Distributed Multilevel Diversity Coding

In distributed multilevel diversity coding, $K$ correlated sources (each with $K$ components) are encoded in a distributed manner such that, given the outputs from any $\alpha$ encoders, the decoder can reconstruct the first $\alpha$ components of each of the corresponding $\alpha$ sources. For this problem, the optimality of a multilayer Slepian-Wolf coding scheme based on binning and superposition is established when $K\leq 3$. The same conclusion is shown to hold for general $K$ under a certain symmetry condition, which generalizes a celebrated result by Yeung and Zhang.