|Office Hours||By appointment|
|Teaching Assistant||Amin (Troublemaker) Karbasi|
|Lectures||Wednesday 13:15 – 15:00|
|Exercises||Wednesday 15:15 – 17:00|
This course is a one semester doctoral school course given once every two years. We are concerned exclusively with iterative coding systems. If you are interested in classical algebraic coding we highly recommend the course by Prof. Amin Shokrollahi.
Iterative methods have fundamentally changed coding, and more generally, communications in the last 10 years. We are interested in the basic principles underlying iterative coding. We will learn what makes a system perform well and how to determine its fundamental limitations? Contrary to classical coding, which is based mainly on abstract algebra, the analysis of iterative coding systems is heavily based on methods from graph theory, the probabilistic method, and ideas from statistical physics. An important objective of this course is to convey some of these fundamental tools.
|Feb 20||Why you are all already world experts on iterative coding. (inspired by A. Montanari)||read Introduction; problems 1.1, 1.2, 1.6, 1.8||Mar 5|
|Feb 27||Factor Graphs||HW2||Mar 12||Chapter 2|
|Mar 5||sum-product versus min-sum, LDPC ensemble; how many small cycles are there in an average graph||HW3||Mar 19|
|Mar 12||how to prove convergence to Poisson distribution; weight distribution; Hayman approximation||no homework||Mar 26|
|Mar 19||belief propagation for the BEC; all-one codeword assumption; computation graph;||HW4||Apr 9||Chapter 3|
|Apr 2||BEC: density evolution; irregular ensembles; tresholds; stability; capacity achieving ensembles||problems 3.2, 3.3, 3.4, 3.6, 3.20||Apr 16||Chapter 3|
|Apr 9||BMS channels; message-passing decoders; all-one codeword assumption; density evolution for Gallager A, threshold; density evolution for BP||HW6||Apr 23||Chapter 4|
|Apr 16||expander codes and the flipping algorithm||HW7||Apr 30||Chapter 8|
|Apr 23||density evolution for BP; threshold; stability; optimization of degree distributions||no homework|
|April 30||duality rule, extremes of information combining, symmetry of distributions for BMS channels, basic properties of density evolution||no homework|
|April 30||LP decoding and pseudocodewords||no homework||–|
|May 14||Wormald method and scaling laws||HW8||May 28||Chapter 3 and Appendix C|
|May 21||MAP versus BP; Azuma inequality and some applications||3.21, 3.31, C.5||June 4th||Section 3.20, Appendix C|
|May 28||rateless codes|
|June 2||Take Home Exam||June 9th at noon|
Additional Reading Material
Papers: A short selection out of the thousands of papers written on iterative decoding. More will be added as we go on.
Binary Erasure Channel:
Binary Memoryless Symmetric Channel:
Linear Program Decoder:
Other Classes of Codes:
EXIT and GEXIT Charts:
The following is a set of links that contain some useful information on iterative coding. Some are links to courses on iterative coding given at other universities, some concern, products, and some point you to interesting demos.