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 and memoryless Gaussian
cases. 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 compression using Wyner-Ziv binning are
optimal. The scheme that uses Wyner-Ziv binning shares elements with Cover and
El Gamal original compress-and-forward, but differs from it mainly in that
backward decoding is employed instead of forward decoding and the compression
indices are not decoded uniquely. Finally, by exploring the properties of our
outer bound, we show that, although not required in general, the compression
indices can in fact be decoded uniquely essentially without altering the
capacity region, but at the expense of larger alphabets sizes for the auxiliary
random variables.Comment: Submitted for publication to the 2012 IEEE International Symposium on
Information Theory, 5 pages, 1 figur
