学术报告
系列讲座Shannon’s theorems: the strength of a simple idea-Alain CHENCINER 教授 （巴黎七大，巴黎天文台）
题目：Shannon’s theorems: the strength of a simple idea
报告人：Alain CHENCINER 教授 （巴黎七大，巴黎天文台）
Abstract
A corrupted word (or sentence), is correctly recognized as long as it differs less from the original word (or sentence) than from any other word (or sentence). Combined to the law of large numbers and its fundamental corollary, the Asymptotic Equipartition Property, this simple looking statement is at the root of the discovery by Claude Shannon of the limit H < C imposed to any coding which allows a reliable transmission of information through a noisy channel, a limit which is almost achieved today by the turbocodes. In the course, after recalling the basic notions of probabilities, the entropy H of a source, and the capacity C of a channel will be defined, and Shannon’s theorem will be proved in the simple case of Bernoulli sources. In the last part of the course, the more realistic setting of Markov sources and ergodic sources will be introduced and this will be the occasion to give a short introduction to Ergodic Theory through a proof of Birkhoff’s ergodic theorem, which is a very strong version of the Law of Large Numbers.
时间：
9月14日（星期三）上午10:00-12:00，北一区202
9月21日（星期三）上午10:00-12:00， 北一区202
9月23日（星期五）上午 9:00-11:00，北一区316
9月26日 （星期一）下午1:30-3:30， 北一区708
9月30日（星期五）上午 9:00-11:00，北一区316
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