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### Browsing by Author "Sarvotham, Shriram"

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Item Additive and Multiplicative Mixture Trees for Network Traffic Modeling(2002-05-01) Sarvotham, Shriram; Wang, Xuguang; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and long range dependence at very large time scales to highly non-Gaussian marginals and multifractal scaling on small scales. This behavior can be explained by forming two components of the traffic according to the speed of connections, one component absorbing most traffic and being mostly Gaussian, the other constituting virtually all the small scale bursts. Towards a better understanding of this phenomenon, we propose a novel tree-based model which is flexible enough to accommodate Gaussian as well as bursty behavior on different scales in a parsimonious way.Show more Item Analysis and modeling of bursty long-range-dependent network traffic(2001) Sarvotham, Shriram; Baraniuk, Richard G.Show more In this thesis, we study the cause and impact of burstiness in computer network traffic. A connection-level analysis of traffic at coarse time scales (time scales greater than a round-trip-time) reveals that a single connection dominates during the period of the burst. The number of dominating connections that cause bursts is found to be a small fraction of the total number of connections. Removing the burst causing connections from the traffic yields a trace whose marginal is close to a Gaussian. This observation motivates a network traffic model comprised of two components, namely the Gaussian part and the bursty part. The Gaussian part of the traffic models the aggregate of majority of the connections, whereas the bursty part models the behavior of few dominant connections that transmit data at unusually high rates. The Gaussian component imparts long-range-dependence (LRD) to the traffic, whereas the bursty component gives rise to spikiness. We argue that heterogeneity in bottleneck link speeds gives rise to burstiness, and heavy tailed connection durations results in LRD. We perform simulations in ns to validate the proposed model and synthesize realistic traffic that is both non-Gaussian and LRD. We demonstrate the impact of the bursty component in queueing behavior. Although the bursty component constitutes a small fraction of the total traffic, it significantly affects the queueing behavior, in particular at large queue sizes.Show more Item Analysis of the DCS one-stage Greedy Algorothm for Common Sparse Supports(2005-11-01) Baron, Dror; Duarte, Marco F.; Wakin, Michael; Sarvotham, Shriram; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Analysis of the DCS one-stage Greedy Algorothm for Common Sparse SupportsShow more Item Bounds for optimal compressed sensing matrices and practical reconstruction schemes(2008) Sarvotham, Shriram; Baraniuk, Richard G.Show more Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal x ∈ Rn that has only k << n non-zero coefficients from a small number m << n of linear projections. The projections can be thought of as a vector that is obtained by multiplying a k-sparse signal in Rn by a matrix (called CS matrix) of size m x n where k < m << n. The central theme of this thesis is to study the role of the CS matrix on robustness in reconstruction as well as the complexity involved in reconstruction schemes. In the first part of the thesis, we explore the impact of the CS matrix on robustness, as measured by the Restricted Isometry Property (RIP). We derive two converse bounds for RIP of the CS matrix in terms of n, m and k. For the first bound (structural bound), ee employ results from algebra of Singular Value Decomposition (SVD) of sub-matrices. The second bound (packing bound) is based on sphere packing arguments which we motivate by showing the equivalence of the RIP measure and codes on grassmannian spaces. The derivation of the two bounds offer rich geometric interpretation and illuminate the relationship between CS matrices and many diverse concepts such as equi-angular tight frames, codes on Euclidean spheres, and the generalized Pythagorean Theorem. In the second part of the thesis, we propose strategies to design the CS matrix so that it lends itself to low-complexity reconstruction schemes. We argue that sparse matrices are a good choice in CS and present two strategies for reconstruction involving group testing and belief propagation respectively.Show more Item Connection-level Analysis and Modeling of Network Traffic(2001-11-01) Sarvotham, Shriram; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits long-range-dependent (LRD) correlations and non-Gaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connection-level information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few high-volume connections that dominate all others. We term such dominating connections alpha traflc. