  In this work, we study two problems: three-user Multiple-Access Channel (MAC)
with correlated sources, and MAC with Feedback (MAC-FB) with independent
messages. For the first problem, we identify a structure in the joint
probability distribution of discrete memoryless sources, and define a new
common information called ``conferencing common information". We develop a
multi-user joint-source channel coding methodology based on structured mappings
to encode this common information efficiently and to transmit it over a MAC. We
derive a new set of sufficient conditions for this coding strategy using
single-letter information quantities for arbitrary sources and channel
distributions. Next, we make a fundamental connection between this problem and
the problem of communication of independent messages over three-user MAC-FB. In
the latter problem, although the messages are independent to begin with, they
become progressively correlated given the channel output feedback. Subsequent
communication can be modeled as transmission of correlated sources over MAC.
Exploiting this connection, we develop a new coding scheme for the problem. We
characterize its performance using single-letter information quantities, and
derive an inner bound to the capacity region. For both problems, we provide a
set of examples where these rate regions are shown to be optimal. Moreover, we
analytically prove that this performance is not achievable using random
unstructured random mappings/codes.
