  We consider a two-user state-dependent multiaccess channel in which the
states of the channel are known non-causally to one of the encoders and only
strictly causally to the other encoder. Both encoders transmit a common message
and, in addition, the encoder that knows the states non-causally transmits an
individual message. We find explicit characterizations of the capacity region
of this communication model in both discrete memoryless (DM) and memoryless
Gaussian cases. In particular the capacity region analysis demonstrates the
utility of the knowledge of the states only strictly causally at the encoder
that sends only the common message in general. More specifically, in the DM
setting we show that such a knowledge is beneficial and increases the capacity
region in general. In the Gaussian setting, we show that such a knowledge does
not help, and the capacity is same as if the states were completely unknown at
the encoder that sends only the common message. The analysis also reveals
optimal ways of exploiting the knowledge of the state only strictly causally at
the encoder that sends only the common message when such a knowledge is
beneficial. The encoders collaborate to convey to the decoder a lossy version
of the state, in addition to transmitting the information messages through a
generalized Gel'fand-Pinsker binning. Particularly important in this problem
are the questions of 1) optimal ways of performing the state compression and 2)
whether or not the compression indices should be decoded uniquely. We show that
both compression \`a-la noisy network coding, i.e., with no binning and
non-unique decoding, and compression using Wyner-Ziv binning with backward
decoding and non-unique or unique decoding are optimal.
