A dichotomy of functions in distributed coding: An information spectral approach
A dichotomy of functions in distributed coding: An information spectral approach
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分布式编码中函数的二分法：信息谱方法
DOI：
10.1109/tit.2015.2458871
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Shigeaki Kuzuoka and Shun Watanabe
中科院分区：
文献类型：
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作者：
Shigeaki Kuzuoka and Shun Watanabe
考虑了函数计算的分布式数据压缩问题，其中：1）被计算的函数不一定是符号函数; 2）信源具有记忆性，不一定是平稳的或遍历的。我们引入了光滑源类，并给出了函数的一个充分条件，使得计算的可达速率区域与Slepian-Wolf区域重合（即，用于再现整个源的速率区域）。对于符号函数，给出了重合的充分必要条件。我们的结果为充分的边信息的情况下是一个推广的结果Ahlswede和Csiszár的来源与记忆;我们的二分法定理是不同的韩和小林的二分法定理，它揭示了记忆的效果在分布函数计算。所有的结果，不仅给出了固定长度的编码，但也为可变长度的编码在一个统一的方式。此外，对于完全边信息的情况，还研究了中等偏差区域的错误概率。
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.