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This course intends to provide students with the necessary background on advanced probability theories for communications. It is our hope that students, after taking this course, are capable of self-reading {\em theoretical} papers in communications. Enhancing students' capability for theoretical research is another objective of this course. Accordingly, not only proofs for theories will be introduced in detail, but also their implications in communications will be stated in lectures. Students who take this course are recommended to have certain knowledge on fundamental probabilistic theories.

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The slides can be downloaded from http://shannon.cm.nctu.edu.tw/probability.htm

The final grade of the course will be contributed 50% from the final exam and 50% from a study report. The final exam will cover all materials delivered in this course. The study report is due one week after the final exam. A late submission will be deducted 50% from its final grade. In the study report, students may try to apply what they have learned from this course to a self-created or application-oriented problem. As an example, a partial solution with some conjectures on the unsolved part of the self-created problem will make a fine report.It can also be a summary with novel personal extension about a theoretical paper that you are interested in, and that is relevant to what we have lectured. A copy of the studied paper shall be attached when submitting the report. Since it is an advanced course for which the objective is mainly to provide you with the necessary background on probabilities for communications and also to enhance your capability in theoretical research, your attendance in each lecture is essential. I will constantly name the students in the enrolled list to assure your attendance in the course. Students who fail to show up over three times will flunk the course.

• Law of large numbers (including the strong law, and the weak law), Borel-Cantelli lemmas
• Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem
• Random variables, convergence in probabilities.
• Characterization of relation between expectation values and (1) limits, (2) distributions, (3) moments. Several inequalities regarding expectation values will also be covered.
• Sums of independent random variables, and their relation with the strong/weak law and moment generating functions. Komogrov's zero-one law and maximal inequality will also be covered.
• Weak convergence in distributions.
• Characteristic functions inversion, uniqueness theorem, the continuity theorem.
• The central limit theorem, Lindeberg and Lyapounov theorems.
• Infinitely divisible distributions.
• Brownian Motion.
• Derivation of error probability for Differential BPSK
• Berry-Esseen Theorem
• Ordered statistics

Lecture notes

地點

Office

時間

By request

聯絡方式

Phone or email