Novel Recursive Kernel Construction for Polar Codes with Practical Codeword Lengths
Souradip Saha, Marc Adrat, Luis Masny, Matthias Schrammen, Peter Jax · 2021
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 $N=2^{n}$, which is clearly a major limitation when codewords of length $N eq 2^{n}$ are required. In order to systematically construct polarization kernels of size 3 and higher, a recursive construction technique is developed 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 $\zeta$. 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.