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The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.

Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Over 30 hours of lectures

24 lectures

Assignments and exams with solutions.

Reference Texts

The class notes cover all the material in the course, but the following references can provide enrichment and additional examples.


Robert Gray Gallager (born May 29, 1931) is an American electrical engineer known for his work on information theory and communications networks. He was elected an IEEE Fellow in 1968, a member of the National Academy of Engineering (NAE) in 1979, a member of the National Academy of Sciences (NAS) in 1992, a Fellow of the American Academy of Arts and Sciences (AAAS) in 1999. He received the Claude E. Shannon Award from the IEEE Information Theory Society in 1983. He also received the IEEE Medal of Honor in 1990 "For fundamental contributions to communications coding techniques", the Marconi Prize in 2003, and a Dijkstra Prize in 2004, among other honors. For most of his career he was a professor of electrical engineering and computer science at the Massachusetts Institute of Technology.


Lizhong Zheng received the B.S and M.S. degrees, in 1994 and 1997 respectively, from the Department of Electronic Engineering, Tsinghua University, China, , and the Ph.D. degree, in 2002, from the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley. Since 2002, he has been working in the Department of Electrical Engineering and Computer Sciences, where he is currently an associate professor. His research interests include information theory, wireless communications and wireless networks. He received Eli Jury award from UC Berkeley in 2002, IEEE Information Theory Society Paper Award in 2003, and NSF CAREER award in 2004, and the AFOSR Young Investigator Award in 2007. He is currently an associate editor of IEEE transactions on Information Theory.


Creative Commons License
Principles of Digital Communications I by Prof. Lizhong Zheng and Prof. Robert Gallager is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Course content

  • Lecture 1: Introduction

  • Lecture 2: Discrete Source Encoding

  • Lecture 3: Memory-less Sources

  • Lecture 4: Entropy and Asymptotic Equipartition Property

  • Lecture 5: Markov Sources

  • Lecture 6: Quantization

  • Lecture 7: High Rate Quantizers and Waveform Encoding

  • Lecture 8: Measure

  • Lecture 9: Discrete-Time Fourier Transforms

  • Lecture 10: Degrees of Freedom

  • Lecture 11: Signal Space

  • Lecture 12: Nyquist Theory

  • Lecture 13: Random Processes

  • Lecture 14: Jointly Gaussian Random Vectors

  • Lecture 15: Linear Functionals

  • Lecture 16: Review; Introduction to Detection

  • Lecture 17: Detection for Random Vectors and Processes

  • Lecture 18: Theory of Irrelevance

  • Lecture 19: Baseband Detection

  • Lecture 20: Introduction of Wireless Communication

  • Lecture 21: Doppler Spread

  • Lecture 22: Discrete-Time Baseband Models for Wireless Channels

  • Lecture 23: Detection for Flat Rayleigh Fading and Incoherent Channels

  • Lecture 24: Case Study on Code Division Multiple Access

  • Lecture Notes

  • Assignments

  • Exams

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