Symmetrical Multilevel Diversity Coding with an All-Access Encoder

Details Symmetrical Multilevel Diversity Coding with an All-Access Encoder Symmetrical Multilevel Diversity Coding with an All-Access Encoder

2011-11-02

arxiv.org/abs/1111.0689v2

Computer Science

Information Theory

In the previous draft, it was shown that superposition coding is optimal in terms of achieving all possible tradeoffs between

Scientific paper

Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem introduced by Roche (1992) and Yeung (1995). In this setting, a simple separate coding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate (Roche, Yeung, and Hau, 1997) and the entire admissible rate region (Yeung and Zhang, 1999) of the problem. The proofs utilized carefully constructed induction arguments, for which the classical subset entropy inequality of Han played a key role. This paper considers a generalization of SMDC for which, in addition to the randomly accessible encoders, there is also an all-access encoder. It is shown that superposition coding remains optimal in terms of achieving the entire admissible rate region of the problem. Key to our proof is to identify the supporting hyperplanes that define the boundary of the admissible rate region and then builds on the result of Yeung and Zhang on a generalization of Han's subset inequality. As a special case, the $(R_0,R_s)$ admissible rate region, which captures all possible tradeoffs between the encoding rate $R_0$ of the all-access encoder and the sum encoding rate $R_s$ of the randomly accessible encoders, is explicitly characterized. To provide an explicit proof of the optimality of superposition coding, a new sliding-window subset entropy inequality is introduced and is shown to directly imply the classical subset entropy inequality of Han.

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