Research
My research interests lie in the area of network information theory, with a particular focus on distributed computation and information theoretic security. I aim to analyse the fundamental limits of communication in small as well as large networks. The figure below depicts the problems that I have worked on in these areas.
Large Networks
Massive Multiple-Access Channel
The fifth generation (5G) of wireless systems and the Internet of Things (IoT) are gearing up for the explosive growth of devices. Motivated from this, we study a Gaussian multiple-access channel where the number of users grows with the blocklength n. For this setup, the maximum number of bits per unit-energy that can be transmitted reliably as a function of the order of growth of the users is analysed. 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.
1) J. Ravi and T. Koch, "Scaling Laws for Gaussian Random Many-Access Channels," IEEE Transactions on Information Theory, Early Access, Dec. 2021. (ieee) (arxiv)
Index Coding
Index coding is a fundamental problem in network information theory which studies a setup consisting of a server with N files communicating with N users over a noiseless broadcast channel. Each user is assumed to have prior knowledge of a subset of the N files and wants to obtain one of the files. In this setup, we consider a privacy requirement that receivers do not learn anything more than the files they already have as side information and the file they want from the server. We refer to this as private index coding. To achieve the private index coding, we consider the use of secret keys that are shared among various subsets of users and the server.
1) V. Narayanan, J. Ravi, V. K. Mishra, B. K. Dey, N. Karamchandani, and V. M. Prabhakaran, "Private Index Coding,'' IEEE Transactions on Information Theory, Early Access, Nov. 2021. (ieee) (arxiv)
Coded Caching
The coded caching problem in a noiseless broadcast network with one server and many users, each user equipped with a cache, has been studied extensively in the recent past. It has been observed that significant gain in the transmission rate can be achieved by clever design of caching and delivery schemes. 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. We consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user.
1) C. Gujarpadhye, J. Ravi, S. Kamath, B. K. Dey, and N. Karamchandani, "Fundamental Limits of Demand-Private Coded Caching," To appear in IEEE Transactions on Information Theory. (arxiv)
Small Networks
Interactive Computation
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.
1) D. Data, G. R. Kurri, J. Ravi, and V. M. Prabhakaran, “Interactive Secure Function Computation,'' accepted to IEEE Transactions on Information Theory, Feb. 2020. (ieee) (arxiv)
Oblivious Transfer
Oblivious Transfer (OT) which is a primitive for all two party secure computation. In one-out-of-two string OT, one party (Alice) has two files and the other party (Bob) wants one of these files. Bob wants to obtain exactly his file of choice without Alice finding out the identity of the file chosen by Bob. There are noisy and noiseless channels between Alice and Bob. In our work, the noisy channel between them is assumed to be wireless such as OFDM or MIMO channels where only the receiver knows the channel state information. Using a physical layer approach, we have proposed a scheme for performing OT over these channels.
1) J. Ravi, B. K. Dey, and E. Viterbo, “Oblivious Transfer over Wireless Channels,'' IEEE Transactions on Communications, vol 64, no 5, pp 893-905, March 2016. (ieee) (arxiv)
Relay Network
We study the function computation problem in a bidirectional relay network with three nodes. In this network, nodes A and B have two correlated sources X and Y respectively. Both the nodes communicate through a broadcasting relay node C to compute a function f(X,Y). All the links are assumed to be noiseless. The goal is to characterise the rates of the messages required from each node which will help nodes A and B to compute the function. We have studied this problem under zero-error and vanishing error criteria.
1) J. Ravi and B. K. Dey, “Function Computation through a bidirectional relay,'' IEEE Transactions on Information Theory, vol 65, no 2, pp 902-916, Feb. 2019. (ieee) (arxiv)