Assistant Professor, ECE
B-202 Hamerschlag Hall
Carnegie Mellon University
Ph: (412) 268-3644
pgrover at andrew dot cmu dot edu
Image credit: Kris Woyach
Broadly, I am interested in an understanding of information that goes beyond just communication. Our lab seeks to attain this understanding through a mix of thought and laboratory experiments. Current topics of interest include fundamental and practical understanding of circuits for processing and communicating information; and understanding information and its use by exploring the union of control and communication.
We are looking for 1-2 undergraduate students (CMU only), 1-2 MS students (CMU only), and 1-2 Ph.D. students. Read below, and drop me an email if you're interested!
“Understanding Information and Computational Complexity: Theoretical underpinnings and practical designs of “green” radios”
The goal is to develop a fundamental and
relevant understanding of complexity of coding and communication
techniques. Intellectually, complexity of coding is a missing
piece that limits our larger understanding of “information”.
Practically, today's short-distance communication systems require
processing power that dominates transmit power, sometimes by orders of magnitude.
Developing a fundamental understanding of complexity of coding has proven extremely difficult: fundamental limits on complexity of problems are in
general hard to obtain. My work establishes the first such fundamental
limits on encoding and decoding
power. The novelty that allows me to do so is to use models based on communication complexity,
rather than Turing complexity (number of operations). Simultaneously, for today's circuits,
communication complexity turns out to be more closely related to power
consumption than number of operations.
Practice: Taking these results towards practice, I use these bounds
as guiding principles behind code designs. Not only does this lead to new
code-design problems (see [Globecom '12]), we also show that this
approach of jointly designing code/encoder/decoder triples (rather than
designing them in isolation) has the potential to significantly reduce
power consumed in short-distance communication systems.
Our main contribution is to provide fundamental bounds on
encoding/decoding power. These limits offer a different picture when compared with the traditional
Conclusions derived from our “Node Model” and “Wire
Model” are as follows:
[Node model] There is a fundamental tradeoff between transmit and encoding/decoding power. When computational nodes dominate processing power, to minimize total
power, one must fundamentally stay away from capacity.
[Node model] Capacity-approaching LDPC codes optimize over transmit power, but
require large decoding power. Regular LDPC codes are order-optimal in
the Node Model.
[Wire model] When wires dominate the circuit power consumption, the total power
diverges to infinity significantly faster than that for the node
model. Further, the optimal choice of transmit power also increases
unboundedly as the error probability is lowered.
What are the best codes now? A joint theory-practice
approach based on modeling of circuit-power using rigorous circuit
simulation shows that the code construction and the complexity of decoding
algorithm needs to increase as the target error probability is lowered or
as the communication distance is increased.
Our results have the potential to drastically reduce power consumed in
short-distance wireless (e.g. 60 GHz band) and wired (e.g. multi-Gbps
communication in data-centers) communication.
“Understanding Information and its Use: Control and communication in cyber-physical systems”
The goal: How do we connect the “cyber” -- the computational/ communicating/ controlling agents -- with the “physical” -- the world around us? My dissertation lays down the foundations of a theory to help answer this question.
The question: Let us consider two control agents that are connected using a noisy communication link. How should they share their workload? I was surprised to find that we do not know the answer! This is because most of the problem formulations and solution techniques in this field are inspired from those in modern communication theory, and simplify the control agents into “observers” or “controllers.”
The “observers” cannot act on the system, and therefore they
communicate their observations to the “controllers.” The
“controllers” cannot observe the state directly, and thus rely
on the signals sent by the “observers” to decide on their
actions. In a realistic control system, these simplified control agents
may be extremely limiting. However, analytically, they have been simpler
to understand because they disallow implicit communication through
the system from the observer to the controller.
A theory of implicit communication:
The crux of this issue is captured in a deceptively simple problem called the Witsenhausen counterexample, which has been open despite more than 40 years of research effort. In my dissertation, I provide the first provably approximately-optimal solution to the Witsenhausen counterexample by understanding the potential of implicit communication between the controllers. These approximately-optimal solutions were developed in the following sequence of results. In [CDC '08, IJSCC '10, ITW '10], we introduce a vector version of Witsenhausen's counterexample, and obtain approximately-optimal solutions for an asymptotically infinite- length version of the problem. In [ConCom '09, CDC '09, TAC '10 Sub.], we pull the results back to finite-lengths, including the original (scalar) counterexample, using techniques from large-deviation theory.
Building a communication theory for decentralized control: In my dissertation, I argue that the Witsenhausen counterexample has been a major bottleneck in understanding the interplay of control and communication. Because the counterexample was viewed as essentially unsolvable, it forced problem formulations into corners where the obtained engineering insights could only be very limited. Our approach of using semi-deterministic models to obtain approximately-optimal strategies can be extended to understand toy problems of control under commu- nication constraints which could not have been understood earlier. For instance, what happens when controllers can communicate implicitly as well as explicitly [Allerton '10]? How should one communicate implicitly in a dynamic setting with feedback [Ph.D. thesis]? Various extensions of the counterexample appear in [Allerton '09, ISIT '10, CDC '10].