  We consider the problem of reliable communication over multiple-access
channels (MAC) where the channel is driven by an independent and identically
distributed state process and the encoders and the decoder are provided with
various degrees of asymmetric noisy channel state information (CSI). For the
case where the encoders observe causal, asymmetric noisy CSI and the decoder
observes complete CSI, we provide inner and outer bounds to the capacity
region, which are tight for the sum-rate capacity. We then observe that, under
a Markov assumption, similar capacity results also hold in the case where the
receiver observes noisy CSI. Furthermore, we provide a single letter
characterization for the capacity region when the CSI at the encoders are
asymmetric deterministic functions of the CSI at the decoder and the encoders
have non-causal noisy CSI (its causal version is recently solved in
\cite{como-yuksel}). When the encoders observe asymmetric noisy CSI with
asymmetric delays and the decoder observes complete CSI, we provide a single
letter characterization for the capacity region. Finally, we consider a
cooperative scenario with common and private messages, with asymmetric noisy
CSI at the encoders and complete CSI at the decoder. We provide a single letter
expression for the capacity region for such channels. For the cooperative
scenario, we also note that as soon as the common message encoder does not have
access to CSI, then in any noisy setup, covering the cases where no CSI or
noisy CSI at the decoder, it is possible to obtain a single letter
characterization for the capacity region. The main component in these results
is a generalization of a converse coding approach, recently introduced in [1]
for the MAC with asymmetric quantized CSI at the encoders and herein
considerably extended and adapted for the noisy CSI setup.
