  This work provides an algebraic framework for source coding with decoder side
information and its dual problem, channel coding with encoder side information,
showing that nested concatenated codes can achieve the corresponding
rate-distortion and capacity-noise bounds. We show that code concatenation
preserves the nested properties of codes and that only one of the concatenated
codes needs to be nested, which opens up a wide range of possible new code
combinations for these side information based problems. In particular, the
practically important binary version of these problems can be addressed by
concatenating binary inner and non-binary outer linear codes. By observing that
list decoding with folded Reed- Solomon codes is asymptotically optimal for
encoding IID q-ary sources and that in concatenation with inner binary codes it
can asymptotically achieve the rate-distortion bound for a Bernoulli symmetric
source, we illustrate our findings with a new algebraic construction which
comprises concatenated nested cyclic codes and binary linear block codes.
