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 Report | 50% |
| Final Exam | 50% |
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 |
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| 第二週 | 2020/09/26 |
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| 第三週 | 2020/10/03 |
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| 第四週 | 2020/10/10 |
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| 第五週 | 2020/10/17 |
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| 第六週 | 2020/10/24 |
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| 第七週 | 2020/10/31 |
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| 第八週 | 2020/11/07 |
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| 第九週 | 2020/11/14 |
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| 第十週 | 2020/11/21 |
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| 第十一週 | 2020/11/28 |
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| 第十二週 | 2020/12/05 |
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| 第十三週 | 2020/12/12 |
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| 第十四週 | 2020/12/19 |
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| 第十五週 | 2020/12/26 |
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| 第十六週 | 2021/01/02 |
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| 第十七週 | 2021/01/09 |
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課程講義 Course Handout
| 章節 | 下載連結 |
| Syllabus | |
| Section 6 The Law of Large Numbers | |
| Section 9 Large Deviations and The Law of The Iterated Logarithm | |
| Section 20 Random Variables and Distributions | |
| Section 21 Expected Values | |
| Section 22 Sums of Independent Random Variables | |
| Section 25 Convergence of Distributions | |
| Section 26 Characteristic Functions | |
| Section 27 The Central Limit Theorem | |
| Section 28 Infinitely Divisible Distributions | |
| Ninness’s Strong Law of Large Numbers | |
| Section 37 Brownian Motion | |
| Berry-Esseen Theorem | |
| Basic Order Statistics | |
| Basic Theories On Order Statistics | |
| Order Statistics of Cumulative Sums | |
| Induced Order Statistics |