We analyse the common information problem for the generalised Gray-Wyner problem. We aim to explore the problem and solution in relation to the non-orthogonality among the source decoders' components. We consider a simple networked control system consisting of 2 groups of users: (i) one sender or Observer named Alice; and (ii) a group of multiple receivers or Controllers, named Bobs. In order to tackle the possible risk arisen from the common information among Bobs, Alice provides a redundancy creating some virtual messages which are in the null of each specific Bob, but not for others. The aforementioned possible risk is inevitable since, non-impossibly speaking, some/all of them may instantaneously act as potential Eavesdropper(s) with the abuse of the aforementioned common information. This novel discipline, which has not been investigated yet to the best of our knowledge, is theoretically interpreted from a mirror-game-theoretical point-of-view. Novel mathematical problems are derived specifically including some proofs for the information-theoretic relaxations and non-stationarity as well as the existence of the Nash equiblirium. Finally speaking, simulations approve our scheme.
翻译:我们分析通用的格雷-怀伊纳问题的共同信息问题。 我们的目标是探讨与源解码器部件之间非垂直性有关的问题和解决办法。 我们考虑一个简单的网络化控制系统,由两组用户组成:(一) 一个发件人或观察员名为爱丽丝;(二) 一个由多个接收人或主计长组成的小组,名为鲍勃斯。为了解决鲍伯之间共同信息可能产生的风险,爱丽丝提供了冗余,产生了一些虚拟信息,这些信息存在于每个特定鲍勃的空格中,而不是对其他人。上述可能的风险是不可避免的,因为,不可避免地说,其中一些/所有这些风险都可能瞬间成为潜在的Eavesdroper,并滥用上述共同信息。这个尚未调查过的新的学科,从理论上从我们所知的最佳角度加以解释。 最新数学问题特别包括信息-理论的放松和不静止性的一些证据,以及我们纳什基贝里欧的模拟方案。最后,我们说,“纳什基贝里姆”的模拟方案。