223 research outputs found
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
Comparison of Channels: Criteria for Domination by a Symmetric Channel
This paper studies the basic question of whether a given channel can be
dominated (in the precise sense of being more noisy) by a -ary symmetric
channel. The concept of "less noisy" relation between channels originated in
network information theory (broadcast channels) and is defined in terms of
mutual information or Kullback-Leibler divergence. We provide an equivalent
characterization in terms of -divergence. Furthermore, we develop a
simple criterion for domination by a -ary symmetric channel in terms of the
minimum entry of the stochastic matrix defining the channel . The criterion
is strengthened for the special case of additive noise channels over finite
Abelian groups. Finally, it is shown that domination by a symmetric channel
implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality
for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium
on Information Theory (ISIT
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