Multi-terminal Strong Coordination Over Noisy Channels with Secrecy Constraints

We investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel (MAC-WT). In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver on observing the channel output must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. Furthermore, we demand that an external eavesdropper learns essentially nothing about the sources and the simulated output sequence by observing its corresponding MAC-WT output. This is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder. The shared randomness rate tuples which permit such channel simulation with strong secrecy are of interest. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are independent and the legitimate receiver's channel is composed of deterministic links.