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An earlier version of this paper was presented in part at the 2019 IEEE International Symposium on Information Theory [DOI:10.1109/ISIT.2019.8849751], in part at the 2020 International Zurich Seminar on Information and Communication [DOI:10.3929/ethz-b-000403243], and in part at the 2020 IEEE International Symposium on Information Theory [DOI:10.1109/ISIT44484.2020.9174091]. ; This paper considers a Gaussian multiple-access channel with random user activity where the total number of users ℓn and the average number of active users kn may grow with the blocklength n . For this channel, it studies the maximum number of bits that can be transmitted reliably per unit-energy as a function of ℓn and kn . When all users are active with probability one, i.e., ℓn=kn , it is demonstrated that, if kn is of an order strictly below n/logn , then each user can achieve the single-user capacity per unit-energy (loge)/N0 (where N0/2 is the noise power) by using an orthogonal-access scheme. In contrast, if kn is of an order strictly above n/logn , then the users cannot achieve any positive rate per unit-energy. Consequently, there is a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate per unit-energy is infeasible. It is further demonstrated that orthogonal-access schemes in combination with orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. When the user activity is random, i.e., when ℓn and kn are different, it is demonstrated that, if knlogℓn is sublinear in n , then each user can achieve the single-user capacity per unit-energy (loge)/N0 . Conversely, if knlogℓn is superlinear in n , then the users cannot achieve any positive rate per unit-energy. Consequently, there is again a sharp transition between orders of growth where interference-free communication is feasible and orders of growth where reliable communication at a positive rate is infeasible that depends on the asymptotic behaviors of both ℓn and kn . It is further demonstrated that orthogonal-ac. ; The work of Jithin Ravi was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program under Grant 714161. The work of Tobias Koch was supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program under Grant 714161; and in part by the Spanish Ministerio de Ciencia e Innovación under Grant RYC-2014-16332, Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU), and Grant PID2020-116683GB-C21 / AEI / 10.13039/501100011033.

Proceeding of: 55th Asilomar Conference on Signals, Systems, and Computers, October 31 - November 3, 2021 Pacific Grove, California, USA. ; In the emerging Internet of Things, a massive number of devices may connect to one common receiver. Consequently, models that study this setting are variants of the classical multiple-access channel where the number of users grows with the blocklength. Roughly, these models can be classified into three groups based on two criteria: the notion of probability of error and whether users use the same codebook. The first group follows the classical notion of probability of error and assumes that users use different codebooks. In the second group, users use different codebooks, but a new notion of probability of error called per-user probability of error is considered. The third group considers the per-user probability of error and that users are restricted to use the same codebook. This group is also known as unsourced random access. For the first and second groups of models, scaling laws that describe the capacity per unit-energy as a function of the order of growth of users were characterized by Ravi and Koch (arxiv.org/abs/2012.10350). In this paper, we first review these results. We then present scaling laws for the third group of models, i.e., unsourced random access. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Ciencia e Innovación under Grant PID2020-116683GB-C21 / AEI / 10.13039/501100011033.

Proceeding of: 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 21-26 June 2020 ; We consider a Gaussian multiple-access channel with random user activity where the total number of userslₙ and the average number of active users kₙ may be unbounded. For this channel, we characterize the maximum number of bits that can be transmitted reliably per unit-energy in terms of lₙ and kₙ . We show that if kₙ log lₙ is sublinear in n, then each user can achieve the single-user capacity per unit-energy. Conversely, if kₙ log lₙ is superlinear in n, then the capacity per unit-energy is zero. We further demonstrate that orthogonal-access schemes, which are optimal when all users are active with probability one, can be strictly suboptimal. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU).

