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**1 - 7**of**7**### Spatial coupling as a proof technique

- in ISIT, 2013. [Online]. Available: http: //arxiv.org/abs/1301.5676v2

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### Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation

, 2013

"... We investigate an encoding scheme for lossy com-pression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The ..."

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We investigate an encoding scheme for lossy com-pression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The performance of a low complexity Belief Propagation Guided Decimation algorithm is excellent. The algorithmic rate-distortion curve approaches the optimal curve of the ensemble as the width of the coupling window grows. Moreover, as the check degree grows both curves approach the ultimate Shannon rate-distortion limit. The Belief Propagation Guided Decimation encoder is based on the posterior measure of a binary symmetric test-channel. This measure can be interpreted as a random Gibbs measure at a “temperature ” directly related to the “noise level of the test-channel”. We investigate the links between the algorith-mic performance of the Belief Propagation Guided Decimation encoder and the phase diagram of this Gibbs measure. The phase diagram is investigated thanks to the cavity method of spin glass theory which predicts a number of phase transition thresholds. In particular the dynamical and condensation “phase transition temperatures” (equivalently test-channel noise thresholds) are computed. We observe that: (i) the dynamical temperature of the spatially coupled construction saturates towards the condensation temperature; (ii) for large degrees the condensation temper-ature approaches the temperature (i.e. noise level) related to the information theoretic Shannon test-channel noise parameter of rate-distortion theory. This provides heuristic insight into the excellent performance of the Belief Propagation Guided Decimation algorithm. The paper contains an introduction to the cavity method.

### Physics-Inspired Methods for Networking and Communications

"... Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior into simple local interactions. Thus, central-i ..."

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Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior into simple local interactions. Thus, central-ized problems can be solved or approximated in a distributed manner with iterative lightweight local messaging. This survey discusses how statistical physics methodology can provide efficient solutions to hard network problems that are intractable by classical methods. We highlight three typical examples in the realm of networking and communications. In each case we show how a fundamental idea of statistical physics helps in solving the problem in an efficient manner. In particular, we discuss how to perform multicast scheduling with message passing methods, how to improve coding using the crystallization process and how to compute optimal routing by thinking of routes as interacting polymers.

### Research Statement

"... Uncertainty is a key factor in real-world problems and I am interested in intelligent and adaptive systems that can cope with complex and uncertain environments. My research is centered on topics in machine learning (where uncertainty typically resides in the observations and data), communication th ..."

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Uncertainty is a key factor in real-world problems and I am interested in intelligent and adaptive systems that can cope with complex and uncertain environments. My research is centered on topics in machine learning (where uncertainty typically resides in the observations and data), communication theory (where uncertainty is due to the transmission medium), and random combinatorial structures (where uncertainty is in the underlying graphical model). The main theme, which unifies these three fields, is information theory. My research focus is on constructing an information theoretic framework to describe the role of uncertainty in data and models. Within such a framework, I develop algorithms by drawing upon probabilistic reasoning, message passing techniques, stochastic optimisation, and approximation algorithms to study questions such as: How can we build systems that acquire the most important information at the lowest cost? How can we design efficient algorithms, often involving large amounts of variables and data, for inference problems? How can we summarise massive amounts of data into a small number of informative representatives and use the smaller set for processing tasks? How can we design practical coding schemes to transfer data inside networks of possibly many individuals? Moreover, I use concepts and techniques from information theory, probability theory, and optimisation to analyse the performance of algorithms and find fundamental trade-offs. My dissertation research was in the fields of information theory and graphical models. I investigated