arXiv2013

Interference Channels with Coordinated Multi-Point Transmission: Degrees of Freedom, Message Assignment, and Fractional Reuse

Coordinated Multi-Point (CoMP) transmission is an infrastructural enhancement under consideration for next generation wireless networks. In this work, the capacity gain achieved through CoMP transmission is studied in various models of wireless networks that have practical significance. The capacity gain is analyzed through the degrees of freedom (DoF) criterion. The DoF available for communication provides an analytically tractable way to characterize the capacity of interference channels. The considered channel model has K transmitter/receiver pairs, and each receiver is interested in one unique message from a set of K independent messages. Each message can be available at more than one transmitter. The maximum number of transmitters at which each message can be available, is defined as the cooperation order M. For fully connected interference channels, it is shown that the asymptotic per user DoF, as K goes to infinity, remains at 1/2 as M is increased from 1 to 2. Furthermore, the same negative result is shown to hold for all M > 1 for any message assignment that satisfies a local cooperation constraint. On the other hand, when the assumption of full connectivity is relaxed to local connectivity, and each transmitter is connected only to its own receiver as well as L neighboring receivers, it is shown that local cooperation is optimal. The asymptotic per user DoF is shown to be at least max {1/2,2M/(2M+L)} for locally connected channels, and is shown to be 2M/(2M+1) for the special case of Wyner's asymmetric model where L=1. An interesting feature of the proposed achievability scheme is that it relies on simple zero-forcing transmit beams and does not require symbol extensions. Also, to achieve the optimal per user DoF for Wyner's model, messages are assigned to transmitters in an asymmetric fashion unlike traditional assignments where message i has to be available at transmitter i.

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arXiv2013

Controlled Sensing for Multihypothesis Testing

The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error probability corresponds to the maximum Chernoff information over the choice of controls, and a pure stationary open-loop control policy is asymptotically optimal within the larger class of all causal control policies. For multihypothesis testing in the fixed sample size setting, lower and upper bounds on the optimal error exponent are derived. It is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open-loop control policy. In the sequential setting, a test based on earlier work by Chernoff for binary hypothesis testing, is shown to be first-order asymptotically optimal for multihypothesis testing in a strong sense, using the notion of decision making risk in place of the overall probability of error. Another test is also designed to meet hard risk constrains while retaining asymptotic optimality. The role of past information and randomization in designing optimal control policies is discussed.

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arXiv2012

Data-Efficient Quickest Change Detection in Minimax Settings

The classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process. The change point is modeled as an unknown constant, and minimax formulations are proposed for the problem. The objective in these formulations is to find a stopping time and an on-off observation control policy for the observation sequence, to minimize a version of the worst possible average delay, subject to constraints on the false alarm rate and the fraction of time observations are taken before change. An algorithm called DE-CuSum is proposed and is shown to be asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. Numerical results are used to show that the DE-CuSum algorithm has good trade-off curves and performs significantly better than the approach of fractional sampling, in which the observations are skipped using the outcome of a sequence of coin tosses, independent of the observation process. This work is guided by the insights gained from an earlier study of a Bayesian version of this problem.

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arXiv2012

Quickest Change Detection

The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to biomedical signal processing. In all of these applications the observations being monitored undergo a change in distribution in response to a change or anomaly in the environment, and the goal is to detect the change as quickly as possibly, subject to false alarm constraints. In this chapter, two formulations of the quickest change detection problem, Bayesian and minimax, are introduced, and optimal or asymptotically optimal solutions to these formulations are discussed. Then some generalizations and extensions of the quickest change detection problem are described. The chapter is concluded with a discussion of applications and open issues.

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arXiv2012

Ensemble Properties of RVQ-Based Limited-Feedback Beamforming Codebooks

The ensemble properties of Random Vector Quantization (RVQ) codebooks for limited-feedback beamforming in multi-input multi-output (MIMO) systems are studied with the metrics of interest being the received SNR loss and mutual information loss, both relative to a perfect channel state information (CSI) benchmark. The simplest case of unskewed codebooks is studied in the correlated MIMO setting and these loss metrics are computed as a function of the number of bits of feedback ($B$), transmit antenna dimension ($N_t$), and spatial correlation. In particular, it is established that: i) the loss metrics are a product of two components -- a quantization component and a channel-dependent component; ii) the quantization component, which is also common to analysis of channels with independent and identically distributed (i.i.d.) fading, decays as $B$ increases at the rate $2^{-B/(N_t-1)}$; iii) the channel-dependent component reflects the condition number of the channel. Further, the precise connection between the received SNR loss and the squared singular values of the channel is shown to be a Schur-convex majorization relationship. Finally, the ensemble properties of skewed codebooks that are generated by skewing RVQ codebooks with an appropriately designed fixed skewing matrix are studied. Based on an estimate of the loss expression for skewed codebooks, it is established that the optimal skewing matrix is critically dependent on the condition numbers of the effective channel (product of the true channel and the skewing matrix) and the skewing matrix.

