Shortened Polarization Kernels

@article{Trofimiuk2021ShortenedPK,
  title={Shortened Polarization Kernels},
  author={Grigorii Trofimiuk},
  journal={2021 IEEE Globecom Workshops (GC Wkshps)},
  year={2021},
  pages={1-6}
}
  • Grigorii Trofimiuk
  • Published 14 October 2021
  • Computer Science, Mathematics
  • 2021 IEEE Globecom Workshops (GC Wkshps)
A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick elimination of unsuitable shortening patterns.The proposed algorithm is applied to some kernels of sizes 16 and 32 to obtain shortened kernels of sizes from 9 to 31. These kernels are used in mixed-kernel polar codes of various lengths. Numerical results… 
2 Citations

Figures and Tables from this paper

Sub-4.7 Scaling Exponent of Polar Codes

TLDR
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard, however, the per- formance of short-length polar code has rooms for improvement that could hinder its adoption by a wider class of applications.

Accelerating Polarization via Alphabet Extension

TLDR
The main contribution is showing that the dynamic of TECs converges to an almost– one-parameter family of channels, which then leads to an upper bound of 3 .

References

SHOWING 1-10 OF 25 REFERENCES

A Search Method for Large Polarization Kernels

  • Grigorii Trofimiuk
  • Computer Science
    2021 IEEE International Symposium on Information Theory (ISIT)
  • 2021
TLDR
Almost all existing lower bounds on the maximum rate of polarization for kernels of size from 17 to 27 are improved and kernels which admit low complexity processing by the recently proposed recursive trellis algorithm are obtained.

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.

Window Processing of Binary Polarization Kernels

TLDR
An improved version of WP is proposed, which has significantly lower arithmetic complexity and operates in log-likelihood ratios (LLRs) domain and enables polar (sub)codes with the considered kernels to simultaneously provide better performance and lower decoding complexity.

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.

Convolutional Polar Kernels

  • R. Morozov
  • Computer Science
    IEEE Transactions on Communications
  • 2020
TLDR
A family of polarizing kernels is presented together with polynomial-complexity algorithm for computing scaling exponent and polarization rate for convolutional polar kernels of size up to 1024, and the results are obtained.

Recursive Trellis Processing of Large Polarization Kernels

  • P. Trifonov
  • Computer Science
    2021 IEEE International Symposium on Information Theory (ISIT)
  • 2021
TLDR
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.

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.

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.

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.