# A Short Course in Information Theory

## 8 lectures by David J.C. MacKay

### Summary

Is it possible to communicate reliably from one point to another if we only have a noisy communication channel? How can the information content of a random variable be measured? This course will discuss the remarkable theorems of Claude Shannon, starting from the source coding theorem, which motivates the entropy as the measure of information, and culminating in the noisy channel coding theorem. Along the way we will study simple examples of codes for data compression and error correction.

This will be an informal course. All are welcome to attend. The level of presentation is intended to be appropriate for graduate students and final year undergraduates.

You might also be interested in my book on Information Theory, Inference and Learning Algorithms (640 pages long, published by C.U.P. Sept 2003, and available online), which grew out of this short course.
The postscript files can be obtained not only from my UK web server but also from a mirror in North America (Toronto). Please click appropriately.
Course outline (postscript, 1 page). | ps mirror | pdf | pdf mirror |
Lecture 1 notes (postscript, 2 pages). | ps mirror | pdf | pdf mirror |
Definitions of Probabilities and Entropies. These notes do not include the main part of lecture 1, viz, the 45 minute overview of the noisy channel coding theorem. (You can find that in the first chapter of my book)
Lecture 2 notes (postscript, 3 pages). | ps mirror | pdf | pdf mirror |
Why is entropy a fundamental measure of information content?
Assymptotic equipartition and the source coding theorem. Note: there is a figure on page 1 of this document which does not appear under ghostview for some reason.
Lecture 3 notes (postscript, 3 pages). | ps mirror | pdf | pdf mirror |
Data compression I: Symbol codes
Lecture 4 notes (postscript, 2 pages). | ps mirror | pdf | pdf mirror |
Data compression II: Arithmetic coding
Lecture 5 notes (postscript, 4 pages). | ps mirror | pdf | pdf mirror |
Noisy Channel Coding Theorem I
Lecture 6 notes (postscript, 2 pages). | ps mirror | pdf | pdf mirror |
Noisy Channel Coding Theorem II
Lectures 7 and 8 notes (postscript, 4 pages). | ps mirror | pdf | pdf mirror |
Error Correcting Codes and Real Channels.
In lecture 7 I also described work on Decoding by variational free energy minimization.
Additional notes (postscript, 3 pages). | ps mirror | pdf | pdf mirror |
Bayesian inference (notes prepared for a lecture that didn't happen)

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David MacKay / mackay@mrao.cam.ac.uk - home page.