## Talks## Coming UpTitle: Rate-Optimal Streaming Codes for Channels with Burst and Isolated Erasures Date: August 8, 2018 Abstract: Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit delay-constrained recovery from an erasure burst of length up to B. A recent work by Badr et al. extended this result and introduced a channel model that accounts for both burst and isolated erasures. Furthermore, they obtained a rate upper bound for streaming codes that can recover with a time delay T, from any erasure patterns permissible under this generalized model. However, constructions matching the bound were absent, except for a few parameter sets. In this work, we present a family of codes that achieves the rate upper bound for all feasible parameters. Speaker Bio: Nikhil Krishnan M. received the B.Tech. degree in electronics and communication engineering from the Amrita School of Engineering, Kollam, in 2011, and the M.E. degree in telecommunication from the Department of ECE, Indian Institute of Science (IISc), Bengaluru, in 2013. He is currently a Ph.D. student in the same department, working with Prof. P. Vijay Kumar. His research interests include coding theory and information theory, with applications to distributed storage systems. ## PreviousTitle: Sparse support recovery via covariance estimation Date:
Abstract: In this talk, we will look at the problem of recovering the common support of a set of k-sparse vectors from compressive measurements and its connection to the problem of covariance estimation. Specifically, we have L vectors of dimension N with the same (unknown) support S of size k, and for each vector we observe a noisy version of its projection onto an m-dimensional subspace of R^N. The goal is to recover S from these compressive measurements. We will consider a Bayesian setting where we impose a Gaussian prior with mean zero and diagonal covariance on the unknown vectors, and formulate the support recovery problem as one of covariance estimation. We will see that the maximum likelihood estimate for the covariance matrix can be obtained as the solution to a non negative quadratic program. Using this approach one can recover the support even when k>m (with L large enough), which is not possible using conventional support recovery algorithms. Speaker Bio: Lekshmi Ramesh is a PhD student in the Department of ECE, IISc, working with Prof. Chandra R. Murthy and Prof. Himanshu Tyagi. Her research interests include sparse signal recovery and estimation theory. Title: Extra Samples can Reduce the Communication for Independence Testing Date: 13 June 2018 Abstract: Two parties observing sequences of bits want to determine if their bits were generated independently or not. To that end, the first party communicates to the second. A simple communication scheme involves taking as few sample bits as determined by the sample complexity of independence testing and sending it to the second party. But is there a scheme that uses fewer bits of communication than the sample complexity, perhaps by observing more sample bits? We show that the answer to this question is in the affirmative when the joint distribution is a binary symmetric source. More generally, for any given joint distribution, we present a distributed independence test that uses linear correlation between functions of the observed random variables. Furthermore, we provide lower bounds for the generalisetting that use hypercontractivity and reverse hypercontractivity to obtain a measure change bound between the joint and the independent distributions. The resulting bounds are tight for both a binary symmetric source and a Gaussian symmetric source. Speaker Bio: K.R. Sahasranand is a PhD student in the Department of ECE, working with Dr. Himanshu Tyagi. His research interests include information theory, detection and estimation theory and distributed statistical inference. Title: Optimal Lossless Source codes for Timely Updates Date: 13 June 2018
Abstract: A transmitter observing a sequence of independent and identically distributed random variables seeks to keep a receiver updated about its latest observations. The receiver need not be apprised about each symbol seen by the transmitter, but needs to output a symbol at each time instant t. If at time t the receiver outputs the symbol seen by the transmitter at time U(t) ≤ t, the age of information at the receiver at time t is t − U(t). We study the design of lossless source codes that enable transmission with minimum average age at the receiver. We show that the asymptotic minimum average age can be attained (up to a constant bits gap) by Shannon codes for a tilted version of the original pmf generating the symbols, which can be computed easily by solving an optimization problem. Underlying our construction for minimum average age codes is a new variational formula for integer moments of random variables, which may be of independent interest. Speaker Bio: Prathamesh is currently pursuing Ph.D. in the Department of ECE at IISc under the guidance of Prof. Himanshu Tyagi. Previously, he worked for TCS. He has a Master's from Industrial Engineering and Operations Research, IIT Bombay in 2015 and, a Bachelors in Electronics and Communication Engineering from K.J.Somaiya College of Engineering, Mumbai in 2013. His research interests lie in the areas of Information Theory, Distributed Optimization, Applied Probability. Currently, He is working on designing communication protocols for Timely updates and, Distributed Optimization. Title: First Order Induced Current Imaging and Electrical Properties Tomography Date: May 9, 2018 (Wednesday) Slides The method manages to reconstruct conductivity profiles of in-vivo measurements without the boundary artefacts found in more commonly used Helmholtz-based EPT methods. It is also inherently more robust to noise because only first-order differencing is required as opposed to second-order differencing as in Helmholtz-based approaches. Moreover, reconstructions can be performed in less than a second, allowing for essentially real-time electrical property mapping. The approach presented here provides a novel look at B1 based electrical properties mapping combining the speed of differencing based approaches with the robustness of the integral maxwell based approaches to provide a practical approach for in-vivo applications. Bio: Patrick Fuchs is a PhD student at the Delft University of Technology currently working in a collaboration with K.V.S Hari at the IISc on low power MRI, speeding up MRI scans and electromagnetic modelling of MRI systems. |