Compressive Sensing for Feedback Reduction in MIMO Broadcast Channels

We propose a generalized feedback model and compressive sensing based opportunistic feedback schemes for feedback resource reduction in MIMO Broadcast Channels under the assumption that both uplink and downlink channels undergo block Rayleigh fading. Feedback resources are shared and are opportunistically accessed by users who are strong, i.e. users whose channel quality information is above a certain fixed threshold. Strong users send same feedback information on all shared channels. They are identified by the base station via compressive sensing. Both analog and digital feedbacks are considered. The proposed analog & digital opportunistic feedback schemes are shown to achieve the same sum-rate throughput as that achieved by dedicated feedback schemes, but with feedback channels growing only logarithmically with number of users. Moreover, there is also a reduction in the feedback load. In the analog feedback case, we show that the propose scheme reduces the feedback noise which eventually results in better throughput, whereas in the digital feedback case the proposed scheme in a noisy scenario achieves almost the throughput obtained in a noiseless dedicated feedback scenario. We also show that for a fixed given budget of feedback bits, there exist a trade-off between the number of shared channels and thresholds accuracy of the feedback SINR.Comment: Submitted to IEEE Transactions on Wireless Communications, April 200

Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems

Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor

The Wiretap Channel with Feedback: Encryption over the Channel

In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the perfect secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-$\Lambda$ channel where it is shown that the perfect secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.Comment: Submitted to IEEE Transactions on Information Theor