Strong Coordination Over Noisy Channels

We study the problem of strong coordination actions two nodes $X$ and $Y$ that communicate over a discrete memoryless channel (DMC) such follow prescribed joint probability distribution. propose novel random coding schemes polar scheme for this noisy problem, derive inner bounds respective capacity region. The first is coordination-channel utilizes randomness provided by DMC to reduce amount local required generate sequence at Node $Y$. Based on scheme, we provide characterization region special cases setup, namely, when are determined deterministic channel. second exploits separate where extracted from after decoding. third coordination. show codes able achieve established bound thus constructive alternative proof. Our also offers solution simulation shared employed together simulate another DMC. Finally, leveraging results present an example in which proposed strictly outperform terms achievable communication rate same injected into both systems. Thus, establish sub-optimality separation with respect