|lectures||Wed 9/23 (4-5:30pm, room 32-155)|
|Wed 10/7 (4-5:30pm, room 66-144) *please note room change for this date*|
|Wed 10/21 (4-5:30pm, room 32-155)|
|Wed 10/28 (4-5:30pm, room 32-155)|
Polar codes, invented by Erdal Arikan in 2008, are error correcting codes that are based on an entirely new principle and have many desirable properties. They are inherently of low complexity both for encoding and decoding, their analysis is simple, they allow to achieve capacity, and the underlying idea is broad and flexible and can hence be applied to a variety of problems.
Starting from scratch, we will see how simple notions of information theory form the basis for the polarization phenomenon, how these codes can be constructed and decoded efficiently, how they perform, and how to extend the basic idea to more complex scenarios.
Lecture 1: The Polarization Phenomenon
binary erasure channel: proof of convergence
binary-input memoryless output-symmetric channels: Mrs. Gerber’s lemma and proof of convergence
Lecture 2: Polar Codes
upper bound on error probability
universality and partial orders
list decoding for improved performance
Lecture 3: Error Exponent, Finite-Length Scaling, and Error Floor
error exponent: tradeoff between error probability and block length at fixed channel
finite-length scaling: tradeoff between channel parameter and block length at fixed error probability
proof that polar codes have no error floor
Lecture 4: Extensions
To date there is a large number of resources on the topic of polar codes. Listed below are some links to videos, slides, and papers that you might find useful.