!Wenjun Hu

EENG 444 / ENAS 944 Digital Communication Systems

!

Introduction

Communication Systems• What’s the first thing that comes to your mind?

Communication Systems• What’s the first thing that comes to your mind?

All figures from the Internet

The (Old) Telephone Network

Figure from http://arstechnica.com/features/2005/05/voip/

POTS: Plain old Telephone Service PSTN: Public Switched Telephone Network

Telephone Networks Nowadays

Figure from http://arstechnica.com/features/2005/05/voip/

POTS: Plain old Telephone Service PSTN: Public Switched Telephone Network

Analog TV

Digital TV

(and its adoption)

A few more examples

Wireless communication

A few more examples

Spot the differences!

Quantization, image compression/resampling

A few more examples

Modulation, error correction

A few more examples

Chu et al, Halftone QR Codes, ACM SIGGRAPH ASIA 2013

Detection, coding, and decoding

A few more examples

Sampling

Anatomy of Digital Communication Systems

Basic system

Basic system (abstractions)

Source encoder

Channel encoder

Source decoder

Channel decoder

Source Destination

Binary interface Binary interface

Channel

Basic system (abstractions)

Source encoder

“Channel” encoder

Source decoder

“Channel” decoder

Source Destination

Network - logical “Channel”

Fundamental ideas• All sources representable by binary sequences

• Steps of communication flow • Source output -> binary sequence • The binary sequence -> a form suitable for transmission

over particular physical media

• Digital sequence as interface between source and channel • Digital: finite, ~ binary

Why digital?• Why CDs, not tapes?

• Why digital TV? Why voice over IP?

Why digital?• Digital hardware has become cheap, reliable, and

miniaturized

• Standardized binary interfaces simplify understanding and implementation

• Source-channel separation theorem • Information can be transmitted over a binary interface, if it

can be transmitted at all • Corner stone of information theory

Interfaces and layering

Input n Output nChannel

Input 1

Input 2

Input 3 Output 3

Output 2

Output 1

Encapsulation

“Peering relation”

Communication sources• Discrete symbols

• E.g., letters from the English alphabet

• Analog waveforms • E.g., Videos, images, voice signals

Communication channels• The physical communication media + related

modules like amplifiers and antennas • Outside the control of the source encoder

• Often unreliable due to various distortions • Noise, interference, etc.

Main topics

Source coding• Discrete source coding

• Just represent each symbol with a binary digit sequence • How long should the sequence be?

• Analog source coding • Discretize - Sample (fast enough) and quantize • Then follow discrete source coding

Channel coding• Encoding: Mapping binary sequences to

waveforms • The elementary waveform • Using amplitude, phase; absolute value vs differentials; …

• Decoding: Find the most likely binary sequence • Received signal is noisy, always somewhat different from

the transmitted signal

Error correction• Simple modulation/demodulation techniques incur

errors • Add error correction to simple modulator (in what order?) • Can achieve arbitrarily low error rate within channel

capacity

• Many well-known error correction codes

Digital interfaces• Complicating factors

• Unmatched rates between source and channel • Think video streaming

• Errors: source (de)coding is usually lossless, channel (de)coding isn’t

• From links to the network • Network protocols

A few recurring themes• Information theory

• Stochastic processes • Probabilistic descriptions of inputs and outputs

• Sampling theory

• Detection, estimation, …

Related courses (F’15)• EENG 442 / AMTH 342 / ENAS 902 Linear Systems

• This course

• EENG 450 Applied Digital Signal Processing

• EENG 452 / ENAS 952 Internet Engineering

Related courses (S’16)• EENG 451 / ENAS 951 Wireless Communications

• EENG 454 / AMTH 364 / ENAS 954 / STAT 364 / STAT 664 Information Theory

• ENAS 496 / ENAS 502 Probability & Stochastic Processes

• ENAS 963 Network Algorithms and Stochastic Optimization

• CPSC 433 / CPSC 533 Computer Networks

Some related courses• Not offered this year

• ENAS 964 Communication Networks

• CPSC 434 / CPSC 534 Mobile Computing and Wireless Networking

This course• Overview of digital communication systems

• A major branch of EE and related disciplines • Focuses on signal representation • Introduction to specialized topics

• E.g., wireless digital communication, sampling theory

• Useful concepts and tools beyond communication • E.g., entropy in the context of security, data privacy

Administrative Details

Personnel• Instructor: Wenjun Hu

• wenjun.hu@yale.edu, Room 325 @ 17HLH • Office hours: 4-6pm Mondays (tentative), or by

appointment • In general, feel free to stop by my office or email any

questions or suggestions

Goals of this course• Understand the principles of digital communication

• Learn the basic concepts and mathematical tools • Concepts as abstractions to reason about systems • Helps you understand the fundamental limitations

• Apply the understanding to system building

Resources• Textbook (on theoretical background)

• Gallager. Principles of Digital Communication

• Resources online • Course material will be posted on the course web site • See also material from MIT OpenCourseWare based on the

same course

• This is the “standard” version…

Three levels of understanding• Non-EE students

• Know the basic concepts (qualitatively) • Maybe build systems

• EE majors • Learn the analytical foundations (quantitatively)

• EE PhD students (the “standard” version) • Understand why everything works • Use the mathematical tools

What do you need to do• Tell me your background and interest

• Help me determine what level suits you • The actual course material will adapt to your level and

interest

• Your workload • 4-5 problem sets, the last one a pseudo final • Intro projects, mostly fixed • Design project, flexible

Grading• Approximate breakdown

• Problem sets 40%, projects 45% • Oral review 10%, classroom participation 5% • Please ask questions!!

• Subject to adjustment after I learn your background

• What you learn is more important than the grades!!

Tentative schedule• Overview and introduction in the first three weeks,

detailed exploration afterwards • Helps you decide whether to take the course • Start planning projects

• Homework starts after shopping period

• Detailed preliminary schedule linked from course site

Warning• It will be more mathematical in future lectures

• I.e., you’ll see formulae!

Any Questions?