| Competences |
| Type A | Code | Competences Specific |
| FB1 | Be able to solve mathematical problems that may arise in engineering. Have the ability to apply knowledge on: linear algebra, differential and integral calculation, numerical methods, numerical algorithmics, statistics and optimisation. | |
| FB3 | Understand and master the basic concepts discrete mathematics, logic, algorithmics and computational complexity, and their application in solving problems inherent in engineering. | |
| Type B | Code | Competences Transversal |
| B2 | Have knowledge in basic and technological subjects, which gives them the ability to learn new methods and theories, and the versatility to adapt to new situations. | |
| Type C | Code | Competences Nuclear |
| Learning outcomes |
| Type A | Code | Learning outcomes |
| FB1 |
Know how to work with polynomials and analyse divisibility relationships. Be familiar with the concept of linear code and know how to handle the generating and control matrices of a linear code. Understand the Hamming codes and know how to construct them. Be familiar with and know how to apply linear code error correction by syndrome. Know the cyclical codes and understand the concept of generator polynomial of a cyclical code. Know how to perform the basic operations of a code using the cyclical polynomial. Be familiar with and know how to construct and work with algebraic code, Reed Solomon code and BCH code. | |
| FB3 |
Know the concepts of divisibility, prime numbers and greatest common divisor. Know how to factorise an integer and determine its primality and know how to calculate the greatest common divisor. Know the Bézout's identity of two integers and know how to calculate the coefficient using Euclid's algorithm. Be familiar with and know how to handle the congruencies of integers and Zm rings. Know how to work with polynomials and analyse divisibility relationships. Be familiar with and know how to handle finite bodies. Distinguish and determine primitive elements of a finite body. Know the concepts of block code, Hamming distance, length and correcting capacity. Know the most significant milestones that relate corrective capacity and code length. Be familiar with the concept of linear code and know how to handle the generating and control matrices of a linear code. Understand the Hamming codes and know how to construct them. Be familiar with and know how to apply linear code error correction by syndrome. Know the cyclical codes and understand the concept of generator polynomial of a cyclical code. Know how to perform the basic operations of a code using the cyclical polynomial. Be familiar with and know how to construct and work with algebraic code, Reed Solomon code and BCH code. | |
| Type B | Code | Learning outcomes |
| B2 |
Know the basic notions of information theory and the meaning of the discipline. Approach the noisy-channel coding theorem, and the problem of detection and correction of errors. Have some idea of advanced concepts and advanced techniques in code theory: local decoding, list decoding, network coding, LDPC and iterative decoders, algebraic-geometric codes, etc. Have some idea of other applications for codes (fingerprinting, steganography, cryptography, privacy, etc.). | |
| Type C | Code | Learning outcomes |
| Contents |
| Topic | Sub-topic |
| Finite arithmetic and finite fields | Divisibility, prime numbers, greatest common divisor. Bézout's identity and Euclidean algorithm. Congruences. Modular rings Zm. Polynomials, polynomial divisibility, primitive elements. Finite fields. |
| Information coding (classical) |
Information theory. Noisy channels. Bloc codes. Hamming distance. Code length and correcting capability. Bounds. Linear codes. Generator matrix and parity check matrix. Error correction by syndrome. Cyclic codes. Generator polynomial. Vandermonde matrices. Algebraic codes. Reed-Solomon codes. |
| Information coding (advanced) |
| Planning |
| Methodologies :: Tests | ||||||||||
| Competences | (*) Class hours |
Hours outside the classroom |
(**) Total hours | |||||||
| Introductory activities |
|
1 | 0 | 1 | ||||||
| Lecture |
|
25 | 40 | 65 | ||||||
| Problem solving, exercises in the classroom |
|
11 | 17 | 28 | ||||||
| Presentations / oral communications |