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (non-Gaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traf/ic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavy-tailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes.Show more Item Distributed Compressed Sensing of Jointly Sparse Signals(2005-11-01) Sarvotham, Shriram; Baron, Dror; Wakin, Michael; Duarte, Marco F.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we expand our theory for distributed compressed sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. We present a second new model for jointly sparse signals that allows for joint recovery of multiple signals from incoherent projections through simultaneous greedy pursuit algorithms. We also characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction.Show more Item Distributed Multiscale Data Analysis and Processing for Sensor Networks(2005-02-01) Wagner, Raymond; Sarvotham, Shriram; Choi, Hyeokho; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more While multiresolution data analysis, processing, and compression hold considerable promise for sensor network applications, progress has been confounded by two factors. First, typical sensor data are irregularly spaced, which is incompatible with standard wavelet techniques. Second, the communication overhead of multiscale algorithms can become prohibitive. In this paper, we take a first step in addressing both shortcomings by introducing two new distributed multiresolution transforms. Our irregularly sampled Haar wavelet pyramid and telescoping Haar orthonormal wavelet basis provide efficient piecewise-constant approximations of sensor data. We illustrate with examples from distributed data compression and in-network wavelet de-noising.Show more Item Measurements vs. Bits: Compressed Sensing meets Information Theory(2006-09-01) Sarvotham, Shriram; Baron, Dror; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Compressed sensing is a new framework for acquiring sparse signals based on the revelation that a small number of linear projections (measurements) of the signal contain enough information for its reconstruction. The foundation of Compressed sensing is built on the availability of noise-free measurements. However, measurement noise is unavoidable in analog systems and must be accounted for. We demonstrate that measurement noise is the crucial factor that dictates the number of measurements needed for reconstruction. To establish this result, we evaluate the information contained in the measurements by viewing the measurement system as an information theoretic channel. Combining the capacity of this channel with the rate-distortion function of the sparse signal, we lower bound the rate-distortion performance of a compressed sensing system. Our approach concisely captures the effect of measurement noise on the performance limits of signal reconstruction, thus enabling to benchmark the performance of specific reconstruction algorithms.Show more Item Method and apparatus for distributed compressed sensing(2009-03-31) Baraniuk, Richard G.; Baron, Dror Z.; Duarte, Marco F.; Sarvotham, Shriram; Wakin, Michael B.; Davenport, Mark A.; Rice University; United States Patent and Trademark OfficeShow more A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.Show more Item Method and apparatus for distributed compressed sensing(2007-09-18) Baraniuk, Richard G.; Baron, Dror Z.; Duarte, Marco F.; Sarvotham, Shriram; Wakin, Michael B.; Davenport, Mark A.; Rice University; United States Patent and Trademark OfficeShow more A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.Show more Item Multifractal Cross-Traffic Estimation(2000-09-01) Ribeiro, Vinay Joseph; Coates, Mark J.; Riedi, Rudolf H.; Sarvotham, Shriram; Hendricks, Brent; Baraniuk, Richard G.; Center for Multimedia Communications (http://cmc.rice.edu/)Show more In this paper we develop a novel model-based technique, the Delphi algorithm, for inferring the instantaneous volume of competing cross-traffic across an end-to-end path. By using only end-to-end measurements, Delphi avoids the need for data collection within the Internet. Unique to the algorithm is an efficient exponentially spaced probing packet train and a parsimonious multifractal parametric model for the cross-traffic that captures its multiscale statistical properties (including long-range dependence) and queuing behavior. The algorithm is adaptive; it requires no a priori traffic statistics and effectively tracks changes in network conditions. NS (network simulator) experiments reveal that Delphi gives accurate ross-traffic estimates for higher link utilization levels while at lower utilizations it over-estimates the cross-traffic. Also, when Delphi's single bottleneck assumption does not hold it over-estimates the cross-traffic.Show more Item Multiscale Connection-Level Analysis of Network Traffic(2002-11-01) Sarvotham, Shriram; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Network traffic exhibits drastically different statistics, ranging from nearly Gaussian marginals and long range dependence at very large time scales to highly