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.

[1]  Tie Liu,et al.  Secure Symmetrical Multilevel Diversity Coding , 2012, IEEE Transactions on Information Theory.

[2]  Raymond W. Yeung,et al.  Symmetrical multilevel diversity coding , 1997, IEEE Trans. Inf. Theory.

[3]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[4]  Richard C. Singleton,et al.  Maximum distance q -nary codes , 1964, IEEE Trans. Inf. Theory.

[5]  Chao Tian,et al.  Broadcasting Correlated Vector Gaussians , 2015, IEEE Transactions on Information Theory.

[6]  Thomas M. Cover,et al.  A Proof of the Data Compression Theorem of Slepian and Wolf for Ergodic Sources , 1971 .

[7]  Suhas N. Diggavi,et al.  Approximating the Gaussian Multiple Description Rate Region Under Symmetric Distortion Constraints , 2009, IEEE Transactions on Information Theory.

[8]  Chao Tian,et al.  Multilevel Diversity Coding With Regeneration , 2016, IEEE Trans. Inf. Theory.

[9]  Raymond W. Yeung,et al.  Multilevel diversity coding with distortion , 1995, IEEE Trans. Inf. Theory.

[10]  Toby Berger,et al.  Robust Distributed Source Coding , 2006, IEEE Transactions on Information Theory.

[11]  Suhas N. Diggavi,et al.  Asymmetric Multilevel Diversity Coding and Asymmetric Gaussian Multiple Descriptions , 2010, IEEE Transactions on Information Theory.

[12]  Imre Csiszár.  Linear codes for sources and source networks: Error exponents, universal coding , 1982, IEEE Trans. Inf. Theory.

[13]  James Richard Roche.  Distributed information storage , 1992 .

[14]  Te Sun Han.  Nonnegative Entropy Measures of Multivariate Symmetric Correlations , 1978, Inf. Control..

[15]  Tie Liu,et al.  Symmetrical Multilevel Diversity Coding and Subset Entropy Inequalities , 2014, IEEE Transactions on Information Theory.