PUBLICATIONS

SITE MAP

Recent manuscripts, preprints, and notes
Network Information Theory
  Two receiver interference channels
  Two receiver broadcast channels
  Three (or more) receiver broadcast channels
  Miscellaneous
Probability, and Random Structures
  Information Inequalities
  REM Conjecture
  Random Assignment Problem
  Miscellaneous
Information Theory (misc)
Algorithms
Older manuscripts and notes

Recent manuscripts, preprint and notes

• On signs of derivatives of entropy along Markov semi-groups:A collection of some recent results [pdf]
  C. Nair
  
  • This is a summary of related work (with different collaborators) that I presented at the Information Theory and Applications Workshop (ITA) 2023.


• Information Inequalities via ideas from Additive Combinatorics [pdf]
  K. Lau and C. Nair
  
  • A conference version will be presented at ISIT 2023.


• A proof of the Noiseberg Conjecture for the Gaussian Z-Interference Channel [pdf]
  M. Costa, A. Gohari, C. Nair and D. Ng
  
  • A conference version will be presented at ISIT 2023.

Network Information Theory

• An Information Inequality Motivated by the Gaussian Z-Interference Channel [pdf]
  A. Gohari, C. Nair, and David Ng
  
  • Presented at 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 2744-2749.


• On the AND-OR Interference Channel and the Sandglass Conjecture [pdf]
  C. Nair, and M. Yazdanpanah
  
  • Presented at ISIT 2020.


• On the structure of certain non-convex functionals and the Gaussian Z-interference channel [pdf]
  M. Costa, C. Nair, D. Ng, and Y. Wang
  
  • Presented at ISIT 2020.


• On Colored Gaussian inputs for the scalar Gaussian Interference Channel [pdf]
  C. Nair and D. Ng
  
  • Presented at the ITA workshop, Feb 2018.
  • Transactions on Information Theory, March 2019 [pdf].


• On the Gaussian Z-Interference channel, [pdf]
  M. Costa, C. Nair, and D. Ng
  
  • Presented at the ITA workshop, February, 2017.


• Some results on the scalar Gaussian interference channel, [pdf]
  S. Beigi, S. Liu, C. Nair, and M. Yazdanpanah
  
  • Presented at the ISIT, July 2016.


• Gaussian Z-interference channel: around the corner, [pdf]
  M. Costa and C. Nair
  
  • Presented at the ITA workshop, February, 2016.


• Sub-optimality of the Han-Kobayashi Achievable Region for Interference Channels [pdf]
  C. Nair, L. Xia, and M. Yazdanpanah
  
  • Proceedings of ISIT, 2015.


• An enhanced genie-based outer bound for sum-rate of interference channels [pdf]
  S. Liu, C. Nair, and L. Xia
  
  • Presented at the ITA workshop, 2015.


• Very Weak Interference Channels [pdf]
  S. Liu, C. Nair, and L. Xia
  
  • Full version of the paper presented at ISIT 2014.
  • The published version: Proceedings of the International Symposium on Information Theory pp. 1031-1035 [pdf]


• On the Achievable Rate Sum for Symmetric Gaussian Interference Channels, [pdf]
  M. Costa and C. Nair
  
  • Presented at the ITA workshop, 2012.

• On Marton's Achievable Region: Local Tensorization for Product Broadcast Channels with a Binary Component [pdf]
  C. Nair
  
  • Presented at the Information Theory and Applications Workshop, Feb 2020.


• On the evaluation of Marton's inner bound for two-receiver broadcast channels [pdf]
  V. Anantharam, A. Gohari, and C. Nair
  
  • IEEE Transactions on Information Theory, March 2019.
  • An earlier version was presented at ISIT, 2013. [pdf].


• On the Optimality of Randomized Time Division and Superposition Coding for the Broadcast Channel, [pdf]
  A. El Gamal, H. Kim, and C. Nair
  
  • Presented at the ITW, 2016.


• Improved cardinality bounds on the auxiliary random variables in Marton's inner bound, [pdf]
  A. Gohari, C. Nair and V. Anantharam
  
  • Proceedings of the International Symposium on Information Theory, pp. 1272-1276, 2013.


• The capacity region of the two-receiver vector Gaussian broadcast channel with private and common messages, [pdf]
  Y. Geng and C. Nair
  
  • Proceedings of the International Symposium on Information Theory, pp. 591-595, 2012.
  • Full version, IEEE Transactions on Information Theory, April 2014.
  • This paper received the 2016 information theory society paper award.


