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arXiv 1208.4415cs.ITmath.IT
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分布式信道综合

Distributed Channel Synthesis

Paul Cuff

摘要:

两个熟悉的概念的相关性被重新发现的离散无记忆信道,其中随机信道输出的基础上产生的压缩描述的信道输入的分布式合成的极端工作点。Wyner的公共信息是所需的最小描述率。然而,当独立于输入的公共随机性是可用的,必要的描述率减少到香农的互信息。这项工作的特点之间的最佳权衡的数量共同使用的随机性和所需的描述率。我们还包括一些相关的推导,包括有限的本地随机性的影响,保密率的要求,博弈论的应用,和新的见解共同的信息对偶。我们的证明利用了软覆盖引理,在文献中已知的作用,在量化的通道的可分解性。直接证明(可验证性)使用软覆盖在系统的所有部分上构造可行的联合分布,从该软覆盖推断编码器和解码器的行为,而没有明确提及联合典型性或分箱。辅助利益,这项工作也推广和加强这种软覆盖工具。

英文摘要:

Two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel, in which a stochastic channel output is generated based on a compressed description of the channel input. Wyner's common information is the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information. This work characterizes the optimal trade-off between the amount of common randomness used and the required rate of description. We also include a number of related derivations, including the effect of limited local randomness, rate requirements for secrecy, applications to game theory, and new insights into common information duality. Our proof makes use of a soft covering lemma, known in the literature for its role in quantifying the resolvability of a channel. The direct proof (achievability) constructs a feasible joint distribution over all parts of the system using a soft covering, from which the behavior of the encoder and decoder is inferred, with no explicit reference to joint typicality or binning. Of auxiliary interest, this work also generalizes and strengthens this soft covering tool.

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