Pulkit Grover EECS Department University of California, Berkeley 264 Cory Hall Berkeley, CA 94720 pulkit at eecs dot berkeley dot edu Ph: +1-510-643-9263

About me

I am a PhD candidate in Electrical Engineering at the University of California, Berkeley. My advisor is Anant Sahai and I am a member of the Wireless Foundations Center. I received my B. Tech from IIT Kanpur in May 2003, and my M. Tech, also from IIT Kanpur, in July 2005. I joined Berkeley in August 2005. From August 2005 to July 2007, I was supported by the US-Vodafone fellowship.

Research Interests

Role of decoding energy in green communications.

Decoding energy has traditionally been ignored in information theory. Decreasing distances between wireless communication devices and their ubiquity have made decoding energy a significant cost. While Shannon theoretic results (that only consider transmit energy) suggest that arbitrary reliability is possible with finite energy-per bit, we show that with decoding energy taken into account, the total energy diverges to infinity as the desired error probability gets small. Further, the transmit energy required is strictly larger than that predicted by Shannon.
For broadcast problem, it turns out that simple time-division based strategies can outperform Shannon-optimal strategies of superposition or dirty-paper coding over the AWGN channel. For source-coding, as we desire higher and higher reliability, the sum of encoding and decoding energy required diverges to infinity.


Role of communication in distributed control systems.

Our recent results provide the first approximately optimal solutions to the long standing Witsenhausen's counterexample. We also provide approximately optimal solutions to any vector extension of the counterexample.

I am also interested in cognitive radios, quantum error-correction and finance.

News

Publications

Click on a title for the pdf. Copyright belongs to the publisher in most cases. The authors assert copyright in all other cases.

I am trying to put all my MATLAB code, sufficiently documented, online. It is an attempt to make my research completely reproducible.

Journal Papers and Preprints

• Pulkit Grover and Anant Sahai, Vector Witsenhausen Counterexample as Assisted Interference Suppression. Accepted for publication in the Special Issue on "Information Processing and Decision Making in Distributed Control Systems" of the International Journal of Systems, Control and Communications (IJSCC), 2008.


• Anant Sahai and Pulkit Grover, The Price of Certainty: `Waterslide Curves' and the Gap to Capacity, Submitted to IEEE Transactions on Information theory, Dec 2007.
  
  
• Pulkit Grover and Ajit Kumar Chaturvedi, Upper Bounds on the Rate of LDPC codes for a class of Finite State Markov Channels, IEEE Transactions on Information Theory, 53(2), Feb. 2007 Page(s):794 - 804 . IEEExplore version.
  
  

Selected Conference Papers (click on [Short description] for short descriptions)

• Pulkit Grover, Anant Sahai and Se Yong Park The finite-dimensional Witsenhausen counterexample. Extended version of the paper to appear in the Proceedings of the 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), Workshop on Control over Communication Channels (ConCom 2009). [Short description] [PDF]
  
  An approximate solution to Witsenhausen's counterexample: we show that quantization based strategies can obtain within a factor of 8 of the optimal costs for the original Witsenhausen counterexample for all values of the problem parameters. Further, lattice based strategies obtain within a constant factor of optimal for vector Witsenhausen counterexample of any length. These are first results that show approximate optimality of any scheme for this longstanding problem.
  
  
  
• Pulkit Grover and Anant Sahai, Time-division multiplexing for Green Broadcasting. Extended version of the paper in the Proceedings of the IEEE International Symposium on Information Theory (ISIT), 2009, to appear. [Short description] [PDF] [Handout] [Slides] [MATLAB code]
  
  At short distances, decoding power can be comparable to transmit power. In such cases, simple time-division multiplexing based schemes outperform transmit-power optimal superposition-based schemes if the decoding power is also taken into account. We also provide an improvement over the best known outer bound on the error exponents for the Gaussian broadcast channel.
  
  
  
• Pulkit Grover and Anant Sahai, A vector version of Witsenhausen's counterexample : Towards convergence of control, communication and computation. Proceedings of the IEEE Conference on Decision and Control in Cancun, Mexico, 2008. [Short description] [PDF] [Handout] [Slides] [MATLAB code]
  
  This paper was the first step to obtaining an approximately optimal solution to the Witsenhausen counterexample. We derive upper and lower bounds on the costs for the vector extension to the counterexample. We show that the ratio of the upper and lower bound is no more than 2 for any choice of problem parameters for infinite vector length.
  We also connected the problem to computation of good control schemes. Our results suggest that there are fundamental tradeoffs between the costs of control, communication, and computation.
  
  
  
• Pulkit Grover and Anant Sahai, Green Codes: Energy-Efficient Short-Range Communication. Proceedings of the 2008 International Symposium on Information Theory in Toronto, 2008. [Short description] [PDF] [Slides]
  
  We consider the problem of decoding energy for short distance wireless communication problems in Verdu's capacity per-unit. We show that as the error probability goes to zero, the required total energy increases to infinity, even if the rate is allowed to be arbitrary. Further, the optimal rate is non-zero, contrary to the prediction of classical theory. For minimizing total energy, therefore, it might be prudent to communicate at a rate higher than desired.
  
  
  
• Pulkit Grover and Anant Sahai, On the need for knowledge of the phase in exploiting known primary transmissions, Proceedings of the IEEE DySPAN 2007, Dublin, Ireland (The linked paper includes follow-up work that appeared in the Proceedings of IEEE International Symposium on Information Theory (ISIT) 2007). [PDF]
  
  
• Pulkit Grover, Bounds on the Tradeoff between decoding complexity and rate for codes on graphs, Proceedings of the IEEE Information Theory Workshop (ITW) 2007, Lake Tahoe, CA, 2007. [PDF]
  
  
• Pulkit Grover and Ajit Kumar Chaturvedi, Upper Bounds on the Rate of LDPC Codes for Gilbert-Elliott Channels, Proceedings of the IEEE Information Theory Workshop (ITW) 2004, San Antonio, Texas, October 2004. [PDF]
  
  
• Pulkit Grover and Ajit Kumar Chaturvedi, Upper Bounds on the Rate of Randomly Constructed LDPC Codes for a Class of Markov Channels, Proceedings of the National Conference on Communications (NCC) 2005, IIT Kharagpur, Kharagpur, India, January 2005. [PDF]

Masters Thesis

Pulkit Grover. LDPC Codes: Bounds on the rate for FSMCs and some results on minimal stopping sets. July 2005, IIT Kanpur [PDF]

Teaching

In the Fall of 2007, I was a Graduate Student Instructor for for EE120: Signals and Systems. During my IIT years, I was a TA for the Electronic Circuits lab for two semesters.