  We study reliable transmission of arbitrarily correlated sources over
multiple-access relay channels (MARCs) and multiple-access broadcast relay
channels (MABRCs). In MARCs only the destination is interested in
reconstructing the sources, while in MABRCs both the relay and the destination
want to reconstruct them. In addition to arbitrary correlation among the source
signals at the users, both the relay and the destination have side information
correlated with the source signals. Our objective is to determine whether a
given pair of sources can be losslessly transmitted to the destination for a
given number of channel symbols per source sample, defined as the
source-channel rate. Sufficient conditions for reliable communication based on
operational separation, as well as necessary conditions on the achievable
source-channel rates are characterized. Since operational separation is
generally not optimal for MARCs and MABRCs, sufficient conditions for reliable
communication using joint source-channel coding schemes based on a combination
of the correlation preserving mapping technique with Slepian-Wolf source coding
are also derived. For correlated sources transmitted over fading Gaussian MARCs
and MABRCs, we present conditions under which separation (i.e., separate and
stand-alone source and channel codes) is optimal. This is the first time
optimality of separation is proved for MARCs and MABRCs.
