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Bit-Level Construction for Multiplicative-Repetition-Based Non-Binary Polar Codes.

Rongchi Xu1, Peiyao Chen1, Ling Liu2

  • 1The State Key Laboratory of ISN, Xidian University, Xi'an 710071, China.

Entropy (Basel, Switzerland)
|April 26, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel bit-level construction for non-binary polar codes, enhancing decoding performance. The new method optimizes information bit allocation in synthesized channels for better error correction capabilities.

Keywords:
channel degradationconstruction algorithmsnon-binary polar codesprobabilistic shaping

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Area of Science:

  • Coding Theory
  • Information Theory
  • Digital Communications

Background:

  • Non-binary polar codes offer advantages over binary codes but face challenges in construction.
  • Conventional methods struggle with channels of intermediate polarization, limiting efficiency.
  • Efficiently assigning information bits to synthesized channels is crucial for performance.

Purpose of the Study:

  • To propose a bit-level construction for multiplicative repetition (MR)-based non-binary polar codes.
  • To address the limitations of conventional non-binary polar code construction for finite block lengths.
  • To improve the decoding performance of non-binary polar codes.

Main Methods:

  • Calculating error probability and channel capacity lower bounds using the channel degradation method.
  • Determining the optimal number and index of information bits per synthesized channel.
  • Employing a Monte-Carlo method to compute error probabilities and minimize the union bound.
  • Introducing an improved construction-based probabilistic shaping method.

Main Results:

  • The proposed bit-level construction effectively assigns bits to synthesized channels based on their capacity.
  • The Monte-Carlo method and probabilistic shaping optimize the construction for reduced error probability.
  • Simulation results demonstrate significant improvements in decoding performance compared to conventional methods.

Conclusions:

  • The proposed bit-level construction method offers a superior approach for MR-based non-binary polar codes.
  • This method enhances the practical application of non-binary polar codes by improving their efficiency and performance.
  • Further research can explore advanced probabilistic shaping techniques for even greater gains.