  We consider a network of two nodes separated by a noisy channel with
two-sided state information, in which the input and output signals have to be
coordinated with the source and its reconstruction. In the case of non-causal
encoding and decoding, we propose a joint source-channel coding scheme and
develop inner and outer bounds for the strong coordination region. While the
inner and outer bounds do not match in general, we provide a complete
characterization of the strong coordination region in three particular cases:
i) when the channel is perfect; ii) when the decoder is lossless; and iii) when
the random variables of the channel are independent from the random variables
of the source. Through the study of these special cases, we prove that the
separation principle does not hold for joint source-channel strong
coordination. Finally, in the absence of state information, we show that polar
codes achieve the best known inner bound for the strong coordination region,
which therefore offers a constructive alternative to random binning and coding
proofs.
