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NEW COURSE

EENG 4
010.
0
4
/59
4
0
.04,

F
ALL
2012


Conceptual Convergence of Information in Error Correction, Compression,
Cryptography and Signal Processing



Mon, Wed 5
-
6:20 PM


Text:

Introduction to Cryptography with Coding Theory”

by Trappe and Washington

ISBN 0
-
13
-
061814
-
4, from Pearson Education, Prentice Hall, 2001



Course
Description
:
This course is an introductory
,

integrating
and
summative treatment of the
extensive fundamental points of Information Theory (Shannon,
Chaitin
-
Kotelnikov, channel and
source encodings, entropy) that relate to the theory and design of error correcting codes (distance,
block codes, convolutional, sequential decoding), compression techniques( lossy, lossless, zip, sub
-
sampling, JPG,MP3), cry
ptographic encodings and implementations (public key, PKzip, RAS, DES,
AES, attacks) and signal processing (sampling, orthogonality, modulation). The unifying concepts
will be emphasized with special attention to comparing redundancy and entropy of informa
tion in
each of the four areas.

Course Objective:

to show the commonalities of applications of the fundamental concepts of
information theory in the areas of avoiding loss

of information
, malicious intrusion, and
preservation of the spectrum and the ways to handle it for best use. We introduce the concept of the
“Infometer” as
an

approach to relate the different topics
.


Part I (5 weeks):
Introduction (information theory, Shannon, A/D, D/
A):

1.
-
Two different approaches to information: information theoretic and algorithmic

1.1 .
-

How does one measure information in each case: in bits or in complexity.

1.2 .
-

Why is measuring information an important endeavor?

1.3
.
-

A

Gedanken


tool to measure in the information theoretic approach: the Infometer.



2.
-
Analog and digital: information of a signal in each case

2.1 .
-

Sufficiency of the sampling theorem: (Nyquist/
Shannon
) and compressed sensing introduction

2.2 .
-

DA and AD: Quantiz
ation error and alternative ways of encoding

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2.3 .
-

The
Lipchitz

condition and its potential for compression

2.4 .
-

Representation of periodic and non
-
periodic signals: speech and movies.

2.4 .
-

Orthogonal transformations in frequency and time domains;
filtering and modulation.


3


Information in Noiseless and Noisy Channels

3.1 .
-

Source encoding: Huffman Codes, Compression without Noise

3.2 .
-

Entropy and Noisy Channel: Equiprobable events

3.3 .
-

Introducing Redundancy for Error Correction and Detecti
on

3.4 .
-

Introduction to Block and Convolutional Codes


Part II (5 weeks):
Source encoding and compression (lossy and lossless)
;
noisy channel and error
correction (block and convolutional

codes
)

4.
-

Source encoding and compression

4.1 .
-

Modeling a
source: discrete and continuous sources

4.2 .
-

The issue of source encoding for a noiseless channel

4.3 .
-

Finite fields: prime number
s

and irreducible polynomials


5.
-

Noisy channel encoding and decoding: error detection and correction

5.1 .
-

Normed space
s: examples

5.2 .
-

More on noisy channels: BSC, erasure channels, burst channels

5.3 .
-

Feedback shift registers and generator matrices

5.4.
-

Cyclic codes and others


MIDTERM

6 .
-

Compression: Lossy and Lossless

6.1 .
-

The nature of the compression method: general purpose, audio, video

6.2 .
-

Examples and use of lossless compression :audio, graphics, executables

6.3 .
-

Examples and use of lossy compression: audio, graphics

6.4 .
-

The dual role of transform coding

in lossy MP3
.

Perception: the lesson from MP3: ‘Information is
not everything.’



Part III (4 weeks):

Encryption (history, symmetric and asymmetric, attack analysis):

7.
-

Networks and Information Security: Encryption

7.1 .
-

Symmetric and Asymmetric
Encryption

7.2 .
-
“Goodness” of Encryption: resistance to attacks and efficient processing


8.
-

Practical problem: security

8
.3 .
-

Attacks

and survivability

8
.3 .
-

Public key systems

8
.3 .
-

RSA, DES, AES

8
.4 .
-

The promise of homomorphic encryption

for a computing utility
: full and partial


9
.
-

The goal: Integrate it all into an embedded system

9
.1


Consi
deratio
ns on the order of the process in the Information Society.

FINAL EXAM