Information Theory and Coding

Code:

M382

Acronym:

M382

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:M	38	Plano de estudos a partir de 2009	1	-	7,5	-	202,5
			2
			3

Teaching language

Portuguese

Objectives

Students should be able to understand Shannon´s model of information theory, relating it to the basic concepts of probability theory. They should also be able to take advantage of the basic concepts of linear algebra in the study of error correcting codes.

Learning outcomes and competences

See the above paragraph.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Probility Theory
Linear Algebra

Program

 

1.  Sources, alphabets and codes: uniquely decipherable codes, instantaneous codes, Kraft and McMillan inequalities, length of a code, Huffman codes.

 

2. Information and entropy. Relation between entropy and average codeword length. Shannon’s first theorem.

 

3. Information channels: alphabets, transmissions errors, channel probabilities, channel matrix, entropies, mutual information. Decoding: decision rules, Hamming distance, Shannon’s second theorem.

4. Introduction to error-correcting codes: examples of codes, minimum distance, Hamming and Gilbert-Varshmov estimates, linear codes, equivalent linear codes, generating and parity check matrices, dual codes, syndrome decoding.

Mandatory literature

Roman Steven; Coding and information theory. ISBN: 0-387-97812-7
Roman Steven; Coding and information theory. ISBN: 0-387-97812-7
Jones Gareth A.; Information and coding theory. ISBN: 1-85233-622-6
Ash Robert B.; Information theory. ISBN: 0-486-66521-6

Teaching methods and learning activities

Lectures and practical classes

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Calculation formula of final grade

Exam only