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Design and Decoding of Polar Codes with Large Kernels: A Survey

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Abstract

We present techniques for the construction of polar codes with large kernels and their decoding. A crucial problem in the implementation of the successive cancellation decoding algorithm and its derivatives is kernel processing, i.e., fast evaluation of the log-likelihood ratios for kernel input symbols. We discuss window and recursive trellis processing methods. We consider techniques for evaluation of the reliability of bit subchannels and for obtaining codes with improved distance properties.

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Fig. 1.

Notes

  1. Here we omit the normalization factors, since they do not affect the decoding.

  2. For symmetric channels, it is sufficient to consider \(u_0^{n-1}=0\).

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Funding

The research was carried out at the expense of the Russian Science Foundation, project no. 22-11-00208.

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  1. ITMO University, St.-Petersburg, Russia

    P. V. Trifonov

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Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 1, pp. 25–45. https://doi.org/10.31857/S0555292323010035

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Trifonov, P.V. Design and Decoding of Polar Codes with Large Kernels: A Survey. Probl Inf Transm 59, 22–40 (2023). https://doi.org/10.1134/S0032946023010039

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