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Low-Density Parity-Check Decoding Algorithm Based on Symmetric Alternating Direction Method of Multipliers.

Ji Zhang1,2, Anmin Chen1, Ying Zhang1

  • 1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China.

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Summary

This study introduces a novel Symmetric Alternating Direction Method of Multipliers (S-ADMM) for decoding low-density parity-check (LDPC) codes. S-ADMM significantly enhances decoding performance and accuracy, especially in low signal-to-noise ratio environments.

Keywords:
alternating direction method of multiplierslow-density parity-check codespenalized decodingsymmetric ADMM

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Area of Science:

  • Coding Theory
  • Signal Processing
  • Information Theory

Background:

  • Linear programming (LP) decoding of low-density parity-check (LDPC) codes is crucial for reliable communication.
  • Conventional Alternating Direction Method of Multipliers (ADMM) offers efficiency but can struggle with non-integral solutions.
  • Penalty terms in ADMM-based decoding improve frame error rate (FER) performance, particularly at low signal-to-noise ratios (SNRs).

Purpose of the Study:

  • To derive explicit iterative steps for LP decoding of LDPC codes using the ADMM framework with penalty functions.
  • To propose a novel Symmetric ADMM (S-ADMM) algorithm for enhanced LDPC code decoding efficiency and accuracy.
  • To analyze the contraction properties of the proposed S-ADMM iterative sequence.

Main Methods:

  • Leveraging the ADMM framework to develop iterative decoding steps for LDPC codes.
  • Introducing penalty functions into the LP decoding objective function.
  • Developing and implementing the Symmetric ADMM (S-ADMM) algorithm.
  • Conducting simulation experiments to evaluate decoder performance.

Main Results:

  • The proposed S-ADMM algorithm effectively solves the LP decoding problem for LDPC codes.
  • S-ADMM demonstrates improved decoding efficiency and accuracy compared to conventional methods.
  • Simulation results confirm superior performance of S-ADMM over standard ADMM penalized decoders across various LDPC and 5G codes.

Conclusions:

  • The S-ADMM decoder offers significant improvements in decoding performance for LDPC codes.
  • The proposed method is particularly effective in low SNR regions.
  • S-ADMM represents a promising advancement for efficient and accurate LDPC code decoding in modern communication systems.