  A class of state-dependent parallel networks with a common state-cognitive
helper, 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 the corresponding
transmitters $1,\dots,K$, 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 include
multiple transmitter-receiver pairs with each receiver corrupted by independent
state. For all models, inner and outer bounds on the capacity region are
derived, and comparison of the two bounds leads to characterization of either
full or partial boundary of the capacity region under various channel
parameters.
