EE Seminar: Polar Codes Constructing over Binary and Non-Binary Kernels

~~Speaker: Michael Milkov, 
M.Sc. student under the supervision of Prof. Simon Litsyn

Wednesday, October 21st, 2015 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering

Polar Codes Constructing over Binary and Non-Binary Kernels

Abstract

Polar codes is a family of codes which was discovered by Arikan. This family is an encoding and decoding scheme that provably achieves channel capacity over the binary symmetric memoryless channels.

 This thesis deals with the subject of polar codes constructing.
 First of all, we describe the problem. Then, we investigate several methods for constructing polar codes using binary kernels when our focus is on the channel degrading and upgrading approximations proposed by Tal and Vardy. With several modifications we decrease the amount of calculations needed for these algorithms while maintaining their performance.
 In addition, lower bounds on bit-error probability were derived as a complementary research to the upper bounds derived by Arikan.
 
 Later, we modify the methods described for the binary case in order to perform code constructing for the non-binary Reed-Solomon 4 kernel. Again, we perform several modifications in order to decrease the amount of calculations while preserving performance. In addition, we formalize the Bhattacharyya parameter recursive relations of the symbol-channels and use them for ranking the quality the symbol-channels. This method also allows to upper bound the block error probability even when its value is too low to attain using a monte-carlo simulation and the degrading approximations.
 
 Finally, we use the methods studied in this thesis for constructing polar codes for non-trivial constellations.