Lalitha Sankar

Science and Technology Postdoctoral Fellow
C-436, Engineering Quadrangle, Olden Street,
Princeton, NJ 08544,
Phone: 609-258-2509
Email: lalitha at princeton dot edu

Research Projects

Fading Wireless Networks: Sum-Capacity and Resource Allocation

Wireless networks are characterized by two distinct features: fading and interference. Signal designs for wireless networks need to be optimized for channel variations for efficient allocation of radio resources. I develop optimal signal designs and scheduling protocols for three wireless network models of practical relevance assuming perfect channel knowledge at all nodes:

(i) multiple-access relay channel where multiple users transmit to a common receiver in the presence of a dedicated relay node, 
(ii) compound multiple-access channels where multiple transmitters transmit to two receivers, and 
(iii) two-user interference channels comprised of two interfering wireless links.

I combine combinatorial algebra and information theory to unify and simplify the analysis of all three problems and make the following observations.
1) Our approach yields a new topology-based sub-classification of all three networks. 
2) The sum-capacity achieving signal design for all three networks turns on its head the conventional assumption that independent information can be multiplexed over the different fading states and instead requires transmitting jointly to exploit all fading states. 
3) Finally, the analysis has direct repercussions on coding and interference management schemes for real-world networks as it reveals topologies and channel statistics for which decoding or ignoring interference is optimal.

Relevant Publications:

Information Security in Relay Networks

In constrast to and in addition to the traditional link layer cryptographic schemes, a relay can exploit the noisy physical channel to assist in ensuring the secrecy of data packets from untrusted eavesdropping nodes. In [1], we develop optimal source and relay signaling schemes that achieve perfect secrecy for a class of half-duplex relay channels and show that the optimal relay signaling can facilitate both cooperative communications and deter decoding at the eavesdropper. This result is particularly applicable to multi-hop networks such as sensor, mesh, and ad hoc networks with secrecy constraints.

Relevant Publications:

Network Information Theory

The capacity region of multi-terminal networks remains a long-standing open problem, with the exception of a few classes of networks. With increasing demand for wireless data networks, developing fundamental performance limits is both essential and imperative to design real-world networks without resorting to heuristics. One such class of networks of practical relevance is the multiaccess relay channel where multiple sources communicate with a common destination in the presence of a dedicated relay node. Analogous to the single-source relay channel, the optimal signaling schemes for this multiple-access relay chanel (MARC) are known only for specific topologies or channel models. In my doctoral work I developed achievable schemes for the MARC. While it may appear that generalizing the schemes for the classic relay channel should suffice the multiple-access nature of the channel where all sources share the relay complicates the problem.

As a part of doctoral work, I developed two theoretical results for the MARC. The first focuses on developing a coding scheme that enables decoding of received bits at the destination in a streaming manner using a new offset encoding scheme. The second develops the sum-capacity for the class of degraded Gaussian multiaccess relay channel where the received signal at the destination is a physically degraded version of that received at the relay. A single-known result on polymatroid intersections is used to develop the result.

Relevant Publications:

Relay and User Cooperative Networks

While cooperation can increase diversity in wireless networks, the tradeoff at every node of using resources for self vs. cooperative transmissions can make dedicated relays desirable. In my doctoral work, I compare the diversity gains achieved by inter-user cooperation with those achieved exclusively via relay cooperation. Introducing a cost model to account for processing and transmission power at every node, we show that relay cooperation can be more energy efficient than user cooperation.

Relevant Publications:

Game-theoretic Analysis of  Cooperation in Wireless Networks

In large wireless networks, heterogeneous users with competing interests may not cooperate to share their resources without incentives. Using information rate as the incentive for every link in a network of multiple interfering links, we use coalitional game theory to determine the stability of the grand coalition of all links when transmitters and/or receivers cooperate. Our results reveal that stable coalitions result only when all users achieve sufficient rate gains.

Relevant Publications: