2102697 Special Problems in Electrical Engineering II - Antenna Systems
2013
Homework #03 Solution
1) If the absorption coefficient of silicon is 0.05 m-1 at 860 nm,
a) Find the penetration depth, i.e. the distance into the material at which P( x) Pin (1/
2102697 Special Problems in Electrical Engineering II - Antenna Systems
Homework #02
2013
(Due Tuesday, 5 November 2013)
1) What characteristics of laser diodes and light-emitting diodes (LEDs) make them suitable for
being used as light sources of fiber o
2102697 Special Problems in Electrical Engineering II - Antenna Systems
2013
Homework #01 Solution
1. Comparison of the optical fiber and the copper wire in terms of the following characteristics.
Characteristics Optical fiber Copper wire
Safety
Weight
RF
Comparison of Optical Fiber to Copper Wire
Sending power over fiber optic cable to aerial platforms is preferred over copper wire for many reasons,
including safety, weight, scalability, and RF emissions.
Optical fiber
Safety
Weight
RF effects
Dat
Trellis Coded Modulation (TCM)
Attaphongse Taparugssanagorn (Pong)
[email protected]
Introductions
Classical View
Error Control Coding Increase in spectrum bandwidth.
Due to the fact that the rate of the encoder o/p is greater than the
rate of the
INFORMATION THEORY
AND
CODING TECHNIQUE
Introduction
Attaphongse Taparugssanagorn
1
What we will study?
Basic concepts of information theory.
Elements of sets theory and probability theory
Measure of information and uncertainty.
Entropy.
Basic concept
2.1 Review of Probability
Basic denitions
Sample space S
Event E S
Probability of event Prcfw_E
Axiom of probability: Let E , F S .
1. Prcfw_S = 1.
2. 0 Prcfw_E 1.
3. If E and F are disjoint, then
Prcfw_E F = Prcfw_E + Prcfw_F
Exercise: Use the axiom to s
Linear Block Codes
Attaphongse Taparugssanagorn (Pong)
[email protected]
Textbook
Error Control Coding Fundamentals &
Applications - Shu Lin, D.J. Costello
Outlines
Introductions
Review of Algebra
Group, Ring, Field, Galois Field
Linear Block Co
Convolutional Codes
Attaphongse Taparugssanagorn (Pong)
[email protected]
Convolutional Codes
Representation and Encoding
Many known codes can be modified by an extra code symbol or
by deleting a symbol:
Can create codes of almost any desired rate,
TC414 INFORMATION THEORY AND CODING
TECHNIQUE
Channel Coding
Instructor: Attaphongse Taparugssanagorn
Asian Institute of Technology
Thailand
August 2012 (modied on July 2013)
1 / 40
Channel Coding
Hard Decision and Soft Decision Decoding
Consider a simple
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 211
Mon 22 Nov 2010
Coherent Detection of Binary Signals in AWGN Channel
In digital communications, detection refers to the decision regarding what data symbol
has bee
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 191
Mon 15 Nov 2010
3.6
Random Signals and LTI Systems
Consider passing a random signal X (t) through an LTI lter whose impulse response is
h(t). Consider the output s
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 181
Thu 11 Nov 2010
Autocorrelation Functions of WSS Random Processes
Consider a WSS random process X (t). Recall that its autocorrelation function RX (t1 , t2 )
can b
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 201
Thu 18 Nov 2010
4
Digital Communication Basics
AWGN Channel
The additive white Gaussian noise (AWGN) channel is the simplest practical mathematical model for descr
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 171
Thu 4 Nov 2010
3
Random Processes
3.1
Denition of Random Processes
Recall that a random variable is a mapping from the sample space S to the set of real
numbers R.
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 161
Mon 1 Nov 2010
2.8
Additional Discussions on Commonly Used PDFs
Chi-Square PDF
Consider a zero-mean Gaussian random variable X with variance 2 . Let Y = X 2 . Usin
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 151
Thu 28 Oct 2010
2.7
2.7.1
Upper Bounds on the Tail Probabilities
Another Look at the Chebyshev Inequality
2
Recall that, for a random variable X with mean X and va
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 131
Thu 21 Oct 2010
2.4.3
Functions of Random Vectors (Continued)
Linear Transformation
Consider random variables Y1 , . . . , YN obtained from linear transformations
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 141
Mon 25 Oct 2010
2.6
Characteristic Functions
The characteristic function of a random variable X is dened as
jX
X ( ) = E e
ejx fX (x)dx
=
Since the integration in
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 121
Mon 18 Oct 2010
2.3
Expected Values
While the PDF or CDF is a complete statistical description of a random variable, we
often do not need the whole statistical inf
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 101
Thu 23 Sep 2010
2
Probability and Random Variables
2.1
2.1.1
Random Variables, Probability Distributions, and Probability Densities
Fundamentals of Probability
The
AT77.02 Signals, Systems and Stochastic Processes
Asian Institute of Technology
Handout 111
Thu 14 Oct 2010
2.1.5
Joint and Conditional CDFs and PDFs
The joint CDF of random variables X and Y is dened as
FXY (x, y ) = Prcfw_X x, Y y
Their joint PDF is de
Slide set 9
5.2 AWGN Channel Model
Additive white Gaussian noise (AWGN) channel model
Assume that N (t ) is WSS with zero mean and PSD
SN (f ) = N0 /2
yielding the covariance function
KN ( ) =
N0
( )
2
1 / 20
White Gaussian noise
Gaussian: result of the
Slide set 13
7 Capacities of Communication Channels
7.1 Discrete Memoryless Channels
Consider a discrete-time channel model
Rj = Sj + Nj , j cfw_1, 2, . . .
Rj , Sj , Nj are observation, signal, and noise RVs.
If the set of input values X and the set of o
Slide set 12
6.3 Binary Linear Convolutional Codes
A binary linear convolutional code can be dened by shift register.
Encoded bits are linear combinations of shift register contents.
input bits
(k bits shifted
in each step)
A link from
to
the mth output
e
Slide set 7
4.4 Passband Modulation: DSB-AM and QAM
Consider a bandpass transmission system with the frequency band
[fc W , fc + W ] and [fc W , fc + W ].
Typically, fc
W
Bandwidth 2W
Moving a baseband PAM signal (band-limited to [W , W ])
sb (t ) =
j =0
Slide set 11
6 Channel Coding
6.1 Hard Decision and Soft Decision Decoding
No discussion on channel code construction in this course.
Focus on performance evaluation of given codes.
Consider a simple repetition code, which repeats each bit 3 times:
0 000
Slide set 6
4 Communication Signals
4.1 L2 Signal Space
Recall that u (t ) is called an L2 signal if
|u (t )|2 dt <
The set of L2 signals together with eld C form a vector space
called the L2 signal space.
The corresponding inner product is dened as
u (t
Slide set 8
4.5 K -Dimensional Signal Sets
PAM: 1-dimensional signal sets
QAM: 2-dimensional signal sets
generalized to K -dimensional signal sets
A data symbol is written as a K -dimensional vector
a = ( a 1 , . . . , aK )
With symbols a0 , a1 , . . .,
Slide set 10
5.5 Detection of Multiple Transmitted Symbols
Transmitted signal for J symbols using M -point K -dimensional
signal set
J 1 K
S (t ) =
j =0 k =1
Aj ,k k (t jT )
T : symbol period
cfw_1 (t ), . . . , K (t ): orthonormal signals with
cfw_k (t j