A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

Shigeaki Kuzuoka; Shun Watanabe

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arXiv · 1408.5971

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

Shigeaki Kuzuoka·Shun Watanabe

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Abstract

The problem of distributed data compression for function computation is considered, where (i) the function to be computed is not necessarily symbol-wise function and (ii) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbol-wise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszar to sources with memory; our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner. Furthermore, for the full side-information case, the error probability in the moderate deviation regime is also investigated.

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Shigeaki Kuzuoka, Shun Watanabe. 2015-05-09. A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach. https://arxiv.org/abs/1408.5971

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