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arXiv:2001.03921 · IEEE Information Theory Workshop (ITW)

Efficient decoding of polar codes with some 16×16 kernels

Grigorii Trofimiuk, Peter Trifonov

Published Nov 1, 2018• 21 citations
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Abstract

A decoding algorithm for polar codes with binary 16×16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the Arikan matrix to significantly reduce the decoding complexity without any performance loss. Simulation results show that polar (sub)codes with 16×16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.

DOI
10.1109/itw.2018.8613307

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A decoding algorithm for polar codes with binary 16×16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the Arikan matrix to significantly reduce the decoding complexity without any performance loss. Simulation results show that polar (sub)codes with 16×16 kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi-kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi-kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms state-of-the-art constructions using puncturing methods.
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms stateof the-art constructions using puncturing methods.
A decoding algorithm for polar (sub)codes with binary 2t×2tpolarization kernels is presented. It is based on the window processing (WP) method, which exploits the linear relationship of the polarization kernels and the Arikan matrix. This relationship enables one to compute the kernel input symbols probabilities by computing the probabilities of several paths in Arikan successive cancellation (SC) decoder. In this paper we propose an improved version of WP, which has significantly lower arithmetic complexity and operates in log-likelihood ratios (LLRs) domain. The algorithm identifies and reuses common subexpressions arising in computation of Arikan SC path scores. The proposed algorithm is applied to kernels of size 16 and 32 with improved polarization properties. It enables polar (sub)codes with the considered kernels to simultaneously provide better performance and lower decoding complexity compared with polar (sub)codes with Arikan kernel.
Window decoding is useful for decoding polar codes defined by kernels that do not have Arıkan's original form. We modify arbitrary polarization kernels of size 2t × 2t 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.