论文标题
用编码的侧面信息进行源源编码问题的紧密指数逆向
Tight Exponential Strong Converse for Source Coding Problem with Encoded Side Information
论文作者
论文摘要
考虑了带有编码侧面信息的源编码问题。强大的匡威指数上的下限是由奥奥哈马（Oohama）得出的，但尚未澄清其紧密度。在本文中，我们得出了一个紧密的匡威指数。对于不存在侧信息的特殊情况，我们证明了Wak问题的紧密指数减少到已知的特殊情况下的紧张表达，而Oohama的下限则严格松动。相反的部分是通过明智地使用了量化论点证明的，而该论点是由Gu-effros引入的，并由Tyagi-Watanabe进一步开发。有趣的是，由Oohama作为证明技术引入的软马尔可夫约束自然纳入了指数的表征中。本文的技术创新是认识到软马尔可夫约束是指数的一部分，而不是应消失的罚款。实际上，通过数值实验，我们提供了证据表明软马尔可夫约束严格是正面的。可实现的部分是通过对类型参数的仔细分析得出的。但是，与可实现的速率区域的常规分析不同，我们需要在正确的概率分析中得出软马尔可夫的约束。此外，我们介绍了强大的逆向指数的推导到隐私放大的应用。
The source coding problem with encoded side information is considered. A lower bound on the strong converse exponent has been derived by Oohama, but its tightness has not been clarified. In this paper, we derive a tight strong converse exponent. For the special case such that the side-information does not exists, we demonstrate that our tight exponent of the WAK problem reduces to the known tight expression of that special case while Oohama's lower bound is strictly loose. The converse part is proved by a judicious use of the change-of-measure argument, which was introduced by Gu-Effros and further developed by Tyagi-Watanabe. Interestingly, the soft Markov constraint, which was introduced by Oohama as a proof technique, is naturally incorporated into the characterization of the exponent. A technical innovation of this paper is recognizing that the soft Markov constraint is a part of the exponent, rather than a penalty term that should be vanished. In fact, via numerical experiment, we provide evidence that the soft Markov constraint is strictly positive. The achievability part is derived by a careful analysis of the type argument; however, unlike the conventional analysis for the achievable rate region, we need to derive the soft Markov constraint in the analysis of the correct probability. Furthermore, we present an application of our derivation of strong converse exponent to the privacy amplification.
