An algebraic framework for concatenated linear block codes in side information based problems

Abstract

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.