Advanced Probability for Communications - 109 Academic Year

通訊高等機率 - 109學年度

本課程是由 國立陽明交通大學電機工程學系 提供。

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  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.

 

課程用書:

Lecture notes

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授課教師 電機工程學系 陳伯寧老師
課程學分 3學分
授課年度 109學年度
授課對象 碩士班
預備知識 機率
課程提供 課程影音   課程綱要   課程行事曆   課程講義 

週次課程內容課程影音課程下載
Lec01 The Law of Large Numbers線上觀看MP4下載
Lec02 Large Deviations and The Law of The Iterated Logarithm線上觀看MP4下載
Lec03 Large Deviations and The Law of The Iterated Logarithm線上觀看MP4下載
Lec04 Random Variables and Distributions線上觀看MP4下載
Lec05 Random Variables and Distributions線上觀看MP4下載
Lec06 Random Variables and Distributions, Expected Values線上觀看MP4下載
Lec07 Sums of Independent Random Variables, Convergence of Distributions線上觀看MP4下載
Lec08 Convergence of Distributions, Characteristic Functions線上觀看MP4下載
Lec09 Characteristic Functions線上觀看MP4下載
Lec10 Characteristic Functions, The Central Limit Theorem線上觀看MP4下載
Lec11 The Central Limit Theorem, Infinitely Divisible Distributions線上觀看MP4下載
Lec12 Infinitely Divisible Distributions, Ninness’s Strong Law of Large Numbers, Brownian Motion, Berry-Esseen Theorem線上觀看MP4下載
Lec13 Berry-Esseen Theorem, Basic Order Statistics, Basic Theories On Order Statistics線上觀看MP4下載
Lec14 Basic Theories On Order Statistics, Order Statistics of Cumulative Sums, Induced Order Statistics線上觀看MP4下載

課程目標

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 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.

 

課程章節

單元主題 內容綱要
單元一Law of large numbers (including the strong law, and the weak law), Borel-Cantelli lemmas
單元二Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem
單元三 Random variables, convergence in probabilities.
單元四Characterization of relation between expectation values and
(1) limits,
(2) distributions,
(3) moments.
Several inequalities regarding expectation values will also be covered.
單元五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.
單元六 Weak convergence in distributions.
單元七Characteristic functions inversion, uniqueness theorem, the continuity theorem.
單元八The central limit theorem, Lindeberg and Lyapounov theorems.
單元九Infinitely divisible distributions.
單元十 Brownian Motion.
單元十一Derivation of error probability for Differential BPSK
單元十二Berry-Esseen Theorem
單元十三Ordered statistics

 

課程書目

Lecture notes

 

評分標準

項目百分比
Study Report50%
Final Exam50%

本課程行事曆提供課程進度與考試資訊參考。

學期週次
上課日期
參考課程進度

第一週

2020/09/19
  • Law of large numbers (including the strong law, and the weak law), Borel-Cantelli lemmas
第二週2020/09/26
  • Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem
第三週2020/10/03
  • Large deviations, the law of the iterated logarithm, moment generating functions versus large deviations, Chernoff's theorem 
第四週2020/10/10
  • Holiday
第五週2020/10/17
  • Random variables, convergence in probabilities.
第六週2020/10/24
  • Characterization of relation between expectation values and (1) limits, (2) distributions, (3) moments. Several inequalities regarding expectation values will also be covered.
第七週2020/10/31
  • 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.
第八週2020/11/07
  • Weak convergence in distributions.
第九週2020/11/14
  • Characteristic functions inversion, uniqueness theorem, the continuity theorem.
第十週2020/11/21
  • The central limit theorem, Lindeberg and Lyapounov theorems.
第十一週2020/11/28
  • The central limit theorem, Lindeberg and Lyapounov theorems.
第十二週2020/12/05
  • Infinitely divisible distributions.
第十三週2020/12/12
  • Brownian Motion.
第十四週2020/12/19
  • Derivation of error probability for Differential BPSK
第十五週2020/12/26
  • Berry-Esseen Theorem
第十六週2021/01/02
  • Ordered statistics
第十七週2021/01/09
  • Ordered statistics

課程講義 Course Handout

章節 下載連結
SyllabusPDF
Section 6 The Law of Large NumbersPDF
Section 9 Large Deviations and The Law of The Iterated LogarithmPDF
Section 20 Random Variables and DistributionsPDF
Section 21 Expected ValuesPDF
Section 22 Sums of Independent Random VariablesPDF
Section 25 Convergence of DistributionsPDF
Section 26 Characteristic FunctionsPDF
Section 27 The Central Limit TheoremPDF
Section 28 Infinitely Divisible DistributionsPDF
Ninness’s Strong Law of Large NumbersPDF
Section 37 Brownian MotionPDF
Berry-Esseen TheoremPDF
Basic Order StatisticsPDF
Basic Theories On Order StatisticsPDF
Order Statistics of Cumulative SumsPDF
Induced Order StatisticsPDF