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 α encoders, the decoder can reconstruct the first α components of each of the corresponding α sources. For this problem, the optimality of a multilayer Slepian-Wolf coding scheme based on binning and superposition is established when K ≤ 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.