State-dependent parallel Gaussian channels with a common helper in high power regime

The state-dependent parallel Gaussian channel with a common helper is investigated, in which transmitters 1 and 2 transmit two messages respectively to receivers 1 and 2 over the parallel channel. Furthermore, both parallel subchannels can be corrupted by independent state sequences, respectively, which are unknown to both transmitters and receivers. There is a common helper that knows the states noncausally and assists communication between transmitters and receivers. Our focus is on the high state power regime, i.e., the state power goes to infinity. Two Gaussian models are studied with model I having only receiver 1 interfered by the state and with model II having both receivers interfered by independent states. Each model has its unique challenge to address. For both models, inner and outer bounds on the capacity region are derived, and comparison of the two bounds leads to capacity results under certain channel parameters.