  We consider optimal signalling and control of discrete-time nonlinear
partially observable stochastic systems in state space form. In the first part
of the paper, we characterize the operational {\it control-coding capacity},
$C_{FB}$ in bits/second, by an information theoretic optimization problem of
encoding signals or messages into randomized controller-encoder strategies, and
reproducing the messages at the output of the system using a decoder or
estimator with arbitrary small asymptotic error probability. Our analysis of
$C_{FB}$ is based on realizations of randomized strategies
(controller-encoders), in terms of information states of nonlinear filtering
theory, and either uniform or arbitrary distributed random variables (RVs). In
the second part of the paper, we analyze the linear-quadratic Gaussian
partially observable stochastic system (LQG-POSS). We show that simultaneous
signalling and control leads to randomized strategies described by
finite-dimensional sufficient statistics, that involve two Kalman-filters, and
consist of control, estimation and signalling strategies. We apply
decentralized optimization techniques to prove a separation principle, and to
derive the optimal control part of randomized strategies explicitly in terms of
a control matrix difference Riccati equation (DRE).
