Publications

Prof. Chandra Nair · Department of Information Engineering, CUHK

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This page lists my papers, preprints, and notes, grouped by topic. Due to copyright agreements the versions here may differ from the final published versions; in general I link to the most complete manuscript.

Recent manuscripts Network information theory Probability & random structures Information theory (misc) Algorithms Older manuscripts and notes
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Recent manuscripts Network information theory Two receiver interference channels Two receiver broadcast channels Three (or more) receiver broadcast channels NIT – miscellaneous Probability & random structures Information inequalities REM conjecture Random assignment problem Combinatorics – miscellaneous Information theory (misc) Algorithms Older manuscripts and notes
Recent manuscripts, preprint and notes
  • A New Outer Bound for the Discrete Memoryless Two-User Interference Channel [pdf]
    A.Gohari, C. Nair, and J. Zhao
    • Presented at Information Theory and Applications Workshop, February 2026.


  • Inequalities in Additive Combinatorics and Information Theory: A Short Survey of the Translation Programme [pdf]
    C. Nair
    • Manuscript, February 2026.


  • The Capacity Region for Classes of Sum-Broadcast Channels [pdf]
    A. Gohari, Y. Liu, and C. Nair
    • Manuscript, January 2026.


  • A Two Auxiliary Receiver Outer Bound to the Capacity Region of a Two-Receiver Discrete Memoryless Broadcast Channel [pdf]
    A. Gohari, Y. Liu, and C. Nair
    • Manuscript, January 2026.


  • A maximal-coupling information inequality of sums on finite subsets of Abelian groups [pdf]
    K. Lau, C. Nair, and Z. Zhu
    • Manuscript, January 2026.


  • On the Local Optimality of Gaussian distributions for the Han-Kobayashi Inner Bound for the Gaussian Z-interference channel [pdf]
    C. Nair, and J. Zhao
    • Manuscript, January 2026.

Network Information Theory


Two receiver interference channels


  • Proof of a conjecture on the Gaussian signaling region for the Gaussian Z-interference channel [pdf]
    C. Nair and J. Zhao
    • A conference version was presented at ISIT 2025.

  • Critical points in the noiseberg achievable region of the Gaussian Z-interference channel [pdf]
    M. H. M. Costa, C. Nair and D. Ng
    • Entropy, vol. 26, no. 11, 2024.

  • On the capacity region of some classes of Interference Channels [pdf]
    A. Gohari, C. Nair, and J. Zhao
    • A conference version was presented at ISIT 2024.


  • 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 wwas be presented at ISIT 2023.

  • 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.


Two receiver broadcast channels


  • A Conjecture Regarding the Optimizers of Marton's Inner Bound for the Two-Receiver Broadcast Channel [pdf]
    A. Gohari, Y. Liu, and C. Nair
    • A conference version was presented at ISIT 2025.

  • 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.

Three (or more) receiver broadcast channels

  • 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.


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. 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.)

PROBABILITY AND RANDOM STRUCTURES

Information Inequalities: Strong data-processing, hypercontractive, etc



  • A Differential Equation Approach to the Most-Informative Boolean Function Conjecture [pdf]
    Z. Chen, A. Gohari, and C. Nair
    • A conference version was presented at ISIT 2025.

  • An extension of the unified Brascamp-Lieb and the Entropy Power Inequality to finite Abelian groups [pdf]
    K. Lau and C. Nair
    • A conference version was presented at ISIT 2024.
    • A journal version along with a doubling trick perspective of the proof of the PFR conjecture is to appear in a Festschrift for Andrew Barron. [pdf]

  • On the Optimality of Dictator functions and Isoperimetric Inequalities on Boolean Hypercubes [pdf]
    Z. Chen and C. Nair
    • A conference version was presented at ISIT 2024.


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

  • 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.


  • 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]

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. 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.

Random Assignment Problem

  • 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.

Miscellaneous

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

    • 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.

    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.

    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.