• On Marton's inner bound for broadcast channels, [pdf]
  A. Gohari, C. Nair and V. Anantharam
  
  • Proceedings of the International Symposium on Information Theory, pp. 586-590, 2012.
  • Full version, arXiv 1202.0898.


• The capacity region of classes of product broadcast channels, [pdf]
  Y. Geng and A. Gohari and C. Nair and Y. Yu
  
  • Proceedings of the International Symposium on Information Theory, pp. 1549-1553, 2011
  • IEEE Transactions on Information Theory, vol. IT-60, pp. 22-41, 2014.


• On broadcast channels with binary inputs and symmetric outputs, [pdf]
  Y. Geng, C. Nair, S. Shamai, and Z. Wang.
  
  • Proceedings of the International Symposium on Information Theory, 2010.
• IEEE Transactions on Information Theory, vol. IT-59, pp. 6980-6989, 2013.


• An information inequality and evaluation of Marton's inner bound for binary input broadcast channels, [pdf]
  Y. Geng, V. Jog, C.Nair, and Z. Wang
  
  • IEEE Transactions on Information Theory, vol. IT-59, pp. 4095-4105, 2013.
  (Note: This paper is a combination of my work with Jog, and the one with Geng and Wang.)


• On Marton's inner bound for two receiver broadcast channels, [pdf]
  Y. Geng, A. Gohari, C. Nair, and Y. Yu
  
  • Presented at the ITA workshop, 2011.


• An information inequality and evaluation of Marton's inner bound for binary input broadcast channels, [pdf]
  C. Nair, Z. Wang, and Y. Geng.
  
  • Proceedings of the International Symposium on Information Theory, 2010.


• Capacity regions of two new classes of 2-receiver broadcast channels, [pdf]
  C. Nair.
  
  • IEEE Transactions on Information Theory, vol. IT-56, pp. 4207-4214, 2010.
  • Proceedings of the International Symposium on Information Theory, pp. 1839-1843, 2009.


• An information inequality for the BSSC channel, [pdf]
  V. Jog and C. Nair.
  
  • Proceedings of the ITA workshop, San Diego, 2010.


• Comments on: Broadcast Channels with Arbitrarily Correlated Sources, [pdf]
  G. Kramer and C.Nair
  
  • Proceedings of the International Symposium on Information Theory, pp. 2777-2779, 2009.


• An achievable rate region for the 2-receiver broadcast channel obtained by viewing it as an interference channel, (Invited), [pdf]
  C. Nair.
  
  • Proceedings of the International Conference on Wireless Communications and Signal Processing, Nanjing, 2009.


• On the inner and outer bounds for 2-receiver discrete memoryless broadcast channels, (Invited), [pdf]
  C. Nair and V.W. Zizhou.
  
  • Proceedings of the ITA workshop, San Diego, 2008.


• An outer bound to the capacity region of the broadcast channel, [pdf]
  C. Nair and A. El Gamal.
  
  • Proceedings of the International Symposium on Information Theory, pp. 2205-2209, 2006.
  • IEEE Transactions on Information Theory, vol. IT-53, pp. 350-355, January, 2007.

• Sub-optimality of superposition coding region for three receiver broadcast channel with two degraded message sets [pdf]
  C. Nair and M. Yazdanpanah
  
  • Presented at ISIT, July 2017.


• On three-receiver more capable channels, [pdf]
  C. Nair and L. Xia
  
  • Proceedings of the International Symposium on Information Theory, 2012.


• The capacity region of the three receiver less noisy broadcast channel, [pdf]
  C. Nair and Z. Wang
  
  • IEEE Transactions on Information Theory, vol. IT-57, no. 7, pp. 4058-4062, July, 2011.
  • Proceedings of the International Symposium on Information Theory, 2010.


• On the inner and outer bounds of 3-receiver broadcast channels with 2-degraded message sets, [pdf]
  C. Nair and V.W. Zizhou.
  
  • Proceedings of the International Symposium on Information Theory, pp. 1844-1848, 2009.

The Capacity Region of a Class of 3-Receiver Broadcast Channels with Degraded Message Sets, [pdf]
C. Nair and A. El Gamal.

• Proceedings of the International Symposium on Information Theory, 2008.
• IEEE Transactions on Information Theory, vol. IT-55, no. 10, pp. 4479-4493, October, 2009.

