Information theory is the basis of modern telecommunication systems. Main topics of information theory are source coding, channel coding, multi-user communication systems, and cryptology. These topics are based on Shannons work on information theory, which allows to describe information with measures like entropy and redundancy.

After a short overview of the whole area of information theory, we will consider concepts for statistic modeling of information sources and derive the source coding theorem. Afterwards, important source coding algorithms like Huffman, Tunstall, Lempel-Ziv and Elias-Willems will be described.

The second part of the lecture investigates channel coding. Important properties of codes and fundamental decoding strategies will be explained. Moreover, we will introduce possibilities for estimating the error probability and analyze the most important channel models according to the channel capacity introduced by Shannon.The Gaussian Channel is very important and therefore described extensively.

The third part deals with aspects of multi-user communication systems. We will introduce several models and investigate methods that can achieve the capacity regions.

Finally, we will give an introduction on data encryption and secure communication.

In the projects several information theoretic topics (e.g., Lempel-Ziv-coding) will be investigated by means of implementation tasks.

Basics:

• Uncertainty (entropy), mutual information
• Fano's lemma, data processing inequality

Source Coding:

• Shannon's source coding theorem
• Coding methods for memoryless sources: Shannon-Fano-, Huffman-, Tunstall, and arithmetic coding
• Coding for sources with memory

Channel Coding:

• Concepts of linear binary block codes
• Shannon's channel coding theorem
• Random coding and error exponent
• MAP and ML decoding
• Bounds
• Channels and capacities: Gaussian channel, fading channel

Multi-User Systems:

• Duplex transmission
• MAC channel
• BC channel
• MIMO channel

Cryptography:

• Basics

• Thomas M. Cover and Joy A. Thomas, "Elements of Information Theory", Library ID: QAA 170/2006 C
• Rolf Johannesson, "Informationstheorie", Library ID: QAA 170/1992 J (in German, can also be bought in our secretariat for 20€)
• James L. Massey, Lecture Notes on "Applied Digital Information Theory I", ETH Zürich, external link to ETH Zürich (pdf)
• Former german lecture notes by Prof. Bossert (pdf)

• Introduction (pdf)
• Introduction Stochastic (pdf)
• Basics of Information Theory (pdf)
• Source Coding Theorem (pdf)
• Source Coding (pdf)
• Arithmetic Coding (pdf)
• Sources with Memory (pdf)
• Channel Coding (pdf)
• Channel Coding Theorem (pdf)
• Zero-Error Capacity (pdf)
• Channel Coding Bounds (pdf)
• Gaussian Channels, part I (pdf)
• Gaussian Channels, part II (pdf)
• Multi-User Communication, part I (pdf)
• Multi-User Communication, part II (pdf)
• MIMO (pdf)
• Cryptography (pdf)

• Sheet 1: Exercises (pdf) Solutions (pdf)
• Sheet 2: Exercises (pdf) Solutions (pdf)
• Sheet 3: Exercises (pdf) Solutions (pdf)
• Sheet 4: Exercises (pdf) Solutions (pdf)
• Sheet 5: Exercises (pdf) Solutions (pdf)
• Sheet 6: Exercises (pdf) Solutions (pdf)
• Sheet 7: Exercises (pdf) Solutions (pdf)
• Sheet 8: Exercises (pdf) Solutions (pdf)
• Sheet 9: Exercises (pdf) Solutions (pdf)

• Lab 1: Lempel Ziv, Introduction and Tasks (pdf) Materials (zip)
• Lab 2: Mutual Information of Finite Alphabets, Introduction and Tasks (pdf) Materials (zip)

Example for arithmetic coding (pdf)

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