Tutorial on Assignment 2
ECE 428
University of Waterloo
Winter 2012
Question 1 (6.1)
Public-key cryptography can be used for encryption
and key exchange. Furthermore, it has some
properties (such as nonrepudiation) which are not
offered by secret key cryp
Lecture 11: Lempel-Ziv Coding
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Lempel-Ziv codes are universal codes which are based on
string matching. Since the original work of Ziv and Lempel in
later 1970s, many variant
ECE 415: Multimedia Communications
Homework Set 1
1
Due Monday, Jan. 23, 2012 (Hand in to your TA)
The following problems are from Section 5 (Exercises) of Chapter 3 of Reference Book [1]:
1. Problem 2
2. Problem 4
3. Problem 5
4. Problem 6
5. Problem 8
ECE 415: Multimedia Communications
Homework Set 2
1
Due Monday, Jan. 23, 2012 (Hand in to your TA)
Problem 1 Determine which of the following codes is uniquely decodable.
(a) cfw_0, 10, 11.
(b) cfw_0, 01, 11.
(c) cfw_0, 01, 10.
(d) cfw_00, 01, 11, 001, 01
ECE 415: Multimedia Communications
Homework Set 3
1
Due Monday, Jan. 30, 2012 (Hand in to your TA)
Problem 1 The probability mass function of X is given in (1):
x
1
2
3
4
p(x) 0.124 0.187 0.3 0.389
(1)
(a) Let
nj = log p(X = j ) , 1 j 4.
Design a prex cod
ECE428 Winter 2012
Part II: Cryptography
Assignment 1
1. The following is the result of a Vigenere cipher of unknown period Explain how you would go about
deciphering the cipher? You may use any of the many tools available on the internet to help you actu
KULLIYYAH OF ENGINEERING
MIDTERM EXAMINATION
SEMESTER 3, 2015/2016 SESSION
Programme
Time
Duration
Course Code
Course Title
: Automotive Engineering
Level of Study
: 11.30 am 13.30 pm
Date
: 3 Hours
: MEC 4607
Section(s)
: Kinematics and Dynamics of Machi
Ch. 3: Forward and Inverse Kinematics
Recap: The Denavit-Hartenberg (DH) Convention
Representing each individual homogeneous transformation as the
product of four basic transformations:
Ai = Rot z, i Trans z,d i Trans x ,ai Rot x , i
c i
s
= i
0
0
si
c i
Lecture 10: Run Length Coding
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Basic Idea
Run length coding is efcient for data sequences where long
segments of repeated symbols (runs) appear. Consider, for
example, a bina
Lecture 9: Adaptive Arithmetic Coding
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Universal Source Coding
In Huffman coding and arithmetic coding discussed so far, both
the encoder and decoder are assumed to know the
Lecture 1 (Part 2): Introduction
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Classical Model of a Digital Communication Systems
Layered Structure
Binary interface
Source
Source
encoder
Encrypter
Channel
encoder
Distor
Lecture 2: Digital Images
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Digital Representation of Images
An image consists of a set of units called pixels which are
organized in the form of a two-dimensional array. On a
Lecture 3: Digital Video
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Representation of Digital Video
Digital video is represented by a sequence of moving digital
images shown in quick succession. Each moving image is
Lecture 4: The Notion of Lossless Codes
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
General Lossless Codes
Notation
X : a source alphabet with its cardinality 2; in typical text
compression, X = cfw_0, 1, , 255.
X n (
Lecture 5: Entropy
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Entropy
Let X be a random variable taking values in X with probability
mass function (pmf) p(x ) = Prcfw_X = x , x X , where
X = cfw_a0 , a1 , , aJ 1 .
De
Lecture 6: Connecting Entropy to Uniquely
Decodable Codes
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Kraft Inequality
C (X1 )C (X2 )
X = X1 X2 Memoryless
coder C
DMS
Rate R
Kraft inequality
Entropy H (X )
Figure: 6.
Lecture 7: Huffman Coding
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Given a pmf pj = p(aj ), 0 j J 1, over
X = cfw_a0 , a1 , , aJ 1
we now look at how to design an optimal prex code C such that
J 1
R=
pj |C (aj )|
Lecture 8: Arithmetic CodingBasic Idea
En-hui Yang
University of Waterloo
En-hui Yang
ECE 415: Multimedia Communications
Drawbacks of Huffman Coding
In principle, the Huffman coding algorithm can also be applied
to design optimal prex codes with block len