Distributed Multilevel Diversity Coding

TL;DR

This paper investigates the optimality of distributed multilevel diversity coding schemes, establishing their effectiveness for up to three sources and under symmetry conditions for general cases, extending previous theoretical results.

Contribution

It proves the optimality of multilayer Slepian-Wolf coding for up to three sources and extends this to general sources under symmetry, generalizing prior work.

Findings

Optimality of multilayer Slepian-Wolf coding for K ≤ 3

Extension of optimality to general K under symmetry

Generalization of Yeung and Zhang's results

Abstract

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.