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Belief Propagation as a Dynamical System: The Linear Case and Open Problems
"... Systems and control theory have found wide application in the analysis and design of numerical algorithms. We present a discretetime dynamical system interpretation of an algorithm commonly used in information theory called Belief Propagation. Belief Propagation (BP) is one instance of the socalle ..."
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Cited by 2 (2 self)
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Systems and control theory have found wide application in the analysis and design of numerical algorithms. We present a discretetime dynamical system interpretation of an algorithm commonly used in information theory called Belief Propagation. Belief Propagation (BP) is one instance of the socalled SumProduct Algorithm and arises, e.g., in the context of iterative decoding of LowDensity ParityCheck codes. We review a few known results from information theory in the language of dynamical systems and show that the typically very high dimensional, nonlinear dynamical system corresponding to BP has interesting structural properties. For the linear case we completely characterize the behavior of this dynamical system in terms of its asymptotic inputoutput map. Finally, we state some of the open problems concerning BP in terms of the dynamical system presented.
1 Source modeling for Distributed Video Coding
"... Abstract—This paper studies source and correlation models for Distributed Video Coding (DVC). It first considers a twostates HMM, i.e. a GilbertElliott process, to model the bitplanes produced by DVC schemes. A statistical analysis shows that this model allows us to accurately capture the memory p ..."
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Abstract—This paper studies source and correlation models for Distributed Video Coding (DVC). It first considers a twostates HMM, i.e. a GilbertElliott process, to model the bitplanes produced by DVC schemes. A statistical analysis shows that this model allows us to accurately capture the memory present in the video bitplanes. The achievable rate bounds are derived for these ergodic sources, first assuming an additive binary symmetric correlation channel between the two sources. These bounds show that a rate gain can be achieved by exploiting the sources memory with the additive BSC model. A SlepianWolf (SW) decoding algorithm which jointly estimates the sources and the source model parameters is then described. Simulation results show that the additive correlation model does not always fit well with the correlation between the actual video bitplanes. This has led us to consider a second correlation model (the predictive model). The rate bounds are then derived for the predictive correlation model in the case of memory sources, showing that exploiting the source memory does not bring any rate gain and that the noise statistic is a sufficient statistic for the MAP decoder. We also evaluate the rate loss when the correlation model assumed by the decoder is not matched to the true one. An a posteriori estimation of the correlation channel has hence been added to the decoder in order to use the most appropriate correlation model for each bitplane. The new decoding algorithm has been integrated in a DVC decoder, leading to a rate saving of up to 10.14 % for the same PSNR, with respect to the case where the bitplanes are assumed to be memoryless uniform sources correlated with the SI via an additive channel model.
Statistical Analysis of Linear Analog Circuits Using Gaussian Message Passing in Factor Graphs
, 2009
"... This thesis introduces a novel application of factor graphs to the domain of analog circuits. It proposes a technique of leveraging factor graphs for performing statistical yield analysis of analog circuits that is much faster than the standard Monte Carlo/Simulation Program With Integrated Circuit ..."
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This thesis introduces a novel application of factor graphs to the domain of analog circuits. It proposes a technique of leveraging factor graphs for performing statistical yield analysis of analog circuits that is much faster than the standard Monte Carlo/Simulation Program With Integrated Circuit Emphasis (SPICE) simulation techniques. We have designed a tool chain to model an analog circuit and its corresponding factor graph and then use a Gaussian message passing approach along the edges of the graph for yield calculation. The tool is also capable of estimating unknown parameters of the circuit given known output statistics through backward message propagation in the factor graph. The tool builds upon the concept of domainspecific modeling leveraged for modeling and interpreting different kinds of analog circuits. Generic Modeling Environment (GME) is used to design modeling environment for analog circuits. It is a configurable tool set that supports creation of domainspecific design environments for different applications. This research has developed a generalized methodology that could be applied towards design automation of different kinds of analog circuits, both linear and nonlinear. The tool has been successfully used to model linear amplifier circuits and a nonlinear Metal Oxide Semiconductor Field Effect Transistor (MOSFET) circuit. The results obtained by Monte Carlo simulationsiv performed on these circuits are used as a reference in the project to compare against the tool’s results. The tool is tested for its efficiency in terms of time and accuracy against the standard results. (104 pages) To my loving family and friends.... v vi
Sparse Measurement Systems: Applications, Analysis, Algorithms and Design
"... This thesis deals with ‘largescale ’ detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred f ..."
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This thesis deals with ‘largescale ’ detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred from noisy observations and where the transformation from input to measurement occurs because of a physical process. In particular, we focus on sparse measurement systems. We use the term sparse measurement system to refer to applications where every observation is a (stochastic) function of a small number of inputs. Here, small is relative to the total input size. Such a system can conveniently be represented by a (sparse) structured graphical model. We study the fundamental limits of performance of these sparse measurement systems through an information theoretic lens and analyze robustness to noise, model mismatch and parameter uncertainty. We also look at these problems from an algorithmic point of view and develop practical algorithms, aided by the representation of the system as a graphical model. We analyze how the computational cost of detection with sparse measurements changes with
Author manuscript, published in "IEEE Transactions on Circuits and Systems for Video Technology (2011)" 1 Source modeling for Distributed Video Coding
, 2011
"... Abstract—This paper studies source and correlation models for Distributed Video Coding (DVC). It first considers a twostates HMM, i.e. a GilbertElliott process, to model the bitplanes produced by DVC schemes. A statistical analysis shows that this model allows us to accurately capture the memory p ..."
Abstract
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Abstract—This paper studies source and correlation models for Distributed Video Coding (DVC). It first considers a twostates HMM, i.e. a GilbertElliott process, to model the bitplanes produced by DVC schemes. A statistical analysis shows that this model allows us to accurately capture the memory present in the video bitplanes. The achievable rate bounds are derived for these ergodic sources, first assuming an additive binary symmetric correlation channel between the two sources. These bounds show that a rate gain can be achieved by exploiting the sources memory with the additive BSC model. A SlepianWolf (SW) decoding algorithm which jointly estimates the sources and the source model parameters is then described. Simulation results show that the additive correlation model does not always fit well with the correlation between the actual video bitplanes. This has led us to consider a second correlation model (the predictive model). The rate bounds are then derived for the predictive correlation model in the case of memory sources, showing that exploiting the source memory does not bring any rate gain and that the noise statistic is a sufficient statistic for the MAP decoder. We also evaluate the rate loss when the correlation model assumed by the decoder is not matched to the true one. An a posteriori estimation of the correlation channel has hence been added to the decoder in order to use the most appropriate correlation model for each bitplane. The new decoding algorithm has been integrated in a DVC decoder, leading to a rate saving of up to 10.14 % for the same PSNR, with respect to the case where the bitplanes are assumed to be memoryless uniform sources correlated with the SI via an additive channel model.
INVITED PAPER The Factor Graph Approach to ModelBased Signal Processing
"... algorithms for detection and estimation problems. ..."