On symmetrical multilevel diversity coding

Symmetrical multilevel diversity coding with independent data streams has been studied by Roche et al. (1992), and the admissible coding rate region was determined for the case of three levels. In particular, it was shown that coding by superposition is optimal, which means that optimality can be achieved by very simple coding. However, it is very difficult to generalize their proof to an arbitrary number of levels. In this paper, we use a new approach to study this problem, and we show that coding by superposition is optimal for symmetrical multilevel diversity coding in general. We also discuss how our result can be applied when the source consists of correlated data streams. The techniques we use are new in multiuser information theory, and our work sheds some light on the standing problem of characterizing those multilevel diversity coding systems for which coding by superposition is optimal.