Diversity Order Gain with Noisy Feedback in Multiple Access Channels

In this paper, we study the effect of feedback channel noise on the diversity-multiplexing tradeoff in multiuser MIMO systems using quantized feedback, where each user has m transmit antennas and the base-station receiver has n antennas. We derive an achievable tradeoff and use it to show that in SNR-symmetric channels, a single bit of imperfect feedback is sufficient to double the maximum diversity order to 2mn compared to when there is no feedback (maximum is mn at multiplexing gain of zero). Further, additional feedback bits do not increase this maximum diversity order beyond 2mn. Finally, the above diversity order gain of mn over non-feedback systems can also be achieved for higher multiplexing gains, albeit requiring more than one bit of feedback.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 200

Bits About the Channel: Multi-round Protocols for Two-way Fading Channels

Most communication systems use some form of feedback, often related to channel state information. In this paper, we study diversity multiplexing tradeoff for both FDD and TDD systems, when both receiver and transmitter knowledge about the channel is noisy and potentially mismatched. For FDD systems, we first extend the achievable tradeoff region for 1.5 rounds of message passing to get higher diversity compared to the best known scheme, in the regime of higher multiplexing gains. We then break the mold of all current channel state based protocols by using multiple rounds of conferencing to extract more bits about the actual channel. This iterative refinement of the channel increases the diversity order with every round of communication. The protocols are on-demand in nature, using high powers for training and feedback only when the channel is in poor states. The key result is that the diversity multiplexing tradeoff with perfect training and K levels of perfect feedback can be achieved, even when there are errors in training the receiver and errors in the feedback link, with a multi-round protocol which has K rounds of training and K-1 rounds of binary feedback. The above result can be viewed as a generalization of Zheng and Tse, and Aggarwal and Sabharwal, where the result was shown to hold for K=1 and K=2 respectively. For TDD systems, we also develop new achievable strategies with multiple rounds of communication between the transmitter and the receiver, which use the reciprocity of the forward and the feedback channel. The multi-round TDD protocol achieves a diversity-multiplexing tradeoff which uniformly dominates its FDD counterparts, where no channel reciprocity is available.Comment: Submitted to IEEE Transactions on Information Theor

Boolean Functions, Projection Operators and Quantum Error Correcting Codes

This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and non-additive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5,6,2)) code found by Rains [21]. It also extends to operator quantum error correcting codes.Comment: Submitted to IEEE Transactions on Information Theory, October 2006, to appear in IEEE Transactions on Information Theory, 200