Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
T wodimensional Random Vectors
Joint Cumulative Distribution Function
Definitions:
Y
FX ,Y ( x, y ) P X x and Y y
Properties:
X
1) FX ,Y (, ) 1
2) FX ,Y ( , y ) FX ,Y ( x, ) 0
3) FX ,Y ( a, y ) lim FX ,Y ( x, y )
x a
4) P x1 X x2 , Y y FX ,Y ( x2 , y )
Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
Functions of Two Random Variables
MAXIMUM
Define W max X , Y
Then FW ( w) P W w P X w and Y w FX ,Y ( w, w)
When X and Y are independent, FW ( w) FX ( w) FY ( w) .
In this case, we have fW ( w) f X ( w) FY ( w) fY ( w) FX ( w)
W=X
W=Y
1
MINIMUM
Define W
Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
Elements of Information Theory
Second Edition
Solutions to Problems
Thomas M. Cover
Joy A. Thomas
September 22, 2006
1
COPYRIGHT 2006
Thomas Cover
Joy Thomas
All rights reserved
2
Contents
1 Introduction
7
2 Entropy, Relative Entropy and Mutual Informatio
Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
EE 522 Communication
Theory
Error Control Coding
(Trellis Coded Modulation)
Prof. Hyuckjae Lee
Dept. of Electrical Engr.
KAIST
Bandwidth Efficiency and Coding
2
QPSK and 8PSK
3
Proposition:
Trellis Coded Modulation
4
Trellis Coded Modulation
5
Geometric
Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
Communication Theory EE
522
Signal Space
Representation and
Modulation
Prof. Hyuckjae Lee
Dept. of Electrical Engr.
KAIST
*quoted mainly from lecture note of
rof. Buehrer of Virginia Tech.
Modulation Principles
Almost all communication systems
transmit d
Korea Advanced Institute of Science and Technology
digital communications
EE 112

Spring 2012
EE 522 Communication
Theory
Error Control Coding
(Viterbi Decoding)
Prof. Hyuckjae Lee
Dept. of Electrical Engr.
KAIST
Maximum Likelihood Decoding of
Convolution Code
Maximum Likelihood Decoding (MLD) involves
searching the entire code space for the code