6.450 Principles of Digital Communication MIT, Fall 2002
Wednesday, Sept. 4, 2002 Handout #4 Due: Wednesday, Sept. 11
Problem Set 1
Problem 1.1 Lecture 1 pointed out that voice waveforms could be converted to binary data by sampling at 8000 times per sec

ENSC 428 Digital Communications Contents
Emphasis on theory, not implementation. If you want to learn how to implement a communication circuits, etc., this is not the course.
1. Introduction and Signal-Space Analysis (2 weeks; Gal_L10, Proakis_7.1-4) o o

6.401/6.450 Introduction to Digital Communication
MIT, Fall 2001
September 12, 2001
Handout #7
Solutions to problem set #1
Problem 1.1
What follows is one way of thinking about the problem. It is deﬁnitely not the only way –
the important point in this qu

SCHOOL OF ENGINEERING SCIENCE SIMON FRASER UNIVERSITY
ENSC 428 Digital Communications Spring 2008 Homework #3 due Feb. 1, 2008 Friday
1. A vector space V over a given field F is a set of elements (called vectors) closed under and operation + called vector

SCHOOL OF ENGINEERING SCIENCE
SIMON FRASER UNIVERSITY
ENSC 428 – Digital Communications Spring 2008
Homework #4 due Feb. 15, 2008 Friday
Dear class,
Apparently, many of you need to brush up on your knowledge of Fourier series and
Fourier transforms. The p

6.401/6.450 Introduction to Digital Communication
MIT, Fall 2001
September 12, 2001
Handout #7
Solutions to problem set #1
Problem 1.1
What follows is one way of thinking about the problem. It is deﬁnitely not the only way –
the important point in this qu

6.450 Principles of Digital Communication MIT, Fall 2001
Wednesday, December 4, 2000 Handout #35 Due: Not to be passed in
Problem Set 12 Problem 12.1 (Orthogonal signal sets, continued) Consider the set of m orthogonal signals from problem set 10.5. Each

6.450 Principles of Digital Communication MIT, Fall 2002
Monday, November 25, 2002 Handout #35 Due: Wednesday, December 4, 2002
Problem Set 11
Problem 11.1 The following problem relates to a digital modulation scheme often referred to as minimum shift ke

6.450 Principles of Digital Communication MIT, Fall 2002
Wednesday, November 7, 2002 Handout #35 Due: Wednesday, November 14, 2001
Problem Set 10 Problem 10.1 The purpose of this problem is to show that if cfw_Nj ; j Z is a sequence of Gaussian rvs N (0,

6.450 Principles of Digital Communication MIT, Fall 2002
Wednesday, November 6, 2002 Handout #32 Due: Wednesday, November 13, 2001
Problem Set 9
Problem 9.1 (Carrierless modulation) In Lecture 13, we saw how to modulate a baseband QAM waveform to passban

6.450 Principles of Digital Communication MIT, Fall 2002 Problem Set 8
Wednesday, October 30, 2002 Handout #29 Due: Wednesday, November 6, 2002
Problem 8.1 Given two waveforms u1 , u2 L2 let V be the set of all waveforms v that are equi-distant from u1 an

6.450 Principles of Digital Communication MIT, Fall 2002
Wednesday, October 17, 2002 Handout #24 Due: Wednesday, October 24, 2001
Problem Set 7
Problem 7.1 Prove the following statement using the theorems about linear vector spaces in lecture 10: Every s

6.450 Introduction to Digital Communication MIT, Fall 2002 Lecture 17-18: Detection
November 13, 2002
1
Introduction
We have studied modulation and demodulation, and studied how noise processes can corrupt the received waveform, and thus corrupt the demod

6.450 Introduction to Digital Communication MIT, Fall 2002
October 16, 2002
Lecture 11: Introduction to Channels and PAM
1
Introduction
In the first lecture, we discussed the general block diagram of a communication system which is repeated below. We disc

6.450 Introduction to Digital Communication MIT, Fall 2002 Lecture 10: Waveforms as vectors in signal-space
October 9, 2002
The set of L2 functions, viewed as a vector space, is usually called signal-space. The signal-space viewpoint is one of the foundat

