Redundancy of Variable Rate Slepian-Wolf Codes from the Decoder´s Perspective

The Slepian-Wolf coding problem is often viewed as a channel coding problem for the purpose of gaining insight into its properties. In this perspective, source sequences are associated with balls of side information sequences, and then one packs in each bin as many of these balls as possible with little or no overlap. Alternatively, one can treat the problem as a source coding problem in which for a given side information sequence, the set of conditionally probable source sequences is distributed in as many bins as required by a fidelity criterion. In an earlier series of publications we developed the theory of redundancy of variable rate Slepian-Wolf codes using the first viewpoint. In this work, we obtain similar results from the second viewpoint; this direction has unique technical challenges but also reinforces the fundamental role of our previously introduced notion of intrinsic entropy. In one of our key technical contributions, we use an averaging argument resembling Shannon´s random coding idea that we expect will be useful in studying other problems of source coding with side information.