EE Seminar: Methods in Polar Coding

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Speaker: Noam Presman
Ph.D. student under the supervision of Prof. Simon Litsyn

Wednesday, September 9th, 2015 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering

Methods in Polar Coding

Abstract
Polar codes, introduced by Arikan in 2008, are capacity achieving error correction codes with polynomial encoding and decoding complexities. They are constructed by employing small codes, referred to as kernels that are recursively concatenated together for generating codes of the desired length. In this talk we study two problems related to the selection of such kernels and their combining for generating good error correction codes.

We begin by designing good kernels, resulting in the optimal polarization rate per their number of dimensions. The polarization rate is the “speed” of decay of the frame error (p) under Successive Cancellation decoding as function of the code length N. It is known that p = O(2^{-N^E}) where E is the polar coding exponent that is dependent of  the kernel of choice.  In order to design good kernels we utilize the classical notion of code decompositions. We further develop new upper-bounds on the maximum exponent per the number of kernel dimensions. Using these upper-bounds we are able to prove optimality of kernels of dimensions l = {1,2,…11,14,15,16}.

In the second part of the talk we use general code decompositions (having decomposition steps with various number of sub-codes) for designing good polar codes. Such decompositions induce polar code structures based on several standard (homogeneous) kernels over alphabets of different sizes. We call such constructions mixed-kernels polar codes. An asymptotic analysis of mixed-kernels shows that their polarization properties are strongly related to the ones of their constituent kernels. Furthermore, simulations of finite length instances of the scheme indicate their advantages both in error correction performance and complexity compared to the known polar coding structures.