The Hidden Links in Communication Mathematics and Their Applications

Announcements

★★★ 2026/03/20 ★★★ Your Pi Day artwork has been uploaded to this webpage. Please scroll to the bottom of the page to find your creation :)

★★★ 2026/03/10 ★★★ Resources for the first programming assignment has been announced (see eCourse2 for the resources, and the assignment has been told in class); please submit your work before due date and late submission is not allowed! 

★★★ 2026/02/28 ★★★ This course will be delivered as an EMI (English-medium instruction) course, in line with the government’s bilingual education policy. This course is designed to show how linear algebra, differential equations, signals and systems, and probability are used in communication-system design. A solid background in these subjects is essential to keep up. Please do not take this course just for GPA boosting or as a basic review of prerequisites. Since this is the first time I’m offering the course, there will likely be room for improvement. Please leave feedback on eCourse2 as often as you can as it will directly help me refine the course.

Course Information

Instructor: Jian-Jia Weng

Time: Tuesdays and Thursdays, 08:45-10:00

Location: R103, Innovation Building

Office Hour: Upon Request

Teaching Method: Chalkboard Teaching with Video Recording Supplementary

Textbook: No Textbook for this course, but your textbooks on  linear algebra, differential equations, signals and systems, and probability will be helpful!!! 

 Grade Evaluation:  Homeworks (50%) + Final Project (25%) + Notes&In-Class Participation (25%) 

Contact Information

Office: R428, Innovation Building  (please make an appointment before coming)

Campus Internal Phone Number：33528

Email: jjweng AT ccu.edu.tw

If you have any questions regarding the course, you can email me from your school email account with:  

• Subject: [HLCM 2026] Inquiry - Your name and Student ID number (example: [HLCM 2026] Inquiry - 周杰倫 1234567)

• Contents: (1) topics you want to discuss and (2) your preferred time to meet in person (please specify at least 3 time slots)

for a special accommodation. I should reply to your email within 24hours; if not, please send the email again.

Tentative Schedule (To be updated)

• Week 1 (02/24, 02/26): 

  1. Overview of this course

  2. A Block Diagram of Communication Systems with Required Math

  3. Signals and Compression (e.g., Shannon-Niquist Sampling Theorem, review Signals and Systems, A. Oppenheim Sec. 7)

• Week 2 (03/03, 03/05): 

  1. Signal Modeling for Lossy Compression of Sampled Sequence

  2. Auto-Regressive Model with Least Square Optimization

  3. Linear Model with Probabilistic Method

• Week 3 (03/10, 03/12): No classes & Two video recordings have been released on eCourse2

• Week 4 (03/17, 03/19):

  1. Data Representation using Different Bases

  2. Data-Independent Bases (Hadamard, Discrete Sine, and Discrete Cosine Bases)

  3. Data-Dependent Bases (Principal Component Analysis/Karhunen-Loeve Expansion)

• Week 5 (03/24, 03/26):

  1. Lossless and Lossy Data Compression

  2. Huffman Coding

  3. Scalar Quantization

• Week 6 (03/31, 04/02):

  1. Open Loop and Closed Loop Prediction for Correlated Sources

  2. Introduction to Error Correction Codes

• Week 7 (04/07, 04/09):

  1. Maximum-Likelihood Decoding for BSC Channels

  2. Minimum Distance Decoding

  3. Block Codes and Convolution Codes

  4. Linear Block Codes

  5. Standard Array Decoding

• Week 8 (04/14, 04/16): No classes & video recordings have been released on eCourse2

• Week 9 (04/21, 04/23):

  1. Syndrome-based Decoding

  2. Convolutional Codes (from the perspective of Signals and Systems)

• Week 10 (04/28, 04/30)

  1. Feedforward/Feedback Encoders and Termination (Cont'd)

  2. Viterbi Algorithm (a.k.a. Dynamic Programming)

  3. Modulation (PAM/PSK/QAM)

  4. Three Channel Models (AWGN, Block Fading, Multipath Channels)

• Week 11 (05/05, 05/07)

  1. Optimal Data Dection and Channel Estimation

• Week 12 (05/12, 05/14): 

  1. Linear and Circular Convolutions

  2.  Discrete Fourier Transform (DFT)

  3. Zero-Padding OFDM (ZP-OFDM)

  4. Cyclic-Prefix OFDM (CP-OFDM)

  5. CP-OFDM over Multipath Channels

• Week 13 (05/19, 05/21): 

