  We consider a setting of Slepian--Wolf coding, where the random bin of the
source vector undergoes channel coding, and then decoded at the receiver, based
on additional side information, correlated to the source. For a given
distribution of the randomly selected channel codewords, we propose a universal
decoder that depends on the statistics of neither the correlated sources nor
the channel, assuming first that they are both memoryless. Exact analysis of
the random-binning/random-coding error exponent of this universal decoder shows
that it is the same as the one achieved by the optimal maximum a-posteriori
(MAP) decoder. Previously known results on universal Slepian-Wolf source
decoding, universal channel decoding, and universal source-channel decoding,
are all obtained as special cases of this result. Subsequently, we further
generalize the results in several directions, including: (i) finite-state
sources and finite-state channels, along with a universal decoding metric that
is based on Lempel-Ziv parsing, (ii) arbitrary sources and channels, where the
universal decoding is with respect to a given class of decoding metrics, and
(iii) full (symmetric) Slepian-Wolf coding, where both source streams are
separately fed into random-binning source encoders, followed by random channel
encoders, which are then jointly decoded by a universal decoder.
