PUBLICATIONS
Disclaimer: Due to copyright agreements the versions of papers on this page may differ slightly from the actual published versions. In general I have
attempted to link the pdf to the most complete versions. Please contact me directly for a particular conference or a journal version.
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 semigroups: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 ZInterference Channel
[pdf]
M. Costa, A. Gohari, C. Nair and D. Ng
 A conference version will be presented at ISIT 2023.
Network Information Theory
Two receiver interference channels

An Information Inequality Motivated by the Gaussian ZInterference Channel
[pdf]
A. Gohari, C. Nair, and David Ng
 Presented at 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 27442749.

On the ANDOR Interference Channel and the
Sandglass Conjecture
[pdf]
C. Nair, and M. Yazdanpanah

On the structure of certain nonconvex functionals
and the Gaussian Zinterference channel
[pdf]
M. Costa, C. Nair, D. Ng, and Y. Wang

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 ZInterference 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 Zinterference channel: around the corner,
[pdf]
M. Costa and C. Nair
 Presented at the ITA workshop, February, 2016.

Suboptimality of the HanKobayashi Achievable Region
for Interference Channels
[pdf]
C. Nair, L. Xia, and M. Yazdanpanah
 Proceedings of ISIT, 2015.

An enhanced geniebased outer bound for sumrate 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. 10311035 [pdf]

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

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 tworeceiver 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. 12721276, 2013.

The capacity region of the tworeceiver vector Gaussian broadcast
channel with private and common messages,
[pdf]
Y. Geng and C. Nair
 Proceedings of the International Symposium on Information Theory, pp. 591595, 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. 586590, 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. 15491553, 2011
 IEEE Transactions on Information Theory, vol. IT60, pp. 2241, 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. IT59, pp. 69806989, 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. IT59, pp. 40954105, 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 2receiver broadcast channels,
[pdf]
C. Nair.
 IEEE Transactions on Information Theory, vol. IT56, pp. 42074214, 2010.
 Proceedings of the International Symposium on Information Theory, pp. 18391843, 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. 27772779, 2009.

An achievable rate region for the 2receiver 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 2receiver 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. 22052209, 2006.
 IEEE Transactions on Information Theory, vol. IT53, pp. 350355, January, 2007.
Three (or more) receiver broadcast channels

Suboptimality 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 threereceiver 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. IT57, no. 7, pp. 40584062, July, 2011.
 Proceedings of the International Symposium on Information Theory, 2010.

On the inner and outer bounds of 3receiver broadcast channels
with 2degraded message sets,
[pdf]
C. Nair and V.W. Zizhou.
 Proceedings of the International Symposium on Information Theory, pp. 18441848, 2009.
The Capacity Region of a Class of 3Receiver 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. IT55, no. 10, pp. 44794493, October, 2009.
Miscellaneous

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. 16

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. 13441349.
 IEEE Transactions on Information Theory, vol. IT68, pp. 50125043, 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 tworeceiver broadcast channels".
 IEEE Transactions on Information Theory, vol. IT68, pp. 701736, Feb, 2022.

On optimal weightedsum rates for the modulo sum problem
[pdf]
Y. Wang and C. Nair

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 1220, 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 almamater, IIT Madras, to commemorate its 50 years of existence.)
PROBABILITY AND RANDOM STRUCTURES
Information Inequalities: Strong dataprocessing, 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. 951956.

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. 27382743.

Logconvexity of Fisher information along heat flow
[pdf]
M. Ledoux, C. Nair, and Y. Wang

Unifying the BrascampLieb Inequality and the Entropy Power
Inequality
[pdf]
V. Anantharam, V. Jog, and C. Nair
 IEEE Transactions on Information Theory, vol. IT68, pp. 76657684, 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 BrascampLieb 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. 1319

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. 30223026
 Earlier version: uploaded to ArXiv, 2013. [pdf]
REM Conjecture

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. 217240, 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. 241284, 2009.
Random Assignment Problem

Proofs of the Parisi and CoppersmithSorkin 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 CoppersmithSorkin random assignment conjectures,
[pdf]
C. Nair, B. Prabhakar, and M. Sharma.

Random Structures and Algorithms, vol. 27(4), pp. 413444, 2005.

Proceedings of the IEEE Foundations of Computer Science (FOCS), pp. 168178, 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 CoppersmithSorkin conjectures,
[pdf]
C. Nair.

Proceedings of the 40th Annual Allerton Conference on Communication, Control and Computing, pp. 667673, 2002.
Miscellaneous

On the size of pairwisecolliding permutations
[pdf]
J. Korner, C. Nair, and D. Ng
 Presented at ISIT, July 2019.
INFORMATION THEORY (misc)

Uniqueness of local maximizers for some nonconvex logdeterminant optimization problems using information theory
[pdf]
K. Lau, C. Nair, and C. Yao
 Proceedings of the 2022 IEEE International Symposium on Information Theory pp. 432437.

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. 18381842, 2005.
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. 122127, 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.

Energyefficient 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. 17731782, 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. 563572, 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. 912921, 2001.
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 YK Chia

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

An outer bound for 2receiver discrete memoryless broadcast channels,
[pdf]
C. Nair.

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