Kraft Inequality and Zero-Error Source Coding with Decoder Side Information

This paper tackles the problem of zero-error instantaneous coding with decoder side information in light of the Kraft inequality. Specifically, a bounded Kraft sum over all cliques in the characteristic graph of the source/side-information pair is envisioned to be a sufficient condition for the existence of a valid code with given codeword lengths. It is shown that (i) if such a sufficient condition exists for a class of graphs, it is possible to universally bound the rate redundancy in the class, (ii) there exist graph classes of interest for which such sufficient conditions can indeed be found, and finally (iii) no such condition can be found for the class of all graphs.