47,881 research outputs found
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
Control-theoretic Approach to Communication with Feedback: Fundamental Limits and Code Design
Feedback communication is studied from a control-theoretic perspective,
mapping the communication problem to a control problem in which the control
signal is received through the same noisy channel as in the communication
problem, and the (nonlinear and time-varying) dynamics of the system determine
a subclass of encoders available at the transmitter. The MMSE capacity is
defined to be the supremum exponential decay rate of the mean square decoding
error. This is upper bounded by the information-theoretic feedback capacity,
which is the supremum of the achievable rates. A sufficient condition is
provided under which the upper bound holds with equality. For the special class
of stationary Gaussian channels, a simple application of Bode's integral
formula shows that the feedback capacity, recently characterized by Kim, is
equal to the maximum instability that can be tolerated by the controller under
a given power constraint. Finally, the control mapping is generalized to the
N-sender AWGN multiple access channel. It is shown that Kramer's code for this
channel, which is known to be sum rate optimal in the class of generalized
linear feedback codes, can be obtained by solving a linear quadratic Gaussian
control problem.Comment: Submitted to IEEE Transactions on Automatic Contro
Communicating over Filter-and-Forward Relay Networks with Channel Output Feedback
Relay networks aid in increasing the rate of communication from source to
destination. However, the capacity of even a three-terminal relay channel is an
open problem. In this work, we propose a new lower bound for the capacity of
the three-terminal relay channel with destination-to-source feedback in the
presence of correlated noise. Our lower bound improves on the existing bounds
in the literature. We then extend our lower bound to general relay network
configurations using an arbitrary number of filter-and-forward relay nodes.
Such network configurations are common in many multi-hop communication systems
where the intermediate nodes can only perform minimal processing due to limited
computational power. Simulation results show that significant improvements in
the achievable rate can be obtained through our approach. We next derive a
coding strategy (optimized using post processed signal-to-noise ratio as a
criterion) for the three-terminal relay channel with noisy channel output
feedback for two transmissions. This coding scheme can be used in conjunction
with open-loop codes for applications like automatic repeat request (ARQ) or
hybrid-ARQ.Comment: 15 pages, 8 figures, to appear in IEEE Transactions on Signal
Processin
Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information
In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved
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