  This paper studies a memoryless state-dependent multiple access channel (MAC)
where two transmitters wish to convey a message to a receiver under the
assumption of causal and imperfect channel state information at transmitters
(CSIT) and imperfect channel state information at receiver (CSIR). In order to
emphasize the limitation of transmitter cooperation between physically
distributed nodes, we focus on the so-called distributed CSIT assumption, i.e.
where each transmitter has its individual channel knowledge, while the message
can be assumed to be partially or entirely shared a priori between transmitters
by exploiting some on-board memory. Under this setup, the first part of the
paper characterizes the common message capacity of the channel at hand for
arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon
strategies, i.e. optimal codes are constructed by letting the channel inputs be
a function of current CSIT only. For a special case when CSIT is a
deterministic function of CSIR, the considered scheme also achieves the
capacity region of a common message and two private messages. The second part
addresses an important instance of the previous general result in a context of
a cooperative multi-antenna Gaussian channel under i.i.d. fading operating in
frequency-division duplex mode, such that CSIT is acquired via an explicit
feedback of perfect CSIR. The capacity of the channel at hand is achieved by
distributed linear precoding applied to Gaussian codes. Surprisingly, we
demonstrate that it is suboptimal to send a number of data streams bounded by
the number of transmit antennas as typically considered in a centralized CSIT
setup. Finally, numerical examples are provided to evaluate the sum capacity of
the binary MAC with binary states as well as the Gaussian MAC with i.i.d.
fading.