• Achievable rates for the relay channel with orthogonal receiver components [pdf]
  A. El Gamal, A. Gohari, and C. Nair
  
  • Presented at 2021 IEEE Information Theory Workshop (ITW), Kanazawa, Japan, 2021, pp. 1-6


• A Strengthened Cutset Upper Bound on the Capacity of the Relay Channel and Applications [pdf]
  A. El Gamal, A. Gohari, and C. Nair
  
  • Presented at 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 1344-1349.
  • IEEE Transactions on Information Theory, vol. IT-68, pp. 5012-5043, August, 2022.


• Outer Bounds for Multiuser Settings: The Auxiliary Receiver Approach [pdf]
  A. Gohari and C. Nair
  
  • A preliminary version was presented at ISIT 2020 with the title: "New outer bounds for two-receiver broadcast channels".
  • IEEE Transactions on Information Theory, vol. IT-68, pp. 701-736, Feb, 2022.


• On optimal weighted-sum rates for the modulo sum problem [pdf]
  Y. Wang and C. Nair
  
  • Presented at ISIT 2020.


• Upper concave envelopes and auxiliary random variables, [pdf]
  C. Nair
  
  • International Journal of Advances in Engineering Sciences and Applied Mathematics (Springer), volume 5, number 1, pages 12-20, March 2013.
  (Note: This is an article that I wrote (by invitation) for a special issue in Multiterminal Information theory. The journal was started by my undergraduate alma-mater, IIT Madras, to commemorate its 50 years of existence.)

Information Inequalities: Strong data-processing, hypercontractive, etc

• A mutual information inequality and some applications [pdf]
  K. Lau, C. Nair, and D. Ng
  
  • Proceedings of the 2022 IEEE International Symposium on Information Theory pp. 951-956.


• A concavity result for output relative entropy [pdf]
  Q. Ding, K. Lau, C. Nair, and Y. Wang
  
  • Presented at 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 2738-2743.


• Log-convexity of Fisher information along heat flow [pdf]
  M. Ledoux, C. Nair, and Y. Wang
  
  • Uploaded: January 2021.


• Unifying the Brascamp-Lieb Inequality and the Entropy Power Inequality [pdf]
  V. Anantharam, V. Jog, and C. Nair
  
  • IEEE Transactions on Information Theory, vol. IT-68, pp. 7665-7684, December, 2022.
  • Presented at ISIT, July 2019.



• Reverse hypercontractivity region for the binary erasure channel, [pdf]
  C. Nair and Y. Wang
  
  • Presented at ISIT, July 2017.


• A conjecture regarding optimality of the dictator function under Hellinger distance , [pdf]
  V. Anantharam, A. Bogdanov, A. Chakrabarti, T.S. Jayram, and C. Nair
  
  • Presented at the ITA workshop, Feb 2017.


• Equivalent characterization of reverse Brascamp-Lieb type inequalities using information measures, [pdf]
  S. Beigi and C. Nair
  
  • Presented at the ISIT, July 2016.


• Evaluating hypercontractivity parameters using Information Measures, [pdf]
  C. Nair and Y. Wang
  
  • Presented at the ISIT, July 2016.


• The strong data processing constant for sums of i.i.d. random variables [pdf]
  S.Kamath, and C. Nair
  
  • Proceedings of ISIT, 2015.


• Equivalent formulations of Hypercontractivity using Information Measures [pdf]
  C. Nair
  
  • Presented at the IZS workshop, 2014.


• An extremal inequality related to hypercontractivity of Gaussian random variables [pdf]
  C. Nair
  
  • Presented at the ITA workshop, 2014.


• On Hypercontractivity and the Mutual Information between Boolean Functions [pdf]
  V. Anantharam, A. Gohari, S. Kamath, and C. Nair
  
  • 51st Annual Allerton Conference on Communication, Control, and Computing, pp. 13--19


• On Maximal Correlation, Hypercontractivity, and the Data Processing Inequality studied by Erkip and Cover [pdf]
  V. Anantharam, A. Gohari, S. Kamath, and C. Nair
  
  • Proceedings of the 2014 IEEE International Symposium on Information Theory, (Honolulu, USA), pp. 3022-3026
  • Earlier version: uploaded to ArXiv, 2013. [pdf]

• Proof of the local REM conjecture for number partitioning I: Constant energy scales, [pdf]
  C. Borgs, J. T. Chayes, S. Mertens, and C. Nair.
  
  • Random Structures and Algorithms, vol. 34(2), pp. 217-240, 2009.
  
  
• Proof of the local REM conjecture for number partitioning II: Growing energy scales, [pdf]
  C. Borgs, J. T. Chayes, S. Mertens, and C. Nair.
  
  • Random Structures and Algorithms, vol. 34(2), pp. 241-284, 2009.
  
