6.450 Principles of Digital Communication
MIT, Fall 2009
Monday Dec 14, 2009
Final Exam
You have 180 minutes to complete the quiz.
This is an open-book quiz. You may use your book and six pages of
6.450 Introduction to Digital Communication
MIT, Fall 2002
December 9, 2002
Lecture 24: Coding, IS-95, and CDMA
1
Coding and Decoding
We have spent quite a while discussing modulation and demodulation
6.450 Introduction to Digital Communication
MIT, Fall 2002
November 20, 2002
Lecture 19: The irrelevance theorem and orthogonal signal sets
1
Review
We are looking at channels with real valued wavefor
6.450 Principles of Digital Communications
MIT, Fall 2002
Wednesday, Sept. 4
Handout #3
Lecture 1: Introduction to Digital Communication
1
Introduction and Objectives
The digital communication industr
6.450 Introduction to Digital Communication
MIT, Fall 2002
October 2, 2002
Lecture 8: Analog Sources: waveforms sequences
1
Analog sources
We have now studied coding both for discrete sources and anal
6.450 Principles of Digital Communications
MIT, Fall 2002
September 11
Handout #6
Lecture 3: Coding for Discrete Sources (cont.)
Variable-length source codes were introduced in the previous lecture. T
6.450 Principles of Digital Communications
MIT, Fall 2002
September 9
Handout #5
Lecture 2: Coding for Discrete Sources
Literature: Todays lecture and the three subsequent lectures deal with coding fo
6.450 Introduction to Digital Communication
MIT, Fall 2002
September 18, 2002
Lecture 4: Coding for Sequences of Source Symbols
1
Review
We have been considering a discrete memoryless source model who
6.450 Principles of Digital Communications
MIT, Fall 2002
September 18
Handout #12
Lecture 5: Sources with Memory and the Lempel-Ziv Algorithm
1
Markov Sources
In previous lectures, we developed the b
6.450 Introduction to Digital Communication
MIT, Fall 2002
September 25, 2002
Handout #13
Lecture 6: Quantization
1
Review
In previous lectures, we discussed coding for discrete sources. As described
6.450 Introduction to Digital Communication
MIT, Fall 2002
October 23, 2002
Lecture 13: QAM and Noise
1
Implementation of QAM
Last time we described QAM and the principles of its implementation. The i
6.450 Introduction to Digital Communication
MIT, Fall 2002
September 30, 2002
Lecture 7: High-rate entropy-coded quantization
1
Introduction
We will now take a somewhat deeper look at the quantization
6.450 Introduction to Digital Communication
MIT, Fall 2002
October 20, 2002
Lecture 12: QAM
1
Review
In the previous lecture, we discussed pulse amplitude modulation (PAM) as a very simple
mode of dig
6.450 Introduction to Digital Communication
MIT, Fall 2002
October 30, 2002
Lecture 14: Noise and Gaussian random processes
1
Review
The previous lecture started to introduce channel noise into the pr
6.450 Introduction to Digital Communication
MIT, Fall 2002
November 27, 2002
Lecture 21: Input/output models for wireless
1
Input/Output Models of Wireless Channels
Suppose a transmitting antenna send
6.450 Introduction to Digital Communication
MIT, Fall 2002
December 2, 2002
Lecture 22: Stochastic wireless models
1
Statistical Channel Models
We defined Doppler spread and multipath spread in the pr
6.450 Introduction to Digital Communication
MIT, Fall 2002
December 4, 2002
Lecture 23: Channel measurement and Rake receivers
1
Channel measurement
The lesson learned from binary detection in Rayleig
6.450: Principles of Digital Communication 1
Digital Communication: Enormous and normally
rapidly growing industry, roughly comparable in size
to the computer industry.
Objective: Study those asp ects
DISCRETE MEMORYLESS SOURCE
(DMS) Review
The source output is an unending sequence,
X1, X2, X3, . . . , of random letters, each from
a nite alphabet X .
Each source output X1, X2, . . . is selected
ENTROPY OF X , |X | = M , Pr(X =j ) = pj
H (X ) =
pj log pj = E[ log pX (X )]
j
log pX (X ) is a rv, called the log pmf.
H(X ) 0; Equality if X deterministic.
H(X ) log M ; Equality if X equiprobable
MARKOV CHAINS
A nite state Markov chain is a sequence S0, S1, . . .
of discrete cvs from a nite alphab et S where
q0(s) is a pmf on S0 and for n 1,
Q(s|s ) = Pr(Sn=s|Sn1=s )
= Pr(Sn=s|Sn1=s , Sn2 = sn
The Lemp el-Ziv algorithm matches the longest
string of yet unenco ded symb ols with strings
starting in the window.
Window size w is large p ower of 2, mayb e 217.
log w bits to enco de u, 2 log n +
Measure and complements
We listed the rational numb ers in [T /2, T /2]
as a1, a2, . . .
cfw_
k
ai =
k
([ai, ai]) = 0
i=1
i=1
The complement of k=1 ai is k=1 ai where ai
i
i
is all t [T /2.T /2] exce
Functions not limited in time
We can segment an arbitrary L2 function into
segments of width T . The mth segment is
um(t) = u(t)rect(t/T m). We then have
u(t) = l.i.m.m0
m0
m=m0
um(t)
This works b eca
Fourier
series
f
2ik 2f
W rect
u (f ) = k u k e
2W
f
1 W u(f )e2ik 2W d
u k = 2W W
f
T/F dual
t
uk e2ikt/T rect( T )
k=
1 T /2
uk = T T /2 u(t)e2ikt/T dt
DTFT
u(t) =
Fourier
transform
Sampling
u
6.450 Principles of Digital Communication
MIT, Fall 2009
Due Mon, Sep 21, at beginning of class
Problem Set 1
Problem 1- Problem 2.14 from Gallagers book.
Problem 2- In class, we proved Kraft inequali
6.450 Principles of Digital Communication
MIT, Fall 2009
Wednesday October 21, 2009
Quiz 1
You have 90 minutes to complete the quiz.
This is an open-book quiz. You may use your book and three page
6.450 Introduction to Digital Communication
MIT, Fall 2002
November 6, 2002
Lecture 16: Spectral Density, Orthonormal Expansions
1
Review of linear functionals and filters
Let g 1 , . . . , g j0 be a
6.450 Introduction to Digital Communication
MIT, Fall 2002
November 25, 2002
Lecture 20: Wireless Communication Systems
1
Introduction
During the next three weeks we provide a brief treatment of wirel