Bio: Gerald Matz is Associate Professor and Head of the Communication Theory Group with the Institute of Telecommunications, Vienna University of Technology, Austria. He received the Dipl.-Ing. (1994) and Dr. techn. (2000) degrees in Electrical Engineering and the Habilitation degree (2004) for Communication Systems from Vienna University of Technology. From March 2004 to Feb. 2005 he was on leave as an Erwin Schrödinger Fellow with the Laboratoire des Signaux et Systèmes, Ecole Supérieure d’Electricité (France). In 2007 he was a Visiting Researcher with the Communication Theory Lab at ETH Zurich (Switzerland), and in 2011 he was a Guest Professor with Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique et d’Hydraulique de Toulouse (France). Prof. Matz has directed or actively participated in numerous research projects funded by the Austrian Science Fund (FWF), by the Viennese Science and Technology Fund (WWTF), and by the European Union. He has published more than 200 scientific articles in international journals, conference proceedings, and edited books. He is co-editor of the book Wireless Communications over Rapidly Time-Varying Channels (New York: Academic, 2011). His research interests include statistical signal processing, information and communication theory, and data science. Prof. Matz served as as a member of the IEEE SPS Technical Committee on Signal Processing Theory and Methods and of the IEEE SPS Technical Committee on Signal Processing for Communications and Networking. He was an Associate Editor of the IEEE Transactions on Information Theory (2013–2015), of the IEEE Transactions on Signal Processing (2006–2010), of the EURASIP Journal Signal Processing (2007–2010), and of the IEEE Signal Processing Letters (2004–2008). He was Technical Chair of the Asilomar Conference on Signals, Systems, and Computers 2016, Technical Program Co-Chair of EUSIPCO 2004, Technical Area Chair for “MIMO Communications and Signal Processing” at Asilomar 2012, and Technical Area Chair for “Array Processing” at Asilomar 2015. He has been a member of the Technical Program Committee of numerous international conferences. In 2006, he received the Kardinal Innitzer Most Promising Young Investigator Award. He is an IEEE Senior Member and a member of the ÖVE.
Lecture outline: Graphs have become a powerful tool for modeling, inference, and computation in numerous fields including signal/data processing and communications. Probabilistic graphical models are a more traditional approach that augments the qualitative properties of the graph structure with quantitative characteristics brought about by statistical models. This type of approach has excelled in the context of error-correcting codes and machine learning. In more recent big data paradigms the graph topology is used to characterize general similarity relations between data items. This concept has led to the novel field of graph signal processing that aims at extending existing conventional signal processing tools (e.g., Fourier transform, filtering, and sampling) to arbitrary graph topologies. Successful application fields here include social networks, customer databases, and biological networks. In this short course, we will present recent advances in processing massive data based on graphs, with an emphasis on the design of efficient algorithms that work under stringent complexity constraints.
We will specifically focus on two themes:
1) Information-optimal Discrete Message Passing on Probabilistic Graphical Models
We begin this part with a brief introduction to probabilistic graphical models and associated message passing algorithms. Efficient digital hardware implementations of message passing require discrete (quantized) messages. To pave the way towards discrete message passing, we discuss the information bottleneck method as a relevance-preserving compression scheme and illustrate its use in devising compress-and-forward algorithms for cooperative communication systems. We then focus on information-optimal discrete message passing for regular and irregular LDPC codes, which leads to highly efficient lookup-table decoders. The theoretical discussion is complemented with a hands-on part, in which the course attendees can experiment with design flow examples for LDPC decoder architectures.
2) Graph Learning and Sampling/Interpolation of Graph Signals
The second part of the course deals with various aspects of graph signal processing (which comprises traditional signal and image processing as special cases). Following a short primer on general notions from graph signal processing, we review relevant concepts from optimization theory. We then discuss the problem of learning graph topologies from given data sets based on graph signal smoothness constraints. Afterwards, an in-depth discussion of the problem of interpolating graph signals (aka graph pinpointing, unsupervised labeling) from small sampling sets is provided. We further show practical application examples for graph learning and graph signal interpolation. Finally, a training session will be offered where attendees will have the opportunity to formulate and solve learning and interpolation problems on real-world graphs.The material in the course is is largely self-contained and suitable for anyone with a background in signal processing, machine learning, communications, control, or computer science.