Research Interests

My main interests lie in the field of information theory and complexity. Classical information theory has been extremely successful in identifying the limits of the achievable performance. However, the complexity of the early schemes that approach these limits is extremely high. Analysis was carried out for these schemes to find the required complexity for achieving a specified performance. By 1970, limits to this performance-complexity tradeoff were well understood for interesting classes of codes (namely, the block codes and the convolution codes) under various decoding algorithms. However, as noted by Forney in his 1995 Shannon lecture, the issue is far from closed.

Over the last fifteen years, researchers have designed codes based on sparse-graphs that perform close to the optimal with low encoding and decoding complexity. These codes have allowed for practical implementation of schemes that approach the optimal performance. Empirically, it was observed that the complexity scales with improved performance for these codes as well. By analyzing some known families of codes (namely, LDPC codes, LDGM codes, IRA codes, ARA codes), performance-complexity tradeoffs have been established for these families. More generally, the question remains whether the sparse-graph codes have an inherent performance-complexity tradeoff. And if so, then what the best possible tradeoff is.

We provide some general bounds on this tradeoff that are applicable to every (possible) family of sparse-graph codes. These bounds provide tools for analyzing some problems of practical importance, such as the tradeoff between the transmit power and the encoding/decoding power for communicating over a channel. The derivations of these bounds use local sphere-packing bounds, tightened and modified from those used earlier in context of delay.

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

Publications

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Journal Papers and Preprints

• 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

• Pulkit Grover and Anant Sahai, A vector Witsenhausen counter-example : Towards convergence of control, communication and computation. Submitted to the IEEE Conference on Decision and Control in Cancun, Mexico, 2008.
  
  
• Pulkit Grover and Anant Sahai, Green Codes: Energy-Efficient Short-Range Communication. Proceedings of the 2008 International Symposium on Information Theory in Toronto, 2008. to appear.
  
  
• Pulkit Grover and Anant Sahai, On the need for knowledge of the phase in exploiting known primary transmissions, Proceedings of the IEEE IEEE DySPAN 2007, Dublin, Ireland (includes follow-up work).
  
  
• 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.
  
  
• 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.

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.