ENSC 428 Digital Communications Semester 2008-1 Project Outlines as of Jan. 7, 2008 1. Purpose To train students to simulate communication systems and to gain intuition about the systems. To learn to use MATLAB and Simulink.
2. Objectives The goal of this

Signal-Space Analysis
ENSC 428 Spring 2008 Reference: Lecture 10 of Gallager
Digital Communication System
Representation of Bandpass Signal
x ( t ) = s ( t ) cos ( 2 f c t )
Bandpass real signal x(t) can be written as:
x ( t ) = 2 Re x ( t ) e j 2 fct whe

Digital Communication System
Source coding
Represent signals into digital data (e.g. bits)
E.g. video, audio
How to use as little amount of digital data as possible without losing any information How to use as little amount of digital data as possible

Channel Coding
ENSC 428 Spring 2007
Digital Communication System
Decoding of Convolutional Codes
ML Decoding Rule
The Viterbi Algorithm
Basic Idea
Algorithm (hard decision)
cont
cont
Example : Decoding
cont
Viterbi Decoder
Other Applications
Summary

Channel Coding
ENSC 428 Spring 2007
Digital Communication System
Interleaving
Example
Block v.s Convolutional Codes
Convolutional Code Examples (1)
y ( ) [ n ] = x[n 2]
1
x[n]
y
( 2)
[ n] = x[n 2] x[n 1] x[n]
Convolutional Codes
At each stage, k bits are

Channel Coding
ENSC 428 Spring 2007
Digital Communication System
Channel Capacity
cont .
cont .
cont .
Channel Coding
Types of Channel Coding
Classes of Block Codes
Block Codes
cont .
Example : (7,4) Hamming Code
Properties of Block Codes
cont .
cont .
Ha

Digital Transmission through bandlimited AWGN channels
ENSC 428 Spring 2008 Reference: Lecture 11 of Gallager Chapter 8 of Proakis & Salehi
Digital Communication System
Review of AWGN channels
Use of complete orthonormal set of L2.
Projection, correlation

Performance of Coherent M-ary Signaling
ENSC 428 Spring 2007
Digital Communication System
1. M-ary PSK
T
sin
cont
cont
Integration over IQ plane
cont
2 Es 2 Eb log 2 M Ps ( e ) 2Q sin N sin M = 2Q N0 M 0
cont
2. M-ary Orthogonal Signaling
cont
3-ar

Performance of Coherent M-ary Signaling
ENSC 428 Spring 2007
Digital Communication System
1. M-ary PSK
T
sin
cont
cont
Integration over IQ plane
cont
2 Es 2 Eb log 2 M Ps ( e ) 2Q sin N sin M = 2Q N0 M 0
cont
2. M-ary Orthogonal Signaling
cont
3-ar

Performance Analysis of Optimum Receiver
ENSC 428 Spring 2007
Digital Communication System
Union Bound
cont
cont
Illustrating the Union Bound
Pairwise Error Probability
cont
cont
Union Bound
Example : QPSK
cont

Performance Analysis of Optimum Receiver
ENSC 428 Spring 2007
Digital Communication System
Average Probability of Error
Case I (BPSK)
cont
cont
cont
cont
cont
Case II (Binary Coherent FSK)
cont
cont
cont
FSK is approximately 3dB worse than BPSK
Ca

Optimum Receiver Design
ENSC 428 Spring 2007
Digital Communication System
What is a Design Problem ?
Noise Model
Equivalent Vector Channel Model
cont
Theorem of Irrelevance:
cfw_rk |1 k K
form sufficient statistics!
cont
MAP Optimum Decision Rule
M

SCHOOL OF ENGINEERING SCIENCE SIMON FRASER UNIVERSITY
ENSC 428 Digital Communications Spring 2008 Homework #6 due March. 26, 2008 Wednesday -Daniel Lee Assume that all random processes discussed in this homework is wide-sense stationary and zeromean. The

6.450 Principles of Digital Communication MIT, Fall 2002
Wednesday, October 9, 2002 Handout #23 Due: Wednesday, October 16, 2002
Problem Set 6 Problem 6.1 (a) Show that for any T > 0 the set of functions cfw_m,k (t) = e2imt/T sinc( tkT ) is an T orthogona