Principles Of Digital Communications I

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.

Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Description

This course is a graduate level introduction to the basic principles of digital communication systems. A digital communication system is one that transmits a source (voice, video, data, etc.) from one point to another, by first converting it into a stream of bits, and then into symbols that can be transmitted over channels (cable, wireless, storage, etc.). The use of the digital bit-stream as the interface between the source and the channel is universal regardless of what kind of source and channel are involved. Digital communication principle, with “bit” as the most important concept of the information age, and applications in computer science, Internet, wireless, etc., is one of the most successful stories of applying mathematics in engineering designs.

The course gives an overview of the designs of digital communication systems. We explain the mathematical foundation of decomposing the systems into separately designed source codes and channel codes. We introduce the principles and some commonly used algorithms in each component, to convert continuous time waveforms into bits, and vice versa. We give a comprehensive introduction to the basics of information theory, a rather thorough treatment of Fourier transforms and the sampling theorem, and an overview of the use of vector spaces in signal processing.

The course would be beneficial particularly to students who are interested in doing research in fields related to communications, networks, and signal processing. The general principle and philosophy of the engineering designs discussed in this course are inspiring to all engineering majors. As a Technical Qualifying Exam (TQE) course, we also try to offer some rigorous mathematical training. The materials of this course are the baselines of further studies in 6.451 (digital communications II), 6.452 (wireless communications), and 6.441 (information theory).

Lecture 1: Introduction

Topics covered: Introduction: A layered view of digital communication

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 2: Discrete Source Encoding

Topics covered: Discrete source encoding

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 3: Memory-less Sources

Topics covered: Memory-less sources, prefix free codes, and entropy

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 4: Entropy and Asymptotic Equipartition Property

Topics covered: Entropy and asymptotic equipartition property

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 5: Markov Sources

Topics covered: Markov sources and Lempel-Ziv universal codes

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 6: Quantization

Topics covered: Quantization

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 7: High Rate Quantizers and Waveform Encoding

Topics covered: High rate quantizers and waveform encoding

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 8: Measure

Topics covered: Measure, fourier series, and fourier transforms

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 9: Discrete-Time Fourier Transforms

Topics covered: Discrete-time fourier transforms and sampling theorem

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 10: Degrees of Freedom

Topics covered: Degrees of freedom, orthonormal expansions, and aliasing

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 11: Signal Space

Topics covered: Signal space, projection theorem, and modulation

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 12: Nyquist Theory

Lecture 13: Random Processes

Topics covered: Random processes

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 14: Jointly Gaussian Random Vectors

Topics covered: Jointly Gaussian random vectors and processes and white Gaussian noise (WGN)

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 15: Linear Functionals

Topics covered: Linear functionals and filtering of random processes

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 16: Review; Introduction to Detection

Topics covered: Review; introduction to detection

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 17: Detection for Random Vectors and Processes

Topics covered: Detection for random vectors and processes

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 18: Theory of Irrelevance

Topics covered: Theorem of irrelevance, M-ary detection, and coding

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 19: Baseband Detection

Topics covered: Baseband detection and complex Gaussian processes

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 20: Introduction of Wireless Communication

Topics covered: Introduction of wireless communication

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 21: Doppler Spread

Topics covered: Doppler spread, time spread, coherence time, and coherence frequency

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 22: Discrete-Time Baseband Models for Wireless Channels

Lecture 23: Detection for Flat Rayleigh Fading and Incoherent Channels

Topics covered: Detection for flat rayleigh fading and incoherent channels, and rake receivers

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng

Lecture 24: Case Study on Code Division Multiple Access

Topics covered: Case study — code division multiple access (CDMA)

Instructors: Prof. Robert Gallager, Prof. Lizhong Zheng