Empirical coordination, state masking and state amplification: Core of the decoder's knowledge

We revisit the problem of state masking and state amplification for state-dependent channel with causal state information at the encoder from the point of view of empirical coordination. Empirical coordination, which requires all sequences of symbols to be jointly typical for a target joint probability distribution, provides a unified perspective to simultaneously study state masking, state amplification, and capacity-distortion trade-off. Our main result is a characterization of the set of achievable rates, information leakages and joint distributions. We also discuss several specializations and extensions of the result, including the cases of zero message rate, without empirical coordination, strictly causal encoding, two-sided state information and noisy channel feedback. We introduce the notion of “core of the decoder's knowledge,” to capture what the decoder can infer about all the signals involved in the model.