  1. Frame Detection/User Identification

  2. Barker Code

  3. Zadoff-Chu Sequences

  4. Matched Correlator

  5. Delayed Correlation

• Week 14 (05/26, 05/28): 

  1. MIMO transmission: System model

  2. MIMO transmission: ML detection, Zero-Forcing (ZF) detector, and LMMSE estimator

• Week 15 (06/02, 06/04):

  1. MIMO transmission: Capacity analysis via SVD decomposition

  2. MIMO transmission: Successive symbol cancellation decoding

  3. MIMO transmission: Channel estimation

• Week 16: (06/09, 06/11): Final Project Submission due on 6/24!!!

Homework Assignments

Please submit your code (MATLAB/Python/C Language) and discussion report on eCourse2. You’re encouraged to work with classmates, but your report must be written independently. Any copying or plagiarism will be penalized. Discussing and comparing ideas is a good way to learn, use collaboration wisely. 

1. Write a program and investigate AR model for signals from different perspectives as many as you can.

2. Represent the data using deterministic bases such as the Hadamard, discrete sine, and discrete cosine bases. Additionally, explore data-dependent representations, including PCA and the Karhunen–Loève (KL) expansion. For simplicity, assume the data are zero-mean in the latter two cases. Compare your results and draw some conclusions from them.

3. Write a computer program to design optimized scalar quantizers based on the in-class derivations. You may also discuss the compression–distortion trade-off under different source probability distributions. Note that the required quantities can be computed directly when the source distribution is known. They can also be estimated from data samples, and by the law of large numbers, these estimates should converge to their true values.

4. For the three channel models discussed in class, write a program to plot the detection error rate versus the signal-to-noise ratio under perfect channel state information. You may choose the modulation scheme by yourself, and you are encouraged to compare different modulation schemes to observe the trade-off between data rate and error rate. Next, write a program to estimate channel fading or multipath coefficients using the method derived in class. Compare the estimation performance, measured by mean squared error or another suitable metric, as a function of the number of channel outputs. Finally, combine the two programs by detecting data using the estimated channel coefficients. Investigate how channel estimation error affects the accuracy of data detection.

5. Use a CP-OFDM system for this programming task. You can choose the number of subcarriers and the CP length by yourself. Your goal is to use the frame detection method discussed in class to find the starting point of the transmitted signal. Please test your method in two cases: 1. an AWGN channel, 2. a multipath channel with noise. Compare the results and explain how the multipath channel affects frame detection. For the data corresponding to the CP part, you may use random data, Barker code, or Zadoff–Chu sequences. Try different choices and observe how they affect the detection result. Enjoy our last programming task :)

References

1. C. E. Shannon, A Mathematical Theory of Communication, 1948. 

Pi-Day Artwork (Thanks for everyone's participation lol

課程安排、教學建議與修課心得分享

1. 我覺得老師很多地方可以多講一點，不是說自學不好，而是老師選擇跳掉不贅述的地方，往往其實有很大的學問，面對完全不懂的資料，不知道該從哪裡開始學習

2. 老師教書很有熱忱，而且內容很豐富，是我目前排前三覺得有趣的課！但希望能有授課大綱，因為每次上課的內容其實蠻瑣碎的，有時候要上到一個段落才能跟其他內容串聯在一起，如果一開始就有個大綱會比較有方向，但這是我個人的讀書習慣，老師可以參考一下

3. 以前學線性代數時，只有學一些矩陣運算和向量空間，但在這門課中，對於實際層面有更多了解，學習到線性代數是如何應用於通訊系統中。

4. 雖然我是旁聽，沒花額外的時間好好念這科，有許多知識並沒有融會貫通，覺得蠻可惜的，但能在畢業前聽過整個通訊系統，讓我至少知道未來研究通訊系統每個部分在做甚麼，很感謝老師在我大四時開這門課，謝謝老師教導

5. 上完課程能對通訊系統有更完整的理解，作業的實作有助於將所學加以驗證與應用。而且能感受到老師的用心與教學熱忱。

6. 建議老師可以讓同學們分組，然後在每次課堂中間提出一個相關的問題讓小組討論，然後讓同學們分享看法，老師再給一些回饋。雖然老師這學期也曾做過類似的事，但因為沒有特別要求同學參與，因此會主動發表意見的同學仍然較少，若能適度引導大家參與討論，相信能提升課堂互動與學習效果。

