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Common Randomness, Efficiency, and Actions

Lei Zhao

出版	Stanford University, 2011
ISBN	STANFORD:bn436fy2758
URL	http://books.google.com.hk/books?id=GJldO8o7QA8C&hl=&source=gbs_api
EBook	SAMPLE

註釋

The source coding theorem and channel coding theorem, first established by Shannon in 1948, are the two pillars of information theory. The insight obtained from Shannon's work greatly changed the way modern communication systems were thought and built. As the original ideas of Shannon were absorbed by researchers, the mathematical tools in information theory were put to great use in statistics, portfolio theory, complexity theory, and probability theory. In this work, we explore the area of common randomness generation, where remote nodes use nature's correlated random resource and communication to generate a random variable in common. In particular, we investigate the initial efficiency of common randomness generation as the communication rate goes down to zero, and the saturation efficiency as the communication exhausts nature's randomness. We also consider the setting where some of the nodes can generate action sequences to influence part of nature's randomness. At last, we consider actions in the framework of source coding. The tools from channel coding and distributed source coding are combined to establish the fundamental limit of compression with actions.