State-Dependent Parallel Gaussian Networks With a Common State-Cognitive Helper

State-dependent parallel networks with a common state-cognitive helper is studied, in which K transmitters wish to send K messages to their corresponding receivers over K state-corrupted parallel channels, and a helper who knows the state information noncausally wishes to assist these receivers to cancel state interference. Furthermore, the helper also has its own message to be sent simultaneously to its corresponding receiver. Since the state information is known only to the helper, but not to other transmitters, transmitter-side state cognition and receiver-side state interference are mismatched. Our focus is on the high state power regime, i.e., the state power goes to infinity. Three (sub)models are studied. Model I serves as a basic model, which consists of only one transmitter-receiver (with state corruption) pair in addition to a helper that assists the receiver to cancel state in addition to transmitting its own message. Model II consists of two transmitter-receiver pairs in addition to a helper, and only one receiver is interfered by a state sequence. Model III generalizes model I to include multiple transmitter- receiver pairs with each receiver corrupted by independent state. For all models, the inner and outer bounds on the capacity region are derived, and comparison of the two bounds yields characterization of either full or partial boundary of the capacity region under various channel parameters.