State-dependent parallel Gaussian channels with a state-cognitive helper

Abstract—The state-dependent parallel channel with differently scaled states and a common state-cognitive helper is studied,
in which two transmitters wish to send two messages to their
corresponding receivers respectively over two parallel Gaussian
subchannels. The two Gaussian channels are corrupted by the
same but differently scaled states. The state is not known to
the transmitters nor to the receivers, but known to a helper noncausally, which assists the receivers to cancel the state. Differently
from previous studies that characterized the capacity region only
in the infinite state power regime and under independent state
corruption at the two receivers, this paper investigates the case
under arbitrary state power and with the same but differently
scaled states. An inner bound on the capacity region is derived
and is compared to an outer bound. Then the channel parameters
are partitioned into various cases, and segments on the capacity
region boundary are characterized for each case.
Index Terms—Dirty paper coding, , Gelf’and-Pinsker scheme,
noncausal channel state information, parallel channel.