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

Structured Mappings and Conferencing Common Information for Multiple-access Channels