
Research topics:

A relay channel refers to a configuration, where the signal transmitted by the source node is forwarded by one or more helping nodes towards the destination node and thereby can achieve a better reliability and rate. In recently defined 4G standards provision for two types of relays are incorporated: 1) a relay station that will enhance the performance of a end user; and 2) a relay which will extend the coverage of the base station beyond its cell limit. We have characterized the fundamental information theoretic performance of such networks including the diversitymultiplexing tradeoff (DMT) of the 3node MIMO relay channel [C4, J2], the dynamic decode and forward (DDF) protocol [J1] and the DMT of relay channel with ARQ [C1]. [C4] Sanjay Karmakar and Mahesh K. Varanasi, ``Diversitymultiplexing tradeoff of the symmetric MIMO halfduplex relay channel", in Proceedings of ISIT, Austin, Texas, June 1318, 2010. [J2] Sanjay Karmakar and Mahesh K. Varanasi, ``The diversitymultiplexing tradeoff of the MIMO halfduplex relay channel", IEEE Transactions on Information Theory, Vol. 58, N0. 12, Dec. 2012, pp. 71687187. [C3] Sanjay Karmakar and Mahesh K. Varanasi, `` Diversity Multiplexing Tradeoff of the DynamicDecode and Forward Protocol on a MIMO HalfDuplex Relay Channel ,'' Proceedings of ISIT 2009, Seoul, Korea, June 28  July 3. [C2] Sanjay Karmakar and Mahesh K. Varanasi, ``Optimal DMT of Dynamic DecodeandForward Protocol on a HalfDuplex Relay Channel With Arbitrary Number of Antennas at Each Node ", Proceedings of Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, CA, Nov. 1  Nov. 4, 2009. [J1] Sanjay Karmakar and Mahesh K. Varanasi, ``DiversityMultiplexing Tradeoff of Dynamic DecodeandForward protocol on a MIMO HalfDuplex Relay Channel", IEEE Transactions on Information Theory, Vol. 57, No. 10, Oct. 2011, pp. 65696590. [C1] Sanjay Karmakar and Mahesh K. Varanasi, ``DiversityMultiplexingDelay Tradeoff of a DDF Protocol on a HalfDuplex ARQ Relay Channel ", Proceedings of Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, CA, Nov. 1  Nov. 4, 2009. The journal version of this paper is under preparation and to be submitted to the Transactions on wireless communications.

Space time Block Code design for MIMO communication systems The discovery of enhanced capacity of a MIMO pointtopoint channel, with respect to the capacity of a channel with single antennas at both the transmitter and receiver (SISO), led to the invention of a new class of codes, namely the space time block codes (STBC). In this class of codes, coding takes place across both the time and antenna dimensions as against to only the time dimension in classical single antenna communication links. In this area of research, we have designed STBCs  for MIMO communication systems  which achieves a relatively better tradeoff between decoding complexity and rate of transmission than the preexisting STBCs. We have pioneered a novel mathematical framework involving the Clifford algebra enabling a systematic construction of these codes [J3]. Several classes of such codes with gradually larger rates and decoding complexities [J1],[J2] were constructed using this framework. [J1] Sanjay Karmakar, K. Pavan Srinath and B. Sundar Rajan, ``Maximum Rate of UnitaryWeight, SingleSymbol Decodable STBCs", IEEE Transactions on Information Theory, Vol. 57, No. 10, Dec. 2011, pp. 79727981. [J2] Sanjay Karmakar and B. Sundar Rajan, ``Highrate, MultiSymbolDecodable STBCs from Clifford Algebras'', IEEE Transactions on Information Theory, Vol. 55, No. 06, Jun. 2009, pp. 26822695. [J3] Sanjay Karmakar and B. Sundar Rajan, ``MultigroupDecodable STBCs from Clifford Algebras'', IEEE Transactions on Information Theory, Vol. 55, No. 01, Jan. 2009, pp. 223231. [C1] Sanjay Karmakar and Mahesh K. Varanasi, `` On the rate versus MLdecoding complexity tradeoff of square LDSTBCs with unitary weight matrices,'' Proceedings of IEEE GLOBECOM 2008, New Orleans, LA, USA, Nov.30Dec.04, 2008. The journal version of this paper is under preparation and to be submitted to the Transactions on Information Theory. [C2] Sanjay Karmakar and B. Sundar Rajan, `` Highrate DoubleSymbolDecodable STBCs from Clifford Algebras," Proceedings of IEEE GLOBECOM 2006, San Francisco, Nov.27Dec.01, 2006. [C3] Sanjay Karmakar and B. Sundar Rajan, `` Multigroup decodable STBCs from Clifford Algebras,'' Proceedings of IEEE Information Theory Workshop (ITW 2006), Chengdu, China, October 2226, 2006, pp.448452. [C4] Sanjay Karmakar and B. Sundar Rajan, `` Minimumdecodingcomplexity maximumrate spacetime block codes from Clifford algebras,'' Proceedings of IEEE International Symposium on Information Theory (ISIT 2006), Seattle, USA, July 0914, 2006, pp.788792. [C5] Sanjay Karmakar and B. Sundar Rajan, `` Nonunitary weight spacetime block codes with minimum decoding complexity,'' Proceedings of IEEE International Symposium on Information Theory (ISIT 2006), Seattle, USA, July 0914, 2006, pp.793797. [C6] Sanjay Karmakar and B. Sundar Rajan, ``Highrate, MultiSymbolDecodable STBCs from Clifford Algebras,''Proceedings of Thirteenth National Conference on Communications (NCC 2007),, IIT Kanpur, January 2729, 2007, pp.368372.

