  We describe and analyze sparse graphical code constructions for the problems
of source coding with decoder side information (the Wyner-Ziv problem), and
channel coding with encoder side information (the Gelfand-Pinsker problem). Our
approach relies on a combination of low-density parity check (LDPC) codes and
low-density generator matrix (LDGM) codes, and produces sparse constructions
that are simultaneously good as both source and channel codes. In particular,
we prove that under maximum likelihood encoding/decoding, there exist
low-density codes (i.e., with finite degrees) from our constructions that can
saturate both the Wyner-Ziv and Gelfand-Pinsker bounds.