non-Gaussian marginals and multifractal scaling on small scales. This behavior can be explained by decomposing traffic into two components according to the connection bandwidth: the small bandwidth component absorbs most traffic and is Gaussian, while large bandwidth component constitutes virtually all of the small scale bursts. Based on this understanding, a novel traffic model is proposed that parsimoniously accounts for user behavior, network topology, and the heterogeneous distribution of network bandwidths.Show more Item A Multiscale Data Representation for Distributed Sensor Networks(2005-03-01) Wagner, Raymond; Sarvotham, Shriram; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Though several wavelet-based compression solutions for wireless sensor network measurements have been proposed, no such technique has yet appreciated the need to couple a wavelet transform tolerant of irregularly sampled data with the data transport protocol governing communications in the network. As power is at a premium in sensor nodes, such a technique is necessary to reduce costly communication overhead. To this end, we present an irregular wavelet transform capable of adapting to an arbitrary, multiscale network routing hierarchy. Inspired by the Haar wavelet in the regular setting, our wavelet basis forms a tight frame adapted to the structure of the network. We demonstrate results highlighting the approximation capabilities of such a transform and the clear reduction in communication cost when transmitting a compressed snapshot of the network to an outside user.Show more Item A Multiscale Data Representation for Distributed Sensor Networks: Proofs of Basis Characteristics and Error Bounds(2004-09-01) Sarvotham, Shriram; Wagner, Raymond; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Provides proofs of Parseval tight-frame membership and approximation properties for the basis proposed in "A Multiscale Data Representation for Distributed Sensor Networks" by R. Wagner, S. Sarvotham, and R. Baraniuk (ICASSP 2005).Show more Item Network and User Driven Alpha-Beta Onâ Off Source Model for Network Traffic(2005-06-01) Sarvotham, Shriram; Riedi, Rudolf H.; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more We shed light on the effect of network resources and user behavior on network traffic through a physically motivated model. The classical onâ off model successfully captures the long-range, second-order correlations of traffic, allowing us to conclude that transport protocol mechanisms have little influence at time scales beyond the round trip time. However, the onâ off model fails to capture the short-range spikiness of traffic, where protocols and congestion control mechanisms have greater influence. Based on observations at the connection-level we conclude that small rate sessions can be characterized by independent duration and rate, while large rate sessions have independent file size and rate. In other words, user patience is the limiting factor of small bandwidth connections, while users with large bandwidth freely choose their files. We incorporate these insights into an improved two-component onâ off modelâ which we call the alpha-beta onâ off modelâ comprising an aggressive alpha component (high rate, large transfer) and passive beta component (residual). We analyze the performance of our alpha-beta onâ off model and use it to better understand the causes of burstiness and long-range dependence in network traffic. Our analysis yields new insights on Internet traffic dynamics, the effectiveness of congestion control, the performance of potential future network architectures, and the key parameters required for realistic traffic synthesis.Show more Item Variable-Rate Universal Slepian-Wolf Coding with Feedback(2005-11-01) Sarvotham, Shriram; Baron, Dror; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)Show more Traditional Slepian-Wolf coding assumes known statistics and relies on asymptotically long sequences. However, in practice the statistics are unknown, and the input sequences are of finite length. In this finite regime, we must allow a non-zero probability of codeword error and also pay a penalty by adding redundant bits in the encoding process. In this paper, we develop a universal scheme for Slepian-Wolf coding that allows encoding at variable rates close to the Slepian-Wolf limit. We illustrate our scheme in a setup where we encode a uniform Bernoulli source sequence and the second sequence, which is correlated to the first via a binary symmetric correlation channel, is available as side information at the decoder. This specific setup is easily extended to more general settings. For length n source sequences and a fixed, we show that the redundancy of our scheme is O(vnF-1()) bits over the Slepian-Wolf limit. The prior art for Slepian-Wolf coding with known statistics shows that the redundancy is O(vnF-1()). Therefore, we infer that for Slepian-Wolf coding, the penalty needed to accommodate universality is T(vnF-1()).Show more