Coordination using implicit communication

We explore a basic noise-free signaling scenario where coordination and communication are naturally merged. A random signal X₁, ..., X_n is processed to produce a control signal or action sequence A₁, ..., A_n, which is observed and further processed (without access to X₁, ..., X_n) to produce a third sequence B₁, ..., B_n. The object of interest is the set of empirical joint distributions p(x, a, b) that can be achieved in this setting. We show that H(A) ≥ I(X;A,B) is the necessary and sufficient condition for achieving p(x, a, b) when no causality constraints are enforced on the encoders. We also give results for various causality constraints. This setting sheds light on the embedding of digital information in analog signals, a concept that is exploited in digital watermarking, steganography, cooperative communication, and strategic play in team games such as bridge.