Information Theory and Coding

2nd year undergraduate course, Universitat Pompeu Fabra

Information theory studies the mathematical foundations of compression and digital data transmission. Originally proposed by Claude Shannon in 1948, information theory not only establishes the fundamental limits of storage and communication, but also studies the codes that achieve these limits. Codes are data processing methods to reduce the probability of error for compressing an information source, and for transmitting information through a communication channel.

Information theory and coding have had a great impact on society in recent decades, facilitating the development of many applications in the digital information era: ZIP files, MP3 or JPG compression, ADSL, compact disc, mobile or satellite communication. More about the life of Claude Shannon and influence of his work in the information society:

https://youtu.be/z2Whj_nL-x8

The objectives of this course are exploring the basic concepts of information theory and coding, familiarizing with the mathematical models of information sources and channels, understanding the proof methodologies of the fundamental limits of source compression and data transmission, as well as the structure and operational meaning of codes.

Information Theory

Barcelona Graduate School of Mathematics

The aims of this course are to review the fundamental principles and methods of information theory. Since Shannon’s landmark work in 1948, information theory has been at the core of information processing systems. Nowadays, information theory finds wide applications in areas such as communications engineering, probability theory, statistics, physics, computer science, mathematics, economics, bioinformatics and computational neuroscience. The course covers data compression, data transmission, joint source-channel coding, mismatched source and channel coding and hypothesis testing. The course will not only review the main results of information theory, but will also describe proof methodologies randing from typical sequences, the method of types and information spectrum and illustrate the key tradeoffs between the underlying system parameters. 

In the last third of the course, quantum information theory will be discussed, which is the generalization of information theory to systems that are described by quantum mechanics, exhibiting a large range of new phenomena, while giving rise to a theory that has at least partially strong similarity to “classical” information theory. No prior knowledge of quantum physics is required.

Digital Communication Theory

Master in Advanced Sciences for Modern Telecommunications

joint Master program with Universitat de València

The objective of this course is to get the student acquainted with advanced topics that are essential to the design and functioning of modern communication systems. In order to provide guiding themes, special emphasis is given to wireless networks and to digital subscriber lines. The topics covered include: review of band-pass and low-pass representation, channel modeling, channel capacity, energy per bit, advanced modulation techniques, fundamental bounds of error probability, intersymbol interference, linear equalization (ZF, MMSE), optimal sequence detection, capacity for parallel channels, SNR gap, Orthogonal Frequency Division Multiplexing (OFDM), bit loading, vector coding, block and convolutional codes, spread spectrum techniques for multiuser communications.