  We consider the problem of compressing memoryless binary data with or without
side information at the decoder. We review the parity- and the syndrome-based
approaches and discuss their theoretical limits, assuming that there exists a
virtual binary symmetric channel between the source and the side information,
and that the source is not necessarily uniformly distributed. We take a
factor-graph-based approach in order to devise how to take full advantage of
the ready-available iterative decoding procedures when turbo codes are
employed, in both a parity- or a syndrome-based fashion. We end up obtaining a
unified decoder formulation that holds both for error-free and for error-prone
encoder-to-decoder transmission over generic channels. To support the
theoretical results, the different compression systems analyzed in the paper
are also experimentally tested. They are compared against several different
approaches proposed in literature and shown to be competitive in a variety of
cases.