  

• Proofs of the Parisi and Coppersmith-Sorkin conjectures in the random assignment problem, [pdf]
  C. Nair.
  
  • Ph.D. Thesis, Stanford University, June 2005.
  Note: My thesis contains some results not published elsewhere including the closing of a gap in V.S. Dotsenko's argument of the validity of Parisi's conjecture.
  
  
• Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures, [pdf]
  C. Nair, B. Prabhakar, and M. Sharma.
  
  • Random Structures and Algorithms, vol. 27(4), pp. 413-444, 2005.
  • Proceedings of the IEEE Foundations of Computer Science (FOCS), pp. 168-178, 2003.
  
  
• Towards the distribution of the smallest matching in the random assignment problem, [pdf]
  C. Nair.
  
  • Proceedings of the 42nd Annual Allerton Conference on Communication, Control and Computing, 2004.
  
  
• A new proof of the Parisi's conjecture for the random assignment problem, [pdf]
  C. Nair, B. Prabhakar, and M. Sharma.
  
  • Extended Abstract: Proceedings of the International Symposium on Information Theory, p. 61, 2004.
  
  
• Towards the resolution of Coppersmith-Sorkin conjectures, [pdf]
  C. Nair.
  
  • Proceedings of the 40th Annual Allerton Conference on Communication, Control and Computing, pp. 667-673, 2002.
  
  

• On the size of pairwise-colliding permutations [pdf]
  J. Korner, C. Nair, and D. Ng
  
  • Presented at ISIT, July 2019.



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INFORMATION THEORY (misc)
• Uniqueness of local maximizers for some non-convex log-determinant optimization problems using information theory [pdf]
  K. Lau, C. Nair, and C. Yao
  
  • Proceedings of the 2022 IEEE International Symposium on Information Theory pp. 432-437.


• A 'chicken & egg' network coding problem, [pdf]
  N. J. A. Harvey, R. Klienberg, C. Nair, and Y. Wu.
  
  • Proceedings of the International symposium on Information Theory, 2007.
  
  
• Conservative network coding, [pdf]
  N. J. A. Harvey, K. Jain, L. C. Lau, C. Nair, and Y. Wu.
  
  • Proceedings of the 44th Annual Allerton Conference on Communication, Control and Computing, 2006.
  
  
• Asymptotic filtering and entropy rate of a hidden Markov process in the rare transitions regime, [pdf]
  C. Nair, E. Ordentlich, and T. Weissman.
  
  • International Symposium on Information Theory, pp. 1838-1842, 2005.
  
  

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ALGORITHMS
• Simple deterministic approximation algorithms for counting matchings, [pdf]
  M. Bayati, D. Gamarnik, D. Katz, C. Nair, and P. Tetali.
  
  • Proceedings of the Symposium on Theory of Computation (STOC), pp. 122-127, 2007.
  
  
• A rigorous proof of the cavity method for counting matchings, [pdf]
  M. Bayati and C. Nair.
  
  • Proceedings of the 44th Annual Allerton Conference on Communication, Control and Computing,2006.
  
  
• Energy-efficient scheduling of packet transmissions over wireless networks, [pdf]
  A. El Gamal, C. Nair, B. Prabhakar, E. Uysal, and S. Zahedi.
  
  • Proceedings of the IEEE Infocom Conference, vol. 3, pp. 1773-1782, June, 2002.
  
  
• Packet dropping schemes: some examples and analysis, [pdf]
  R. Pan, C. Nair, B. Prabhakar, and B. Yang.
  
  • Proceedings of the 39th Annual Allerton Conference on Communication, Control and Computing, pp. 563-572, 2001.
  
  
• The randomness in randomized load balancing, [pdf]
  C. Nair, B. Prabhakar, and D. Shah.
  
  • Proceedings of the 39th Annual Allerton Conference on Communication, Control and Computing, pp. 912-921, 2001.
  
  

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Older manuscripts and notes
• An Achievability Scheme for the Compound Channel with State Noncausally Available at the Encoder, [pdf]
  C. Nair, A. El Gamal, and Y-K Chia
  
  • Uploaded to ArXiv, 2010.


• A note on outer bounds for broadcast channel, [pdf]
  C. Nair.
  
  • Presented at the International Zurich Seminar, 2010.


• An outer bound for 2-receiver discrete memoryless broadcast channels, [pdf]
  C. Nair.
  
  • Uploaded to ArXiv, 2008.


• On entropy for mixtures of discrete and continuous variables, [pdf]
  C. Nair, B. Prabhakar, and D. Shah.
  
  • Uploaded to ArXiv, 2007.