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Research Interests: Physically Embedded Communication Networks

Computation, communication and control involving large numbers of small cooperating elements raises a number of challenging research questions. In the early days of computer science, computing devices were big, massive, and very expensive pieces of equipment. This was the time of IBM mainframes, punched cards, batch processes, and the OS/360. But we know how history unfolded: the early computers lost the cost/performance evolution race to smaller, more powerful, networked computers. Now, the story is very different in the field of communication systems. Today, communications equipment is still the analog of a big computing mainframe, in that performance of a system is increased by adding complexity to a centralized design. By and large, the ideas of decentralization in computing and storage that have pervaded computer science over the last couple of decades have not yet been mirrored by similar developments in communications and information theory.

We have established a research group whose primary objective is to explore questions related to physically embedded communication networks, as illustrated in this figure.

Physically embedded networks

Anatomy of a general class of physically embedded communication networks. A large number of inherently unreliable nodes, equipped with communication, sensing and actuation capabilities, are deployed in space. These nodes communicate over a wireless medium with each other and with a far data collection/analysis/fusion center, measuring and acting on the state of an underlying physical process..

All of our work is in one form or another motivated by this application. We have chosen to study these networks by concentrating our work on two main focus areas: multiterminal information theory problems, and problems in sensor networking systems. Our rationale is simple: we want to find out what the fundamental limits under which these networks must operate, and we don't think we can do meaningful work in identifying those limits without taking into account the structure of the signals observed and controlled by these networks. Our work therefore is structured along the following lines:

Network Information Theory

Multiterminal Source Coding Theory
Source Coding for Sensor Networks
Broadcast and Relay Channels
 Sensor Networking Systems

Time Synchronization and Distributed Modulation
Control of Spatial Waves Under Communication Constraints
Detection and Estimation of Geometric Signals

In the remainder of this page we provide pointers to some of our work.

Network Information Theory

Multiterminal Source Coding Theory

In multiterminal source coding problems, it is of interest to determine rates for compression of depedent sources, when different encoders can only observe subsets of these sources.

Source Coding for Sensor Networks

Sensor networks give rise to a new challenges in data compression, dealing with large scale issues and cost/benefit tradeoffs between communication and computation.

Broadcast and Relay Channels

Broadcast channels involve one transmitter and multiple receiver; relay channels involve one transmitter, one receiver, and one or more relay nodes to assist communication among the first two. We have investigated the capacity of certain network models which incorporate elements from both.

Sensor Networking Systems

We have always intended for our group to not be a "pure theory" group, because we have a strong belief: good theory is theory grounded in a very concrete reality. Thus we are also studying algorithmic problems dealing with real signals observed by physically embedded networks. A survey paper we have written on the subject: For the purpose of doing experimental work, we are concentrating our efforts on acoustic signals. With funding provided by NSF, we have set up a lab equipped with 256 microphones and 64 speakers to carry out such experimental work -- see the web page of our lab.

Time Synchronization and Distributed Modulation

A key service that physically embedded networks must provide is the ability to establish reliable communication with an external node. Now, if there are special nodes within the network, equipped with enough resources to establish that reliable link, this problem can be solved using standard techniques. The challenge however arises when none of the nodes are able to generate individually a strong information-bearing signal that can be detected far away -- yet it may be possible to do so, if nodes cooperate. We are interested in the development of algorithms for time synchronization and distributed modulation problems that arise in this problem setup.

Control of Spatial Waves Under Communication Constraints

Performing actuation using a network with a large number of nodes is a challenging problem, raising many open questions related to distributed control. Our approach to deal with these problems consists of setting up mathematical models for the signals observed by the sensor array (essentially, a PDE), and then using this model to solve a control problem. Specifically, we have chosen to start with wave field models: our goal is to create the wave field that would be created by an ideal source using an array of constrained sources. The following animations provide an illustration of the WFS problem:

Detection and Estimation of Geometric Signals

Given a number of pressure sources, and given a number of sensors capable of measuring pressures at a random set of locations, do the recorded pressure signals contain enough information to allow us to recover the geometry of the membrane in which the waves propagate? This problem is related to the classical problem known as Can you hear the shape of a drum?, for which under some assumptions it was determined that the answer is no. In our work, based on our preliminary results, we see reasons to be a bit more optimistic.

Work in our group is currently funded from the following sources: