2. Professors
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INFORMATION THEORY II

Ugo VACCARO INFORMATION THEORY II

0522200023
DIPARTIMENTO DI MATEMATICA
MATHEMATICS
2014/2015

YEAR OF COURSE 2
YEAR OF DIDACTIC SYSTEM 2010
SECONDO SEMESTRE
CFUHOURSACTIVITY
648LESSONS
UGO VACCARO T Curriculum
Objectives
KNOWLEDGE AND UNDERSTANDING:
THE PRIMARY OBJECTIVE OF THE COURSE IS TO FACTIVELY SHOW HOW CONCEPTS AND RESULTS OF INFORMATION THEORY MAY CONTRIBUTE TO THE EFFICIENT EFFECTIVE SOLUTION OF FUNDAMENTAL PROBLEMS THAT ARISE IN VARIOUS FIELDS OF PURE AND APPLIED SCIENCES.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO ENABLE STUDENTS TO ABSTRACT INFORMATION THEORETICAL FORMAL MODELS AND PROBLEMS FROM CONCRETE PROBLEMS, AND THEN DEVISE SOLUTIONS FOR THEM . THIS WILL BE PERFORMED USING THE FOLLOWING TEACHING METHOD. EVERY PROBLEM WILL BE INTRODUCED WITH MOTIVATING CONCRETE EXAMPLES. THE PRESENTATIONS OF EACH TOPIC WILL DIVIDED INTO THREE PARTS: 1. DESCRIPTION OF THE REAL PROBLEM. 2. MODELING OF PROBLEM WITH A REAL PROBLEM THEORETICAL INFORMATIONAL ABSTRACT. 3. ABSTRACT OF PROBLEM RESOLUTION BY THE APPLICATION OF THE TECHNIQUES GENERAL INTRODUCED IN THE COURSE.

JUDGEMENT:
STUDENTS ARE GUIDED LEARNING IN CRITICAL WAY ALL THAT IS EXPLAINED IN THEIR CLASS, A COMPARE THE DIFFERENT APPROACHES FOR THE SOLUTION OF PROBLEMS, AND TO IDENTIFY AND PROPOSE, IN
INDEPENDENTLY THE MOST EFFICIENT SOLUTION TO LOCATE THEM.

COMMUNICATION SKILLS:
THE COURSE WILL HELP THE DEVELOPMENT OF THE FOLLOWING SKILLS STUDENT: ABILITY TO EXPOSE BY PRECISE AND FORMAL MODEL AN ABSTRACT OF PRACTICAL PROBLEMS, IDENTIFYING KEY CHARACTERISTICS OF THEM AND THE CHARACTERISTICS DISCARDING INESSENTIAL.

CAPACITY 'OF LEARNING
THE STUDENT WILL BE ABLE TO DEAL IN AUTONOMY IN-DEPTH STUDY OF TECHNICAL THEORETICAL INFORMATIONAL TO RESOLVE PROBLEMS OF INTEREST VARIED. THE COURSE WILL PROVIDE STUDENTS THE TOOLS NEEDED TO ALLOW AN UPDATING OF ITS KNOWLEDGE EVEN AFTER THE CONCLUSION OF THE SAME COURSE (LIFE LONG LEARNING).
Prerequisites
STUDENTS ARE REQUIRED TO HAVE ALREADY DEVELOPPED BASIC CAPABILITIES OF FORMAL DEDUCTIVE REASONING. STUDENTS ARE ALSO REQUIRED TO MASTER THE BASIC CONCEPTS OF AN INTRODUCTIVE COURSE IN PROBABILITY AND LINEAR ALGEBRA.
Contents
PART 0. RECAP OF BASIC INFORMATION THEORY: ENTROPY, MUTUAL INFORMATION, THEIR MATHEMATICAL PROPERTIES, RELATIONS, AND MEANING.

PART 1. INFORMATION THEORY AND DATA SECURITY: SECRET SHARING, THEIR INFORMATION THEORETIC ANALYSIS AND RELATIVE ALGORITHMS; KEY DISTRIBUTIONS, THEIR INFORMATION THEORETIC ANALYSIS AND RELATIVE ALGORITHMS;
BASICS OF VISUAL CRYPTOGRAPHY.

PART 3. INFORMATION THEORY AND DATA COMPRESSION: FUNDAMENTAL LIMITATIONS TO DATA COMPRESSION;ALGORITHMS FOR DATA COMPRESSION (LEMPEL &ZIV, ARITHMETIC ENCODING ...)

PART 3. INFORMATION THEORY IN FINANCE END ECONOMETRICS: OPTIMAL PORTFOLIO ALLOCATION VIA INFORMATION THEORETICAL TECHNIQUES, MEASURES OF ECONOMICAL INEQUALITY, ABSOLUTE AND RELATIVE; INFORMATION THEORETICAL ANALYSIS OF BETTING SCHEMATA.

PART 4. INFORMATION THEORY AND STATISTICS: INOFRMATION THEORETIC METHODS IN HYPOTHESIS TESTING.

PART 5. ERROR DATA PROTECTION. BASICS OF ALGEBRAIC ERROR CORRECTING CODES.
Teaching Methods
THE COURSE HAS BOTH LECTURES AIMED AT TEACHING BASIC INFORMATION THEORETIC TOOLS AND TECHNIQUES AND PRACTICE LECTURES AIMED AT ILLUSTRATING, WITH PLENTY OF EXAMPLES, HOW THE ACQUIRED TECHNIQUES CAN BE APPLIED TO SOLVE PROBLEMS OF RELEVANCE.
Verification of learning
THERE WILL BE A FINAL EXAM, CONSISTING IN A WRITTEN TEST AND A ORAL COLLOQUIUM.
Texts
1. THOMAS M. COVER, JOY A. THOMAS, ELEMENTS OF INFORMATION THEORY (2ND EDITION), WILEY-INTERSCIENCE.
2. ROBERT J. MCELIECE, THE THEORY OF INFORMATION AND CODING, CAMBRIDGE UNIVERSITY PRESS
3. NOTES PROVIDED BY THE TEACHER.
More Information
AT THE WEB PAGE HTTP://WWW.DI.UNISA.IT/~UV/TI2/TI2.HTML YOU WILL ADDITIONAL INFORMATION AND MATERIALS
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