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Novel Recursive Kernel Construction for Polar Codes with Practical Codeword Lengths

Authors:
Saha, S. ,  Adrat, M. ,  Massny, L. ,  Schrammen, M.Jax, P.
Book Title:
15th International Conference on Signal Processing and Communication Systems (ICSPCS)
Publisher:
IEEE
Date:
Dec. 2021
DOI:
10.1109/ICSPCS53099.2021.9660284
Language:
English

Abstract

The basic approach introduced by Arikan in [1] to polarize equal capacity channels to unequal capacities, can be used to design only codewords of length N = 2n, which is clearly a major limitation when codewords of length N = 2n are required. In order to systematically construct polarization kernels of size 3 and higher, a recursive construction technique is devel- oped in this paper, that describes each kernel as a concatenation of smaller kernels. Optimally designing and selecting kernels over the underlying system parameters is based on the evolution of z-parameter values (i.e. effect of channel polarization) of the bit channels, which are used to define a design metric ζ. The complex process of optimizing kernel designs, which depends on a wide range of parameters particularly the coderate, is simplified by this metric and its effectiveness is validated by comparative error rate performance.

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