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arXiv2012

Optimal Strategies for Communication and Remote Estimation with an Energy Harvesting Sensor

We consider a remote estimation problem with an energy harvesting sensor and a remote estimator. The sensor observes the state of a discrete-time source which may be a finite state Markov chain or a multi-dimensional linear Gaussian system. It harvests energy from its environment (say, for example, through a solar cell) and uses this energy for the purpose of communicating with the estimator. Due to the randomness of energy available for communication, the sensor may not be able to communicate all the time. The sensor may also want to save its energy for future communications. The estimator relies on messages communicated by the sensor to produce real-time estimates of the source state. We consider the problem of finding a communication scheduling strategy for the sensor and an estimation strategy for the estimator that jointly minimize an expected sum of communication and distortion costs over a finite time horizon. Our goal of joint optimization leads to a decentralized decision-making problem. By viewing the problem from the estimator's perspective, we obtain a dynamic programming characterization for the decentralized decision-making problem that involves optimization over functions. Under some symmetry assumptions on the source statistics and the distortion metric, we show that an optimal communication strategy is described by easily computable thresholds and that the optimal estimate is a simple function of the most recently received sensor observation.

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arXiv2012

On Optimal Message Assignments for Interference Channels with CoMP Transmission

The degrees of freedom (DoF) number of the fully connected K-user Gaussian interference channel is known to be K/2. In [1], the DoF for the same channel model was studied while allowing each message to be available at its own transmitter as well as M-1 successive transmitters. In particular, it was shown that the DoF gain through cooperation does not scale with the number of users K for a fixed value of M, i.e., the per user DoF number is 1/2 . In this work, we relax the cooperation constraint such that each message can be assigned to M transmitters without imposing further constraints on their location. Under the new constraint, we study properties for different message assignments in terms of the gain in the per user DoF number over that achieved without cooperation. In particular, we show that a local cooperation constraint that confines the transmit set of each message within a o(K) radius cannot achieve a per user DoF number that is greater than 1/2. Moreover, we show that the same conclusion about the per user DoF number holds for any assignment of messages such that each message cannot be available at more than two transmitters. Finally, for the case where M > 2, we do not know whether a per user DoF number that is greater than 1/2 is achievable. However, we identify a candidate class of message assignments that could potentially lead to a positive answer. [1] V. S. Annapureddy, A. El Gamal, and V. V. Veervalli, "Degrees of Freedom of Interference Channels with CoMP Transmission and Reception," Submitted to IEEE Trans. Inf. Theory, Sep. 2011

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arXiv2012

Degrees of Freedom (DoF) of Locally Connected Interference Channels with Coordinated Multi-Point (CoMP) Transmission

The degrees of freedom (DoF) available for communication provides an analytically tractable way to characterize the information-theoretic capacity of interference channels. In this paper, the DoF of a K-user interference channel is studied under the assumption that the transmitters can cooperate via coordinated multi-point (CoMP) transmission. In [1], the authors considered the linear asymmetric model of Wyner, where each transmitter is connected to its own receiver and its successor, and is aware of its own message as well as M-1 preceding messages. The per user DoF was shown to go to M/(M+1) as the number of users increases to infinity. In this work, the same model of channel connectivity is considered, with a relaxed cooperation constraint that bounds the maximum number of transmitters at which each message can be available, by a cooperation order M. We show that the relaxation of the cooperation constraint, while maintaining the same load imposed on a backhaul link needed to distribute the messages, results in a gain in the DoF. In particular, the asymptotic limit of the per user DoF under the cooperation order constraint is (2M)/(2M+1) . Moreover, the optimal transmit set selection satisfies a local cooperation constraint. i.e., each message needs only to be available at neighboring transmitters. [1] A. Lapidoth, S. Shamai (Shitz) and M. A. Wigger, "A linear interference network with local Side-Information," in Proc. IEEE International Symposium on Information Theory (ISIT), Nice, Jun. 2007.

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arXiv2011

Data-Efficient Quickest Change Detection with On-Off Observation Control

In this paper we extend the Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on-off observation control policy, that decides whether or not to take a given observation, along with the stopping time at which the change is declared, so as to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem, and using dynamic programming arguments, we obtain an \textit{a posteriori} probability based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal, i.e., the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm, for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves, and provides significant reduction in observation cost as compared to the naive approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.

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