


Politecnico di Torino  
Anno Accademico 2009/10  
01JEVCY, 01JEVBP, 01JEVHT, 01JEVHZ, 01JEVKY, 01JEVKZ Information theory and codes 

Corso di L. Specialistica in Ingegneria Informatica  Torino Corso di L. Specialistica in Ingegneria Delle Telecomunicazioni  Torino Corso di L. Specialistica in Ingegneria Informatica (Computer Engineering)  Torino Espandi... 





Esclusioni: 01KRR; 01GQS 
Obiettivi dell'insegnamento
The course is a general introduction to the Shannon theory of digital communication systems. The key notion of measure of information for both discrete and continuous random variables is introduced and its farreaching properties are derived in detail. In particular, Shannon's fundamental theorems are then formulated, illustrating how they have laid the foundations of a theory that has found applications in many fields of human activity.
The method followed is chiefly oriented to providing the axiomatic and algebraic foundations needed for a full understanding of the abstract principles of information theory and the sophisticated mathematics of error correcting codes. An equally important goal is to prepare the student to master both theoretical and technical concepts sufficiently well to handle immediate practical applications. 
Programma
 Shannon's paradigm of human and artificial communication, and the origins and motivations of fundamental theorems of information theory.
 A measure of information: entropy of discrete random variables, and differential entropy.  Mutual information of discrete and continuous random variables.  Discrete channel capacity, and Additive White Gaussian Noise channel capacity.  Data processing theorem.  First Shannon theorem on source coding. Variable length codes and Huffman coding.  Second Shannon theorem on discrete channel coding. Applications scenario.  Linear block codes and introduction of finite fields, their main properties.  Code parameters, existence conditions, and performance evaluations.  Complete decoding and standard array.  Cyclic codes: definition, existence conditions and BCH bound.  Systematic and nonsystematic encoding algorithms.  GPZ decoding up to BCH bound.  Hamming codes, BCH codes, Golay codes, ReedSolomon codes, and Goppa codes. 
Programma: informazioni integrative

Bibliografia
Mac Williams, N. Sloane, The theory of error correcting codes, NorthHolland, 1977 T.M. Cover, J.A. Thomas. Elements of Information theory, Wiley, 1991 J. H van Lint, Introduction to Coding Theory, Springer, 1982 R.J. McEliece, The Theory of Information and Coding, Cambridge, 2004 M. Elia, Note di Teoria dell'Informazione (in Italian) 
Verifica la disponibilita in biblioteca 
Controlli dell'apprendimento / Modalità d'esame
The examination consists of written exercises, some of which will be in the form of homework, others under supervision.

Orario delle lezioni 
Statistiche superamento esami 