|
4 | 6 | 10 | ||||||
| Personal attention |
|
1 | 0 | 1 | ||||||
| PBL (Problem Based Learning) |
|
10 | 15 | 25 | ||||||
| Practical tests |
|
8 | 12 | 20 | ||||||
| (*) On e-learning, hours of virtual attendance of the teacher. (**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||||||||
| Methodologies |
| Description | |
| Introductory activities | Activitats introductòries |
| Lecture | Desenvolupament dels continguts |
| Problem solving, exercises in the classroom | A principi de curs es disposarà d'una llista de problemes. Alguns dels problemes ja estaran resolts i la resta seran per resoldre. Els problemes resolts volen servir de model o inspiració als alumnes per resoldre la resta de problemes. La programació del curs serà pública, amb una llista especificada dels problemes que es resoldran de cada tema, de manera que els alumnes els hauran de preparar abans d’assistir a classe. Les classes de problemes s’intentarà que siguin participatives amb la implicació activa dels alumnes. Els problemes es resoldran de manera col·lectiva sota el guiatge del professor/a. |
| Presentations / oral communications | Les presentacions seran opcionals. La temàtica de les presentacions serà dins la codificació avançada del Bloc 3. Les presentacions seran de dos tipus diferents: presentacions teòriques i presentacions de laboratori. En quant a la temàtica, els alumnes podran escollir entre un tema d’una llista de temes proposats o podran proposar i discutir algun tema amb el professor/a. Si no es presenten treballs s’aprofitaran les hores restants per a presentar temes actuals per part del professor/a. La intenció de presentar un treball opcional s'ha de notificar als professors de l'assignatura un mes abans del final de curs. Altrament no hi haurà l'opció de fer el treball. |
| Personal attention | Atenció personalitzada |
| PBL (Problem Based Learning) | Es proposaran una sèrie de problemes amb la intenció de reflexionar sobre els continguts apresos. Es discutiran en petits grups amb petites ajudes del professor i s'haurà de formalitzar una eventual resolució. |
| Personalized attention |
| Description |
| L'atenció personalitzada s'utilitzarà per a resoldre dubtes dels estudiants |
| Assessment |
| Methodologies | Competences | Description | Weight | ||||
| Practical tests |
|
- Individual resolution of problems on arthmetics. - Individual resolution of problems on vandermonde matrices and linear codes. - Individual resolution of problems on cyclic codes and RS codes. |
33% each, or 25% each depending on the other parameters | ||||
| Others | ABP assignments |
0% or 25% depending on the other parameters |
| Other comments and second exam session | |||
|
The final mark is computed as follows: --- Individual resolution of problems 1 : PROB1 between 0 and 10 Individual resolution of problems 2 : PROB2 between 0 and 10 Individual resolution of problems 3 : PROB3 between 0 and 10 ---Mark ABP 1 : ABP1 between 0 and 10 Mark ABP 2 : ABP2 between 0 and 10 Mark ABP 3 : ABP3 between 0 and 10 Mark ABP 4 : ABP4 between 0 and 10 --- Mark ABP: (ABP1+ABP2+ABP3+ABP4)/4, between 0 and 10 --- FINAL MARK FIRST CALL = MAX( (PROB1+PROB2+PROB3)/3, (PROB1+PROB2+PROB3+ABP)/4 ) FINAL MARK SECOND CALL = 100% of the final test |
|||
| Sources of information |
| Basic |
Maria Bras-Amorós i Josep Rifà, Teoria de la Codificacio. Problemes., 2015, Universitat Rovira i Virgili
R.M. Roth, Introduction to Coding Theory, 2006, Cambridge University Press
, , , |
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| Complementary |
P. Garrett, The Mathematics of Coding Theory, 2003, Prentice Hall
N.L. Biggs , Discrete Mathematics , 2002, Oxford University Press
J.M. Brunat, E. Ventura , Informació i Codis , 2001 , Universitat Politècnica de Catalunya
D. Applebaum , Probability and information : an integrated approach , 1996 , Cambridge University Press
F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes , 2006 , North-Holland
S. Roman , Coding and Information Theory , 1992, Graduate Texts in Mathematics |
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| Recommendations |
| Subjects that it is recommended to have taken before | ||||
|
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(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.