7. 在這堂課中老師會整合很多基礎學科的內容(機率、現代、訊號與系統等等)，來說明我們以前學到的東西是如何應用在通訊系統中，所以其實可以在課堂學習的過程中發現到，有某些觀念、知識很重要，但之前沒有懂得部分，都可以在這時候了解到或是在趕快複習這些內容。對於大三生而言，我覺得我接觸到了很多之前沒有學過的通訊系統知識(比如說怎麼將資料壓縮、錯誤更正碼是如何做到錯誤更正等等)，收穫很多！不過在課堂上老師是用黑板上課，並沒有教材，所以會需要很有精神上課，不然之後回去看筆記會忘記在講什麼，會需要花更多時間看懂。

8. 雖然知道老師之前上課就是沒有教材之類的，老師應該也沒間時間做，但有的話應該會蠻棒的，比如程式碼的部分希望能有例子之類的。修課心得的部分，老實講從這門課確實得到了許多我不會去自己了解的知識，而且老師教得蠻多東西在這學期我修的其他客也都有稍微出現，不如說從大一慢慢到大三，有種之前學的東西慢慢地拼湊起來，感覺蠻有趣的，所以我覺得修到老師開的課真的都是獲益良多。

9. 老師上課的內容很豐富，也會跟同學們互動和討論，這堂課讓我了解到，原來先前學過的線性代數和訊號與系統等等科目，其實跟通訊這個領域的連結很深，也從中學到了很多Matlab程式的寫法！

10. 很喜歡老師開的這門課！上課時能感受到老師滿滿的熱忱，老師準備的內容也整理的很好，讓沒概念的人也能快速抓到重點。

11. 雖然有時候會有跟不上的地方，但是我覺得確實了解了這些數學科目到底是怎麼應用以及怎麼串聯在一起的

12. (1)課程安排方面，主要架構是以通訊系統的流程圖為基礎，從資料處理開始分割成多個主題。而每個主題的內容經過老師整理後在課堂上教學，能讓我對於該主題有基礎的了解，且學習新內容的過程是循序漸進的，不會有突然出現卻不知道為什麼會提到的觀念。(2)教學方面可以感受到老師真的很認真，英語詞彙的使用平易近人，幾乎都能聽懂老師表達的意思，唯一比較可惜的是大家都比較不敢提問，都是回去後自己花時間弄懂。(3)當初選這門課程是想對通訊系統這個詞有一個完整的認識，希望自己能在這個詞留下一個屬於自己的見解。修這門課時會有一種純粹的學習的感覺，不是為了準備期中期末考，就只是想弄懂為什麼是這樣，還有了解後「喔~」那一瞬的快樂。在寫程式作業時，會發現當初以為了解了那個主題的內容，結果寫程式實現時發現好像不是這樣欸，又重頭想了一次。當然也學了真的很多新東西，還回去複習了很多以前可能沒搞懂的內容，每個禮拜整理時真的是6個小時起跳。

13. 對我來說，我覺得作業的自由度太高了，雖然說這樣可以讓我們自由探索想討論的問題，但我一開始寫作業的時候一直感到有好像哪裡可以做的更好的部分，而我又沒有能力可以真的提出什麼特別的想法，所以時常宥於無所改進的焦慮感中。

14. 無 我覺得目前剛好

15. 我的朋友說沒有對應的課本看(教材)，這樣在上課不太清楚的細節在課後沒有對應的東西可以看，但他已經交了所以幫他說一下。 我認為這門課把我之前學過的基礎科目、聽過的進階應用，以及特別的技術等都說明過一次；內容清晰易懂，在介紹複雜的東西前都會先講最核心的想法，再說明細節。 如同其他同學所說的，能感受到老師的用心與教學熱忱

16. 課程內容幾乎涵蓋所有實體層通訊的操作，老師很善於重複利用問題與思考的迴圈呈現一個主題。不同於一般教科書的陳述，上過老師的課加強了我自己對不同通訊問題的連結，也看到了線代、機率的實際作用。更重要的是，老師也教會了我們發掘問題、釐清問題的能力，老師僅在課堂中描述出問題與大致概念，試圖讓我們認識到某個主題的樣貌，而課後的筆記整理，讓我們自己發掘不懂的地方並查資料形成自己的理解，我覺得這對我們之後各種領域的學習都會有很大幫助。