Proceeding of: 2019 IEEE International Symposium on Information Theory (ISIT), 7-12 July 2019, Paris, France ; We consider a Gaussian multiple-access channel where the number of transmitters grows with the blocklength n. For this setup, the maximum number of bits that can be transmitted reliably per unit-energy is analyzed. We show that if the number of users is of an order strictly above n/log n, then the users cannot achieve any positive rate per unit-energy. In contrast, if the number of users is of order strictly below n/log n, then each user can achieve the single-user capacity per unit-energy (log e)/N 0 (where N 0 /2 is the noise power) by using an orthogonal access scheme such as time division multiple access. We further demonstrate that orthogonal codebooks, which achieve the capacity per unit-energy when the number of users is bounded, can be strictly suboptimal. ; J. Ravi and T. Koch have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). T. Koch has further received funding from the Spanish Ministerio de Economía y Competitividad under Grants RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU).

Proceedings of: National Conference on Communications (NCC), 21-23 Feb. 2020, Kharagpur, India. ; The distributed coded caching problem has been studied extensively in the recent past. While the known coded caching schemes achieve an improved transmission rate, they violate the privacy of the users since in these schemes the demand of one user is revealed to others in the delivery phase. In this paper, we consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user. We first show that the memory-rate pair (M, min{ N, K}(1- M / N)) is achievable under information theoretic demand privacy, while using broadcast transmissions. Using this, we show that perfectly demand-private coded caching rate is order optimal for all parameter regimes. We then show that a demand-private scheme for N files and K users can be obtained from a non-private scheme that satisfies only a restricted subset of demands of N K users for N files. We then focus on the demand-private coded caching problem for K = 2 users, N = 2 files. We characterize the exact memory-rate trade-off for this case. To show the achievability, we use our first result to construct a demand-private scheme from a non-private scheme satisfying a restricted demand subset that is known from an earlier work by Tian. Further, by giving a converse based on the extra requirement of privacy, we show that the obtained achievable region is the exact memory-rate trade-off. ; J. Ravi received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). The work of B. K. Dey was supported in part by the Bharti Centre for Communication, lIT Bombay.

We consider the demand-private coded caching problem in a noiseless broadcast network. It is known from past works that a demand-private scheme for N files and K users can be obtained from a non-private scheme for N files and NK users. We first propose a scheme that improves on this idea by removing some redundant transmissions. The memory- rate trade-off achieved using this scheme is shown to be within a multiplicative factor of 3 from the optimal for all the memory regimes when K K = 2. ; J. Ravi has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 714161). The work of B. K. Dey was supported in part by the Bharti Centre for Communication in IIT Bombay. The work of N. Karamchandani is supported in part by a Science and Engineering Research Board (SERB) grant on "Content Caching and Delivery over Wireless Networks".

We consider interactive computation of randomized functions between two users with the following privacy requirement: the interaction should not reveal to either user any extra information about the other user's input and output other than what can be inferred from the user's own input and output. We also consider the case where privacy is required against only one of the users. For both cases, we give single-letter expressions for feasibility and optimal rates of communication. Then we discuss the role of common randomness and interaction in both privacy settings. We also study perfectly secure non-interactive computation when only one of the users computes a randomized function based on a single transmission from the other user. We characterize randomized functions which can be perfectly securely computed in this model and obtain tight bounds on the optimal message lengths in all the privacy settings. ; This work was supported by the Department of Atomic Energy, Government of India, under Project 12-R&D-TFR-5.01-0500. The work of Deepesh Data was supported by a Microsoft Research India Ph.D. Fellowship. The work of Gowtham R. Kurri was supported in part by a Travel Fellowship from the Sarojini Damodaran Foundation and in part by the Department of Science and Technology, Government of India, under an Indo-Israel Grant DST/INT/ISR/P-16/2017. The work of Jithin Ravi was supported by the European Research Council (ERC) through the European Union's Horizon 2020 Research and Innovation Programme under Grant 714161. The work of Vinod M. Prabhakaran was supported in part by a Ramanujan Fellowship from the Department of Science and Technology, Government of India, in part by the Information Technology Research Academy (ITRA), Government of India, under ITRA Mobile Grant ITRA/15(64)/Mobile/USEAADWN/01, and in part by the Department of Science and Technology, Government of India, under an Indo-Israel Grant DST/INT/ISR/P-16/2017.