Abstract
Window decoding is useful for decoding polar codes defined by kernels that do not have Arikan's original form. We modify arbitrary polarization kernels of size $2^t \times 2^t$ to reduce the time complexity of window decoding. This modification is based on the permutation of the columns of the kernel. This method is applied to some of the kernels constructed in the literature of size 16 and 32, with different error exponents and scaling exponents such as eNBCH kernel. It is shown that this method reduces the complexity of the window decoding significantly without affecting the performance.
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