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

The problem of distributed data compression for function computation is considered, where: 1) the function to be computed is not necessarily symbolwise function and 2) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a suffici...

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Vydáno v:IEEE transactions on information theory Ročník 61; číslo 9; s. 5028 - 5041
Hlavní autoři: Kuzuoka, Shigeaki, Watanabe, Shun
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.09.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Coding theory
Computer memory
Cryptography
Data compression
Decoding
Distributed computing
Encoding
Error probability
information-spectrum method
Probability
Random variables
Regions
Slepian-Wolf coding
Distributed computing
information-spectrum method
Slepian-Wolf coding
ISSN:0018-9448, 1557-9654
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Shrnutí:The problem of distributed data compression for function computation is considered, where: 1) the function to be computed is not necessarily symbolwise function and 2) 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 symbolwise 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 Csiszár 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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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2015.2458871