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Analysis of TDMP Algorithm of LDPC Codes Based on Density Evolution and Gaussian Approximation.

Xiumin Wang1, Hong Chang1, Jun Li2

  • 1College of Information Engineering, China Jiliang University, Hangzhou 310018, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

The Turbo Decoding Message Passing (TDMP) algorithm shows faster convergence and fewer iterations than the Belief Propagation (BP) algorithm. This study provides theoretical analysis and simulation results to prove TDMP

Keywords:
BP algorithmGaussian approximationTDMP algorithmconvergence speeddensity evolution

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Area of Science:

  • Information Theory
  • Digital Communications
  • Error Correction Codes

Background:

  • The Belief Propagation (BP) algorithm is a standard for decoding, but its convergence properties require further analysis.
  • Turbo Decoding Message Passing (TDMP) offers potential improvements in decoding efficiency.
  • Existing analysis methods like density evolution and Gaussian approximation face challenges with TDMP's iterative message passing.

Purpose of the Study:

  • To analyze the Turbo Decoding Message Passing (TDMP) algorithm using density evolution and Gaussian approximation.
  • To address convergence issues in TDMP analysis by incorporating symmetry conditions.
  • To provide a theoretical foundation for TDMP's superior performance compared to BP.

Main Methods:

  • Density evolution (DE) analysis was applied to the TDMP algorithm.
  • Gaussian approximation was used to model message passing.
  • Symmetry conditions were researched to ensure convergent analysis.
  • Probability density functions (PDFs) of check-to-variable information were calculated.

Main Results:

  • Direct application of density evolution and Gaussian approximation to TDMP without modifications leads to non-convergence.
  • Incorporating symmetry conditions enables convergent theoretical analysis of TDMP.
  • The TDMP algorithm demonstrates a faster decoding convergence speed.
  • TDMP requires fewer iterations than the BP algorithm under identical conditions.

Conclusions:

  • The TDMP algorithm offers significant performance advantages over the BP algorithm in terms of convergence speed and iteration count.
  • The theoretical analysis using density evolution and symmetry conditions validates the superiority of TDMP.
  • This research provides a robust framework for understanding and optimizing iterative decoding algorithms.