A Search Method for Large Polarization Kernels

@article{Trofimiuk2021ASM,
  title={A Search Method for Large Polarization Kernels},
  author={Grigorii Trofimiuk},
  journal={2021 IEEE International Symposium on Information Theory (ISIT)},
  year={2021},
  pages={2084-2089}
}
  • Grigorii Trofimiuk
  • Published 25 January 2021
  • Computer Science, Mathematics
  • 2021 IEEE International Symposium on Information Theory (ISIT)
A new search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing depth-first search combined with some methods for search space reduction. Using the proposed method, we improved almost all existing lower bounds on the maximum rate of polarization for kernels of size from 17 to 27. We also obtained kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results… 

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  • P. Trifonov
  • Computer Science, Mathematics
    2021 IEEE International Symposium on Information Theory (ISIT)
  • 2021
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The proposed algorithm exploits recursive trellis representation of the codes generated by submatrices of the polarization kernel, and enables codes based on large kernels to provide better performance compared to the code based on Arikan kernel with the same decoding complexity.

References

SHOWING 1-10 OF 33 REFERENCES
Construction of binary polarization kernels for low complexity window processing
TLDR
Simulation results show that polar subcodes with obtained kernels can outperform polar codes with Arikan kernel, while having lower decoding complexity.
Multi-Kernel Polar Codes: Concept and Design Principles
TLDR
A new polar code construction by employing kernels of different sizes in the Kronecker product of the transformation matrix, thus generalizing the original construction by Arikan is proposed.
Binary Polarization Kernels From Code Decompositions
TLDR
In this paper, code decompositions are used to design binary polarization kernels and nonlinear kernels of dimensions 14, 15, and 16 are constructed and are shown to have optimal asymptotic error-correction performance.
Mixed-Kernels Constructions of Polar Codes
TLDR
Simulation of finite length instances of the proposed mixed-kernels construction scheme indicate their advantages both in error correction performance and complexity compared to the known polar coding structures.
Improved Hybrid Design of Polar Codes and Multi-Kernel Polar Codes
TLDR
A novel frozen set design for polar codes and multi-kernel polar codes is proposed, improving the existing hybrid distance-reliability design by minimizing the upper bound of the overall system error probability instead of minimizing its lower bound as previously proposed.
Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions With Maximum Exponents
TLDR
It is proved that the constructed kernels have maximum exponents except in the case of nonlinear kernels of dimension 12 where it is demonstrated that the maximum exponent either equals that of the presented construction or assumes another specified value.
Trellis-based Decoding Techniques for Polar Codes with Large Kernels
  • P. Trifonov
  • Computer Science
    2019 IEEE Information Theory Workshop (ITW)
  • 2019
A recursive trellis-based algorithm is proposed for computing the probabilities arising in the successive cancellation (SC) decoding algorithm for polar codes with arbitrary linear kernels. This
On Construction of Polar Subcodes with Large Kernels
  • P. Trifonov
  • Computer Science
    2019 IEEE International Symposium on Information Theory (ISIT)
  • 2019
TLDR
Methods are presented to estimate the capacities of bit subchannels, as well as to eliminate low-weight non-zero codewords from the obtained codes.
Design of BCH Polarization Kernels With Reduced Processing Complexity
The letter introduces a construction of extended BCH polarization kernels, which admit simple computation of the probabilities or log-likelihood ratios arising in the successive cancellation decoding
Explicit Polar Codes with Small Scaling Exponent
TLDR
A sequence of binary linear codes that approaches capacity on the BEC with quasi-linear complexity and scaling exponent µ < 3.122 is exhibited, which was not previously known to exist.
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